--- /dev/null
+/* Copyright 1988, Brown Computer Graphics Group. All Rights Reserved. */
+
+/* --------------------------------------------------------------------------
+ * This file contains routines that operate on matrices and vectors, or
+ * vectors and vectors.
+ * -------------------------------------------------------------------------*/
+
+/* #include "sphigslocal.h" */
+
+/* -------------------------- Static Routines ---------------------------- */
+
+/* ------------------------- Internal Routines --------------------------- */
+
+/* -------------------------- Public Routines ---------------------------- */
+
+/*
+ * Multiplies a vector by a matrix, setting the result vector.
+ * It assumes all homogeneous coordinates are 1.
+ * The two vectors involved may be the same.
+ */
+
+#include <Math/mat3.h>
+
+#ifndef TRUE
+# define TRUE 1
+#endif
+
+#ifndef FALSE
+# define FALSE 0
+#endif
+
+
+void
+MAT3mult_vec(double *result_vec, register double *vec, register double (*mat)[4])
+{
+ MAT3vec tempvec;
+ register double *temp = tempvec;
+
+ temp[0] = vec[0] * mat[0][0] + vec[1] * mat[1][0] +
+ vec[2] * mat[2][0] + mat[3][0];
+ temp[1] = vec[0] * mat[0][1] + vec[1] * mat[1][1] +
+ vec[2] * mat[2][1] + mat[3][1];
+ temp[2] = vec[0] * mat[0][2] + vec[1] * mat[1][2] +
+ vec[2] * mat[2][2] + mat[3][2];
+
+ MAT3_COPY_VEC(result_vec, temp);
+}
+
+/*
+ * Multiplies a vector of size 4 by a matrix, setting the result vector.
+ * The fourth element of the vector is the homogeneous coordinate, which
+ * may or may not be 1. If the "normalize" parameter is TRUE, then the
+ * result vector will be normalized so that the homogeneous coordinate is 1.
+ * The two vectors involved may be the same.
+ * This returns zero if the vector was to be normalized, but couldn't be.
+ */
+
+int
+MAT3mult_hvec(double *result_vec, register double *vec, register double (*mat)[4], int normalize)
+{
+ MAT3hvec tempvec;
+ double norm_fac;
+ register double *temp = tempvec;
+ register int ret = TRUE;
+
+ temp[0] = vec[0] * mat[0][0] + vec[1] * mat[1][0] +
+ vec[2] * mat[2][0] + vec[3] * mat[3][0];
+ temp[1] = vec[0] * mat[0][1] + vec[1] * mat[1][1] +
+ vec[2] * mat[2][1] + vec[3] * mat[3][1];
+ temp[2] = vec[0] * mat[0][2] + vec[1] * mat[1][2] +
+ vec[2] * mat[2][2] + vec[3] * mat[3][2];
+ temp[3] = vec[0] * mat[0][3] + vec[1] * mat[1][3] +
+ vec[2] * mat[2][3] + vec[3] * mat[3][3];
+
+ /* Normalize if asked for, possible, and necessary */
+ if (normalize) {
+ if (MAT3_IS_ZERO(temp[3])) {
+#ifndef THINK_C
+ fprintf (stderr,
+ "Can't normalize vector: homogeneous coordinate is 0");
+#endif
+ ret = FALSE;
+ }
+ else {
+ norm_fac = 1.0 / temp[3];
+ MAT3_SCALE_VEC(result_vec, temp, norm_fac);
+ result_vec[3] = 1.0;
+ }
+ }
+ else MAT3_COPY_HVEC(result_vec, temp);
+
+ return(ret);
+}
+
+/*
+ * Sets the first vector to be the cross-product of the last two vectors.
+ */
+
+void
+MAT3cross_product(double *result_vec, register double *vec1, register double *vec2)
+{
+ MAT3vec tempvec;
+ register double *temp = tempvec;
+
+ temp[0] = vec1[1] * vec2[2] - vec1[2] * vec2[1];
+ temp[1] = vec1[2] * vec2[0] - vec1[0] * vec2[2];
+ temp[2] = vec1[0] * vec2[1] - vec1[1] * vec2[0];
+
+ MAT3_COPY_VEC(result_vec, temp);
+}
+
+/*
+ * Finds a vector perpendicular to vec and stores it in result_vec.
+ * Method: take any vector (we use <0,1,0>) and subtract the
+ * portion of it pointing in the vec direction. This doesn't
+ * work if vec IS <0,1,0> or is very near it. So if this is
+ * the case, use <0,0,1> instead.
+ * If "is_unit" is TRUE, the given vector is assumed to be unit length.
+ */
+
+#define SELECT .7071 /* selection constant (roughly .5*sqrt(2) */
+
+void
+MAT3perp_vec(double *result_vec, double *vec, int is_unit)
+{
+ MAT3vec norm;
+ double dot;
+
+ MAT3_SET_VEC(result_vec, 0.0, 1.0, 0.0);
+
+ MAT3_COPY_VEC(norm, vec);
+
+ if (! is_unit) MAT3_NORMALIZE_VEC(norm, dot);
+
+ /* See if vector is too close to <0,1,0>. If so, use <0,0,1> */
+ if ((dot = MAT3_DOT_PRODUCT(norm, result_vec)) > SELECT || dot < -SELECT) {
+ result_vec[1] = 0.0;
+ result_vec[2] = 1.0;
+ dot = MAT3_DOT_PRODUCT(norm, result_vec);
+ }
+
+ /* Subtract off non-perpendicular part */
+ result_vec[0] -= dot * norm[0];
+ result_vec[1] -= dot * norm[1];
+ result_vec[2] -= dot * norm[2];
+
+ /* Make result unit length */
+ MAT3_NORMALIZE_VEC(result_vec, dot);
+}
+++ /dev/null
-#---------------------------------------------------------------------------
-# Makefile
-#
-# Written by Curtis Olson, started October 1997.
-#
-# Copyright (C) 1997 Curtis L. Olson - curt@infoplane.com
-#
-# This program is free software; you can redistribute it and/or modify
-# it under the terms of the GNU General Public License as published by
-# the Free Software Foundation; either version 2 of the License, or
-# (at your option) any later version.
-#
-# This program is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-# GNU General Public License for more details.
-#
-# You should have received a copy of the GNU General Public License
-# along with this program; if not, write to the Free Software
-# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
-#
-# $Id$
-# (Log is kept at end of this file)
-#---------------------------------------------------------------------------
-
-
-TARGET = fixobj
-
-CFILES = main.c obj.c
-LDLIBS = -lMath -lm
-
-
-include $(FG_ROOT_SRC)/commondefs
-
-
-#---------------------------------------------------------------------------
-# Rule for TARGET
-#---------------------------------------------------------------------------
-
-$(TARGET): $(OBJECTS)
- $(CC) -o $(TARGET) $(OBJECTS) $(LDFLAGS) $(LDLIBS)
-
-
-include $(COMMONRULES)
-
-
-#---------------------------------------------------------------------------
-# $Log$
-# Revision 1.2 1998/01/21 02:55:53 curt
-# Incorporated new make system from Bob Kuehne <rpk@sgi.com>.
-#
-# Revision 1.1 1997/12/08 19:28:54 curt
-# Initial revision.
-#
--- /dev/null
+#---------------------------------------------------------------------------
+# Makefile
+#
+# Written by Curtis Olson, started October 1997.
+#
+# Copyright (C) 1997 - 1998 Curtis L. Olson - curt@me.umn.edu
+#
+# This program is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 2 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program; if not, write to the Free Software
+# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+#
+# $Id$
+# (Log is kept at end of this file)
+#---------------------------------------------------------------------------
+
+
+bin_PROGRAMS = fixobj
+
+fixobj_SOURCES = main.c mat3.h obj.c obj.h MAT3vec.c
+
+fixobj_LDADD =
+
+INCLUDES += -I../../Simulator
+
+
+#---------------------------------------------------------------------------
+# $Log$
+# Revision 1.1 1998/04/08 23:19:35 curt
+# Adopted Gnu automake/autoconf system.
+#
+# Revision 1.2 1998/01/21 02:55:53 curt
+# Incorporated new make system from Bob Kuehne <rpk@sgi.com>.
+#
+# Revision 1.1 1997/12/08 19:28:54 curt
+# Initial revision.
+#
--- /dev/null
+# Makefile.in generated automatically by automake 1.2h from Makefile.am
+
+# Copyright (C) 1994, 1995, 1996, 1997, 1998 Free Software Foundation, Inc.
+# This Makefile.in is free software; the Free Software Foundation
+# gives unlimited permission to copy and/or distribute it,
+# with or without modifications, as long as this notice is preserved.
+
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY, to the extent permitted by law; without
+# even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+# PARTICULAR PURPOSE.
+
+#---------------------------------------------------------------------------
+# Makefile
+#
+# Written by Curtis Olson, started October 1997.
+#
+# Copyright (C) 1997 - 1998 Curtis L. Olson - curt@me.umn.edu
+#
+# This program is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 2 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program; if not, write to the Free Software
+# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+#
+# $Id$
+# (Log is kept at end of this file)
+#---------------------------------------------------------------------------
+
+
+SHELL = /bin/sh
+
+srcdir = @srcdir@
+top_srcdir = @top_srcdir@
+VPATH = @srcdir@
+prefix = @prefix@
+exec_prefix = @exec_prefix@
+
+bindir = @bindir@
+sbindir = @sbindir@
+libexecdir = @libexecdir@
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+sharedstatedir = @sharedstatedir@
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+libdir = @libdir@
+infodir = @infodir@
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+includedir = @includedir@
+oldincludedir = /usr/include
+
+DISTDIR =
+
+pkgdatadir = $(datadir)/@PACKAGE@
+pkglibdir = $(libdir)/@PACKAGE@
+pkgincludedir = $(includedir)/@PACKAGE@
+
+top_builddir = ../..
+
+ACLOCAL = @ACLOCAL@
+AUTOCONF = @AUTOCONF@
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+AUTOHEADER = @AUTOHEADER@
+
+INSTALL = @INSTALL@
+INSTALL_PROGRAM = @INSTALL_PROGRAM@
+INSTALL_DATA = @INSTALL_DATA@
+INSTALL_SCRIPT = @INSTALL_SCRIPT@
+transform = @program_transform_name@
+
+NORMAL_INSTALL = :
+PRE_INSTALL = :
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+VERSION = @VERSION@
+
+bin_PROGRAMS = fixobj
+
+fixobj_SOURCES = main.c mat3.h obj.c obj.h MAT3vec.c
+
+fixobj_LDADD =
+mkinstalldirs = $(SHELL) $(top_srcdir)/mkinstalldirs
+CONFIG_HEADER = ../../Simulator/Include/config.h
+CONFIG_CLEAN_FILES =
+PROGRAMS = $(bin_PROGRAMS)
+
+
+DEFS = @DEFS@ -I. -I$(srcdir) -I../../Simulator/Include
+CPPFLAGS = @CPPFLAGS@
+LDFLAGS = @LDFLAGS@
+LIBS = @LIBS@
+X_CFLAGS = @X_CFLAGS@
+X_LIBS = @X_LIBS@
+X_EXTRA_LIBS = @X_EXTRA_LIBS@
+X_PRE_LIBS = @X_PRE_LIBS@
+fixobj_OBJECTS = main.o obj.o MAT3vec.o
+fixobj_DEPENDENCIES =
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+LINK = $(LIBTOOL) --mode=link $(CC) $(CFLAGS) $(LDFLAGS) -o $@
+DIST_COMMON = Makefile.am Makefile.in
+
+
+DISTFILES = $(DIST_COMMON) $(SOURCES) $(HEADERS) $(TEXINFOS) $(EXTRA_DIST)
+
+TAR = tar
+GZIP = --best
+DEP_FILES = .deps/MAT3vec.P .deps/main.P .deps/obj.P
+SOURCES = $(fixobj_SOURCES)
+OBJECTS = $(fixobj_OBJECTS)
+
+all: Makefile $(PROGRAMS)
+
+.SUFFIXES:
+.SUFFIXES: .S .c .lo .o .s
+$(srcdir)/Makefile.in: @MAINT@ Makefile.am $(top_srcdir)/configure.in $(ACLOCAL_M4)
+ cd $(top_srcdir) && $(AUTOMAKE) --gnu Tools/FixObj/Makefile
+
+Makefile: $(srcdir)/Makefile.in $(top_builddir)/config.status $(BUILT_SOURCES)
+ cd $(top_builddir) \
+ && CONFIG_FILES=$(subdir)/$@ CONFIG_HEADERS= $(SHELL) ./config.status
+
+
+mostlyclean-binPROGRAMS:
+
+clean-binPROGRAMS:
+ -test -z "$(bin_PROGRAMS)" || rm -f $(bin_PROGRAMS)
+
+distclean-binPROGRAMS:
+
+maintainer-clean-binPROGRAMS:
+
+install-binPROGRAMS: $(bin_PROGRAMS)
+ @$(NORMAL_INSTALL)
+ $(mkinstalldirs) $(DESTDIR)$(bindir)
+ @list='$(bin_PROGRAMS)'; for p in $$list; do \
+ if test -f $$p; then \
+ echo " $(LIBTOOL) --mode=install $(INSTALL_PROGRAM) $$p $(DESTDIR)$(bindir)/`echo $$p|sed '$(transform)'`"; \
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+ else :; fi; \
+ done
+
+uninstall-binPROGRAMS:
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+ list='$(bin_PROGRAMS)'; for p in $$list; do \
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+
+.s.o:
+ $(COMPILE) -c $<
+
+.S.o:
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+
+mostlyclean-compile:
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+
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+ @rm -f fixobj
+ $(LINK) $(fixobj_LDFLAGS) $(fixobj_OBJECTS) $(fixobj_LDADD) $(LIBS)
+
+tags: TAGS
+
+ID: $(HEADERS) $(SOURCES) $(LISP)
+ here=`pwd` && cd $(srcdir) \
+ && mkid -f$$here/ID $(SOURCES) $(HEADERS) $(LISP)
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+ awk ' { files[$$0] = 1; } \
+ END { for (i in files) print i; }'`; \
+ test -z "$(ETAGS_ARGS)$$unique$(LISP)$$tags" \
+ || (cd $(srcdir) && etags $(ETAGS_ARGS) $$tags $$unique $(LISP) -o $$here/TAGS)
+
+mostlyclean-tags:
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+
+subdir = Tools/FixObj
+
+distdir: $(DISTFILES)
+ here=`cd $(top_builddir) && pwd`; \
+ top_distdir=`cd $(top_distdir) && pwd`; \
+ distdir=`cd $(distdir) && pwd`; \
+ cd $(top_srcdir) \
+ && $(AUTOMAKE) --include-deps --build-dir=$$here --srcdir-name=$(top_srcdir) --output-dir=$$top_distdir --gnu Tools/FixObj/Makefile
+ @for file in $(DISTFILES); do \
+ d=$(srcdir); \
+ test -f $(distdir)/$$file \
+ || ln $$d/$$file $(distdir)/$$file 2> /dev/null \
+ || cp -p $$d/$$file $(distdir)/$$file; \
+ done
+
+DEPS_MAGIC := $(shell mkdir .deps > /dev/null 2>&1 || :)
+
+-include $(DEP_FILES)
+
+mostlyclean-depend:
+
+clean-depend:
+
+distclean-depend:
+
+maintainer-clean-depend:
+ -rm -rf .deps
+
+%.o: %.c
+ @echo '$(COMPILE) -c $<'; \
+ $(COMPILE) -Wp,-MD,.deps/$(*F).P -c $<
+
+%.lo: %.c
+ @echo '$(LTCOMPILE) -c $<'; \
+ $(LTCOMPILE) -Wp,-MD,.deps/$(*F).p -c $<
+ @-sed -e 's/^\([^:]*\)\.o:/\1.lo \1.o:/' \
+ < .deps/$(*F).p > .deps/$(*F).P
+ @-rm -f .deps/$(*F).p
+info:
+dvi:
+check: all
+ $(MAKE)
+installcheck:
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+ @$(NORMAL_INSTALL)
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+ @$(NORMAL_INSTALL)
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+ $(MAKE) INSTALL_PROGRAM='$(INSTALL_PROGRAM) -s' INSTALL_SCRIPT='$(INSTALL_PROGRAM)' install
+installdirs:
+ $(mkinstalldirs) $(DATADIR)$(bindir)
+
+
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+ -test -z "$(MOSTLYCLEANFILES)" || rm -f $(MOSTLYCLEANFILES)
+
+clean-generic:
+ -test -z "$(CLEANFILES)" || rm -f $(CLEANFILES)
+
+distclean-generic:
+ -rm -f Makefile $(DISTCLEANFILES)
+ -rm -f config.cache config.log stamp-h stamp-h[0-9]*
+ -test -z "$(CONFIG_CLEAN_FILES)" || rm -f $(CONFIG_CLEAN_FILES)
+
+maintainer-clean-generic:
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+mostlyclean: mostlyclean-binPROGRAMS mostlyclean-compile \
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+ distclean-tags distclean-depend distclean-generic clean
+ -rm -f config.status
+ -rm -f libtool
+
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+ maintainer-clean-libtool maintainer-clean-tags \
+ maintainer-clean-depend maintainer-clean-generic \
+ distclean
+ @echo "This command is intended for maintainers to use;"
+ @echo "it deletes files that may require special tools to rebuild."
+
+.PHONY: mostlyclean-binPROGRAMS distclean-binPROGRAMS clean-binPROGRAMS \
+maintainer-clean-binPROGRAMS uninstall-binPROGRAMS install-binPROGRAMS \
+mostlyclean-compile distclean-compile clean-compile \
+maintainer-clean-compile mostlyclean-libtool distclean-libtool \
+clean-libtool maintainer-clean-libtool tags mostlyclean-tags \
+distclean-tags clean-tags maintainer-clean-tags distdir \
+mostlyclean-depend distclean-depend clean-depend \
+maintainer-clean-depend info dvi installcheck install-exec install-data \
+install uninstall all installdirs mostlyclean-generic distclean-generic \
+clean-generic maintainer-clean-generic clean mostlyclean distclean \
+maintainer-clean
+
+
+INCLUDES += -I../../Simulator
+
+#---------------------------------------------------------------------------
+# $Log$
+# Revision 1.1 1998/04/08 23:19:36 curt
+# Adopted Gnu automake/autoconf system.
+#
+# Revision 1.2 1998/01/21 02:55:53 curt
+# Incorporated new make system from Bob Kuehne <rpk@sgi.com>.
+#
+# Revision 1.1 1997/12/08 19:28:54 curt
+# Initial revision.
+#
+
+# Tell versions [3.59,3.63) of GNU make to not export all variables.
+# Otherwise a system limit (for SysV at least) may be exceeded.
+.NOEXPORT:
--- /dev/null
+/* Copyright 1988, Brown Computer Graphics Group. All Rights Reserved. */
+
+/* -------------------------------------------------------------------------
+ Public MAT3 include file
+ ------------------------------------------------------------------------- */
+
+#ifndef MAT3_HAS_BEEN_INCLUDED
+#define MAT3_HAS_BEEN_INCLUDED
+
+/* ----------------------------- Constants ------------------------------ */
+
+/*
+ * Make sure the math library .h file is included, in case it wasn't.
+ */
+
+#ifndef HUGE
+#include <math.h>
+#endif
+#include <stdio.h>
+
+
+#define MAT3_DET0 -1 /* Indicates singular mat */
+#define MAT3_EPSILON 1e-12 /* Close enough to zero */
+#define MAT3_PI 3.141592653589793 /* Pi */
+
+/* ------------------------------ Types --------------------------------- */
+
+typedef double MAT3mat[4][4]; /* 4x4 matrix */
+typedef double MAT3vec[3]; /* Vector */
+typedef double MAT3hvec[4]; /* Vector with homogeneous coord */
+
+/* ------------------------------ Macros -------------------------------- */
+
+/* Tests if a number is within EPSILON of zero */
+#define MAT3_IS_ZERO(N) ((N) < MAT3_EPSILON && (N) > -MAT3_EPSILON)
+
+/* Sets a vector to the three given values */
+#define MAT3_SET_VEC(V,X,Y,Z) ((V)[0]=(X), (V)[1]=(Y), (V)[2]=(Z))
+
+/* Tests a vector for all components close to zero */
+#define MAT3_IS_ZERO_VEC(V) (MAT3_IS_ZERO((V)[0]) && \
+ MAT3_IS_ZERO((V)[1]) && \
+ MAT3_IS_ZERO((V)[2]))
+
+/* Dot product of two vectors */
+#define MAT3_DOT_PRODUCT(V1,V2) \
+ ((V1)[0]*(V2)[0] + (V1)[1]*(V2)[1] + (V1)[2]*(V2)[2])
+
+/* Copy one vector to other */
+#define MAT3_COPY_VEC(TO,FROM) ((TO)[0] = (FROM)[0], \
+ (TO)[1] = (FROM)[1], \
+ (TO)[2] = (FROM)[2])
+
+/* Normalize vector to unit length, using TEMP as temporary variable.
+ * TEMP will be zero if vector has zero length */
+#define MAT3_NORMALIZE_VEC(V,TEMP) \
+ if ((TEMP = sqrt(MAT3_DOT_PRODUCT(V,V))) > MAT3_EPSILON) { \
+ TEMP = 1.0 / TEMP; \
+ MAT3_SCALE_VEC(V,V,TEMP); \
+ } else TEMP = 0.0
+
+/* Scale vector by given factor, storing result vector in RESULT_V */
+#define MAT3_SCALE_VEC(RESULT_V,V,SCALE) \
+ MAT3_SET_VEC(RESULT_V, (V)[0]*(SCALE), (V)[1]*(SCALE), (V)[2]*(SCALE))
+
+/* Adds vectors V1 and V2, storing result in RESULT_V */
+#define MAT3_ADD_VEC(RESULT_V,V1,V2) \
+ MAT3_SET_VEC(RESULT_V, (V1)[0]+(V2)[0], (V1)[1]+(V2)[1], \
+ (V1)[2]+(V2)[2])
+
+/* Subtracts vector V2 from V1, storing result in RESULT_V */
+#define MAT3_SUB_VEC(RESULT_V,V1,V2) \
+ MAT3_SET_VEC(RESULT_V, (V1)[0]-(V2)[0], (V1)[1]-(V2)[1], \
+ (V1)[2]-(V2)[2])
+
+/* Multiplies vectors V1 and V2, storing result in RESULT_V */
+#define MAT3_MULT_VEC(RESULT_V,V1,V2) \
+ MAT3_SET_VEC(RESULT_V, (V1)[0]*(V2)[0], (V1)[1]*(V2)[1], \
+ (V1)[2]*(V2)[2])
+
+/* Sets RESULT_V to the linear combination of V1 and V2, scaled by
+ * SCALE1 and SCALE2, respectively */
+#define MAT3_LINEAR_COMB(RESULT_V,SCALE1,V1,SCALE2,V2) \
+ MAT3_SET_VEC(RESULT_V, (SCALE1)*(V1)[0] + (SCALE2)*(V2)[0], \
+ (SCALE1)*(V1)[1] + (SCALE2)*(V2)[1], \
+ (SCALE1)*(V1)[2] + (SCALE2)*(V2)[2])
+
+/* Several of the vector macros are useful for homogeneous-coord vectors */
+#define MAT3_SET_HVEC(V,X,Y,Z,W) ((V)[0]=(X), (V)[1]=(Y), \
+ (V)[2]=(Z), (V)[3]=(W))
+
+#define MAT3_COPY_HVEC(TO,FROM) ((TO)[0] = (FROM)[0], \
+ (TO)[1] = (FROM)[1], \
+ (TO)[2] = (FROM)[2], \
+ (TO)[3] = (FROM)[3])
+
+#define MAT3_SCALE_HVEC(RESULT_V,V,SCALE) \
+ MAT3_SET_HVEC(RESULT_V, (V)[0]*(SCALE), (V)[1]*(SCALE), \
+ (V)[2]*(SCALE), (V)[3]*(SCALE))
+
+#define MAT3_ADD_HVEC(RESULT_V,V1,V2) \
+ MAT3_SET_HVEC(RESULT_V, (V1)[0]+(V2)[0], (V1)[1]+(V2)[1], \
+ (V1)[2]+(V2)[2], (V1)[3]+(V2)[3])
+
+#define MAT3_SUB_HVEC(RESULT_V,V1,V2) \
+ MAT3_SET_HVEC(RESULT_V, (V1)[0]-(V2)[0], (V1)[1]-(V2)[1], \
+ (V1)[2]-(V2)[2], (V1)[3]-(V2)[3])
+
+#define MAT3_MULT_HVEC(RESULT_V,V1,V2) \
+ MAT3_SET_HVEC(RESULT_V, (V1)[0]*(V2)[0], (V1)[1]*(V2)[1], \
+ (V1)[2]*(V2)[2], (V1)[3]*(V2)[3])
+
+/* ------------------------------ Entries ------------------------------- */
+
+
+/* In MAT3geom.c */
+void MAT3direction_matrix (MAT3mat result_mat, MAT3mat mat);
+int MAT3normal_matrix (MAT3mat result_mat, MAT3mat mat);
+void MAT3rotate (MAT3mat result_mat, MAT3vec axis, double angle_in_radians);
+void MAT3translate (MAT3mat result_mat, MAT3vec trans);
+void MAT3scale (MAT3mat result_mat, MAT3vec scale);
+void MAT3shear(MAT3mat result_mat, double xshear, double yshear);
+
+/* In MAT3mat.c */
+void MAT3identity(MAT3mat);
+void MAT3zero(MAT3mat);
+void MAT3copy (MAT3mat to, MAT3mat from);
+void MAT3mult (MAT3mat result, MAT3mat, MAT3mat);
+void MAT3transpose (MAT3mat result, MAT3mat);
+int MAT3invert (MAT3mat result, MAT3mat);
+void MAT3print (MAT3mat, FILE *fp);
+void MAT3print_formatted (MAT3mat, FILE *fp,
+ char *title, char *head, char *format, char *tail);
+extern int MAT3equal( void );
+extern double MAT3trace( void );
+extern int MAT3power( void );
+extern int MAT3column_reduce( void );
+extern int MAT3kernel_basis( void );
+
+/* In MAT3vec.c */
+void MAT3mult_vec(MAT3vec result_vec, MAT3vec vec, MAT3mat mat);
+int MAT3mult_hvec (MAT3hvec result_vec, MAT3hvec vec, MAT3mat mat, int normalize);
+void MAT3cross_product(MAT3vec result,MAT3vec,MAT3vec);
+void MAT3perp_vec(MAT3vec result_vec, MAT3vec vec, int is_unit);
+
+#endif /* MAT3_HAS_BEEN_INCLUDED */
+
#include "obj.h"
-#include "../../Src/Math/mat3.h"
+#include "mat3.h"
/* what do ya' know, here's some global variables */
/* $Log$
-/* Revision 1.7 1998/03/19 02:51:41 curt
-/* Added special case handling to compensate for bugs in our beloved tri striper
+/* Revision 1.8 1998/04/08 23:19:37 curt
+/* Adopted Gnu automake/autoconf system.
/*
+ * Revision 1.7 1998/03/19 02:51:41 curt
+ * Added special case handling to compensate for bugs in our beloved tri striper
+ *
* Revision 1.6 1998/03/03 15:36:12 curt
* Tweaks for compiling with g++
*
--- /dev/null
+/* Copyright 1988, Brown Computer Graphics Group. All Rights Reserved. */
+
+/* --------------------------------------------------------------------------
+ * This file contains routines that operate on matrices and vectors, or
+ * vectors and vectors.
+ * -------------------------------------------------------------------------*/
+
+/* #include "sphigslocal.h" */
+
+/* -------------------------- Static Routines ---------------------------- */
+
+/* ------------------------- Internal Routines --------------------------- */
+
+/* -------------------------- Public Routines ---------------------------- */
+
+/*
+ * Multiplies a vector by a matrix, setting the result vector.
+ * It assumes all homogeneous coordinates are 1.
+ * The two vectors involved may be the same.
+ */
+
+#include <Math/mat3.h>
+
+#ifndef TRUE
+# define TRUE 1
+#endif
+
+#ifndef FALSE
+# define FALSE 0
+#endif
+
+
+void
+MAT3mult_vec(double *result_vec, register double *vec, register double (*mat)[4])
+{
+ MAT3vec tempvec;
+ register double *temp = tempvec;
+
+ temp[0] = vec[0] * mat[0][0] + vec[1] * mat[1][0] +
+ vec[2] * mat[2][0] + mat[3][0];
+ temp[1] = vec[0] * mat[0][1] + vec[1] * mat[1][1] +
+ vec[2] * mat[2][1] + mat[3][1];
+ temp[2] = vec[0] * mat[0][2] + vec[1] * mat[1][2] +
+ vec[2] * mat[2][2] + mat[3][2];
+
+ MAT3_COPY_VEC(result_vec, temp);
+}
+
+/*
+ * Multiplies a vector of size 4 by a matrix, setting the result vector.
+ * The fourth element of the vector is the homogeneous coordinate, which
+ * may or may not be 1. If the "normalize" parameter is TRUE, then the
+ * result vector will be normalized so that the homogeneous coordinate is 1.
+ * The two vectors involved may be the same.
+ * This returns zero if the vector was to be normalized, but couldn't be.
+ */
+
+int
+MAT3mult_hvec(double *result_vec, register double *vec, register double (*mat)[4], int normalize)
+{
+ MAT3hvec tempvec;
+ double norm_fac;
+ register double *temp = tempvec;
+ register int ret = TRUE;
+
+ temp[0] = vec[0] * mat[0][0] + vec[1] * mat[1][0] +
+ vec[2] * mat[2][0] + vec[3] * mat[3][0];
+ temp[1] = vec[0] * mat[0][1] + vec[1] * mat[1][1] +
+ vec[2] * mat[2][1] + vec[3] * mat[3][1];
+ temp[2] = vec[0] * mat[0][2] + vec[1] * mat[1][2] +
+ vec[2] * mat[2][2] + vec[3] * mat[3][2];
+ temp[3] = vec[0] * mat[0][3] + vec[1] * mat[1][3] +
+ vec[2] * mat[2][3] + vec[3] * mat[3][3];
+
+ /* Normalize if asked for, possible, and necessary */
+ if (normalize) {
+ if (MAT3_IS_ZERO(temp[3])) {
+#ifndef THINK_C
+ fprintf (stderr,
+ "Can't normalize vector: homogeneous coordinate is 0");
+#endif
+ ret = FALSE;
+ }
+ else {
+ norm_fac = 1.0 / temp[3];
+ MAT3_SCALE_VEC(result_vec, temp, norm_fac);
+ result_vec[3] = 1.0;
+ }
+ }
+ else MAT3_COPY_HVEC(result_vec, temp);
+
+ return(ret);
+}
+
+/*
+ * Sets the first vector to be the cross-product of the last two vectors.
+ */
+
+void
+MAT3cross_product(double *result_vec, register double *vec1, register double *vec2)
+{
+ MAT3vec tempvec;
+ register double *temp = tempvec;
+
+ temp[0] = vec1[1] * vec2[2] - vec1[2] * vec2[1];
+ temp[1] = vec1[2] * vec2[0] - vec1[0] * vec2[2];
+ temp[2] = vec1[0] * vec2[1] - vec1[1] * vec2[0];
+
+ MAT3_COPY_VEC(result_vec, temp);
+}
+
+/*
+ * Finds a vector perpendicular to vec and stores it in result_vec.
+ * Method: take any vector (we use <0,1,0>) and subtract the
+ * portion of it pointing in the vec direction. This doesn't
+ * work if vec IS <0,1,0> or is very near it. So if this is
+ * the case, use <0,0,1> instead.
+ * If "is_unit" is TRUE, the given vector is assumed to be unit length.
+ */
+
+#define SELECT .7071 /* selection constant (roughly .5*sqrt(2) */
+
+void
+MAT3perp_vec(double *result_vec, double *vec, int is_unit)
+{
+ MAT3vec norm;
+ double dot;
+
+ MAT3_SET_VEC(result_vec, 0.0, 1.0, 0.0);
+
+ MAT3_COPY_VEC(norm, vec);
+
+ if (! is_unit) MAT3_NORMALIZE_VEC(norm, dot);
+
+ /* See if vector is too close to <0,1,0>. If so, use <0,0,1> */
+ if ((dot = MAT3_DOT_PRODUCT(norm, result_vec)) > SELECT || dot < -SELECT) {
+ result_vec[1] = 0.0;
+ result_vec[2] = 1.0;
+ dot = MAT3_DOT_PRODUCT(norm, result_vec);
+ }
+
+ /* Subtract off non-perpendicular part */
+ result_vec[0] -= dot * norm[0];
+ result_vec[1] -= dot * norm[1];
+ result_vec[2] -= dot * norm[2];
+
+ /* Make result unit length */
+ MAT3_NORMALIZE_VEC(result_vec, dot);
+}
+++ /dev/null
-#---------------------------------------------------------------------------
-# Makefile
-#
-# Written by Curtis Olson, started January 1998.
-#
-# Copyright (C) 1997 Curtis L. Olson - curt@infoplane.com
-#
-# This program is free software; you can redistribute it and/or modify
-# it under the terms of the GNU General Public License as published by
-# the Free Software Foundation; either version 2 of the License, or
-# (at your option) any later version.
-#
-# This program is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-# GNU General Public License for more details.
-#
-# You should have received a copy of the GNU General Public License
-# along with this program; if not, write to the Free Software
-# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
-#
-# $Id$
-# (Log is kept at end of this file)
-#---------------------------------------------------------------------------
-
-
-TARGET = splittris
-
-CFILES = splittris.c
-LDLIBS = -lMath -lScenery -lm
-
-
-include $(FG_ROOT_SRC)/commondefs
-
-
-#---------------------------------------------------------------------------
-# Rule for TARGET
-#---------------------------------------------------------------------------
-
-$(TARGET): $(OBJECTS)
- $(CC) -o $(TARGET) $(OBJECTS) $(LDFLAGS) $(LDLIBS)
-
-
-include $(COMMONRULES)
-
-
-#---------------------------------------------------------------------------
-# $Log$
-# Revision 1.3 1998/01/21 02:55:55 curt
-# Incorporated new make system from Bob Kuehne <rpk@sgi.com>.
-#
-# Revision 1.2 1998/01/14 15:54:42 curt
-# Initial revision completed.
-#
-# Revision 1.1 1998/01/14 02:11:30 curt
-# Initial revision.
-#
--- /dev/null
+#---------------------------------------------------------------------------
+# Makefile
+#
+# Written by Curtis Olson, started January 1998.
+#
+# Copyright (C) 1998 Curtis L. Olson - curt@me.umn.edu
+#
+# This program is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 2 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program; if not, write to the Free Software
+# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+#
+# $Id$
+# (Log is kept at end of this file)
+#---------------------------------------------------------------------------
+
+
+bin_PROGRAMS = splittris
+
+splittris_SOURCES = \
+ MAT3vec.c \
+ fg_geodesy.c fg_geodesy.h \
+ mat3.h \
+ polar.c polar.h \
+ splittris.c splittris.h
+
+splittris_LDADD = \
+ $(top_builddir)/Simulator/Scenery/Bucket/libBucket.la
+
+INCLUDES += -I../../Simulator
+
+
+#---------------------------------------------------------------------------
+# $Log$
+# Revision 1.1 1998/04/08 23:21:10 curt
+# Adopted Gnu automake/autoconf system.
+#
+# Revision 1.3 1998/01/21 02:55:55 curt
+# Incorporated new make system from Bob Kuehne <rpk@sgi.com>.
+#
+# Revision 1.2 1998/01/14 15:54:42 curt
+# Initial revision completed.
+#
+# Revision 1.1 1998/01/14 02:11:30 curt
+# Initial revision.
+#
--- /dev/null
+# Makefile.in generated automatically by automake 1.2h from Makefile.am
+
+# Copyright (C) 1994, 1995, 1996, 1997, 1998 Free Software Foundation, Inc.
+# This Makefile.in is free software; the Free Software Foundation
+# gives unlimited permission to copy and/or distribute it,
+# with or without modifications, as long as this notice is preserved.
+
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY, to the extent permitted by law; without
+# even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+# PARTICULAR PURPOSE.
+
+#---------------------------------------------------------------------------
+# Makefile
+#
+# Written by Curtis Olson, started January 1998.
+#
+# Copyright (C) 1998 Curtis L. Olson - curt@me.umn.edu
+#
+# This program is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 2 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program; if not, write to the Free Software
+# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+#
+# $Id$
+# (Log is kept at end of this file)
+#---------------------------------------------------------------------------
+
+
+SHELL = /bin/sh
+
+srcdir = @srcdir@
+top_srcdir = @top_srcdir@
+VPATH = @srcdir@
+prefix = @prefix@
+exec_prefix = @exec_prefix@
+
+bindir = @bindir@
+sbindir = @sbindir@
+libexecdir = @libexecdir@
+datadir = @datadir@
+sysconfdir = @sysconfdir@
+sharedstatedir = @sharedstatedir@
+localstatedir = @localstatedir@
+libdir = @libdir@
+infodir = @infodir@
+mandir = @mandir@
+includedir = @includedir@
+oldincludedir = /usr/include
+
+DISTDIR =
+
+pkgdatadir = $(datadir)/@PACKAGE@
+pkglibdir = $(libdir)/@PACKAGE@
+pkgincludedir = $(includedir)/@PACKAGE@
+
+top_builddir = ../..
+
+ACLOCAL = @ACLOCAL@
+AUTOCONF = @AUTOCONF@
+AUTOMAKE = @AUTOMAKE@
+AUTOHEADER = @AUTOHEADER@
+
+INSTALL = @INSTALL@
+INSTALL_PROGRAM = @INSTALL_PROGRAM@
+INSTALL_DATA = @INSTALL_DATA@
+INSTALL_SCRIPT = @INSTALL_SCRIPT@
+transform = @program_transform_name@
+
+NORMAL_INSTALL = :
+PRE_INSTALL = :
+POST_INSTALL = :
+NORMAL_UNINSTALL = :
+PRE_UNINSTALL = :
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+MAKEINFO = @MAKEINFO@
+NM = @NM@
+PACKAGE = @PACKAGE@
+RANLIB = @RANLIB@
+VERSION = @VERSION@
+
+bin_PROGRAMS = splittris
+
+splittris_SOURCES = \
+ MAT3vec.c \
+ fg_geodesy.c fg_geodesy.h \
+ mat3.h \
+ polar.c polar.h \
+ splittris.c splittris.h
+
+splittris_LDADD = \
+ $(top_builddir)/Simulator/Scenery/Bucket/libBucket.la
+mkinstalldirs = $(SHELL) $(top_srcdir)/mkinstalldirs
+CONFIG_HEADER = ../../Simulator/Include/config.h
+CONFIG_CLEAN_FILES =
+PROGRAMS = $(bin_PROGRAMS)
+
+
+DEFS = @DEFS@ -I. -I$(srcdir) -I../../Simulator/Include
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+LDFLAGS = @LDFLAGS@
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+X_EXTRA_LIBS = @X_EXTRA_LIBS@
+X_PRE_LIBS = @X_PRE_LIBS@
+splittris_OBJECTS = MAT3vec.o fg_geodesy.o polar.o splittris.o
+splittris_DEPENDENCIES = \
+$(top_builddir)/Simulator/Scenery/Bucket/libBucket.la
+splittris_LDFLAGS =
+CFLAGS = @CFLAGS@
+COMPILE = $(CC) $(DEFS) $(INCLUDES) $(CPPFLAGS) $(CFLAGS)
+LTCOMPILE = $(LIBTOOL) --mode=compile $(CC) $(DEFS) $(INCLUDES) $(CPPFLAGS) $(CFLAGS)
+LINK = $(LIBTOOL) --mode=link $(CC) $(CFLAGS) $(LDFLAGS) -o $@
+DIST_COMMON = Makefile.am Makefile.in
+
+
+DISTFILES = $(DIST_COMMON) $(SOURCES) $(HEADERS) $(TEXINFOS) $(EXTRA_DIST)
+
+TAR = tar
+GZIP = --best
+DEP_FILES = .deps/MAT3vec.P .deps/fg_geodesy.P .deps/polar.P \
+.deps/splittris.P
+SOURCES = $(splittris_SOURCES)
+OBJECTS = $(splittris_OBJECTS)
+
+all: Makefile $(PROGRAMS)
+
+.SUFFIXES:
+.SUFFIXES: .S .c .lo .o .s
+$(srcdir)/Makefile.in: @MAINT@ Makefile.am $(top_srcdir)/configure.in $(ACLOCAL_M4)
+ cd $(top_srcdir) && $(AUTOMAKE) --gnu Tools/SplitTris/Makefile
+
+Makefile: $(srcdir)/Makefile.in $(top_builddir)/config.status $(BUILT_SOURCES)
+ cd $(top_builddir) \
+ && CONFIG_FILES=$(subdir)/$@ CONFIG_HEADERS= $(SHELL) ./config.status
+
+
+mostlyclean-binPROGRAMS:
+
+clean-binPROGRAMS:
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+
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+
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+
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+
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+
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+
+.S.o:
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+
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+
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+
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+ -rm -f *.lo
+
+clean-libtool:
+ -rm -rf .libs _libs
+
+distclean-libtool:
+
+maintainer-clean-libtool:
+
+splittris: $(splittris_OBJECTS) $(splittris_DEPENDENCIES)
+ @rm -f splittris
+ $(LINK) $(splittris_LDFLAGS) $(splittris_OBJECTS) $(splittris_LDADD) $(LIBS)
+
+tags: TAGS
+
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+ here=`pwd`; \
+ list='$(SOURCES) $(HEADERS)'; \
+ unique=`for i in $$list; do echo $$i; done | \
+ awk ' { files[$$0] = 1; } \
+ END { for (i in files) print i; }'`; \
+ test -z "$(ETAGS_ARGS)$$unique$(LISP)$$tags" \
+ || (cd $(srcdir) && etags $(ETAGS_ARGS) $$tags $$unique $(LISP) -o $$here/TAGS)
+
+mostlyclean-tags:
+
+clean-tags:
+
+distclean-tags:
+ -rm -f TAGS ID
+
+maintainer-clean-tags:
+
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+
+subdir = Tools/SplitTris
+
+distdir: $(DISTFILES)
+ here=`cd $(top_builddir) && pwd`; \
+ top_distdir=`cd $(top_distdir) && pwd`; \
+ distdir=`cd $(distdir) && pwd`; \
+ cd $(top_srcdir) \
+ && $(AUTOMAKE) --include-deps --build-dir=$$here --srcdir-name=$(top_srcdir) --output-dir=$$top_distdir --gnu Tools/SplitTris/Makefile
+ @for file in $(DISTFILES); do \
+ d=$(srcdir); \
+ test -f $(distdir)/$$file \
+ || ln $$d/$$file $(distdir)/$$file 2> /dev/null \
+ || cp -p $$d/$$file $(distdir)/$$file; \
+ done
+
+DEPS_MAGIC := $(shell mkdir .deps > /dev/null 2>&1 || :)
+
+-include $(DEP_FILES)
+
+mostlyclean-depend:
+
+clean-depend:
+
+distclean-depend:
+
+maintainer-clean-depend:
+ -rm -rf .deps
+
+%.o: %.c
+ @echo '$(COMPILE) -c $<'; \
+ $(COMPILE) -Wp,-MD,.deps/$(*F).P -c $<
+
+%.lo: %.c
+ @echo '$(LTCOMPILE) -c $<'; \
+ $(LTCOMPILE) -Wp,-MD,.deps/$(*F).p -c $<
+ @-sed -e 's/^\([^:]*\)\.o:/\1.lo \1.o:/' \
+ < .deps/$(*F).p > .deps/$(*F).P
+ @-rm -f .deps/$(*F).p
+info:
+dvi:
+check: all
+ $(MAKE)
+installcheck:
+install-exec: install-binPROGRAMS
+ @$(NORMAL_INSTALL)
+
+install-data:
+ @$(NORMAL_INSTALL)
+
+install: install-exec install-data all
+ @:
+
+uninstall: uninstall-binPROGRAMS
+
+install-strip:
+ $(MAKE) INSTALL_PROGRAM='$(INSTALL_PROGRAM) -s' INSTALL_SCRIPT='$(INSTALL_PROGRAM)' install
+installdirs:
+ $(mkinstalldirs) $(DATADIR)$(bindir)
+
+
+mostlyclean-generic:
+ -test -z "$(MOSTLYCLEANFILES)" || rm -f $(MOSTLYCLEANFILES)
+
+clean-generic:
+ -test -z "$(CLEANFILES)" || rm -f $(CLEANFILES)
+
+distclean-generic:
+ -rm -f Makefile $(DISTCLEANFILES)
+ -rm -f config.cache config.log stamp-h stamp-h[0-9]*
+ -test -z "$(CONFIG_CLEAN_FILES)" || rm -f $(CONFIG_CLEAN_FILES)
+
+maintainer-clean-generic:
+ -test -z "$(MAINTAINERCLEANFILES)" || rm -f $(MAINTAINERCLEANFILES)
+ -test -z "$(BUILT_SOURCES)" || rm -f $(BUILT_SOURCES)
+mostlyclean: mostlyclean-binPROGRAMS mostlyclean-compile \
+ mostlyclean-libtool mostlyclean-tags mostlyclean-depend \
+ mostlyclean-generic
+
+clean: clean-binPROGRAMS clean-compile clean-libtool clean-tags \
+ clean-depend clean-generic mostlyclean
+
+distclean: distclean-binPROGRAMS distclean-compile distclean-libtool \
+ distclean-tags distclean-depend distclean-generic clean
+ -rm -f config.status
+ -rm -f libtool
+
+maintainer-clean: maintainer-clean-binPROGRAMS maintainer-clean-compile \
+ maintainer-clean-libtool maintainer-clean-tags \
+ maintainer-clean-depend maintainer-clean-generic \
+ distclean
+ @echo "This command is intended for maintainers to use;"
+ @echo "it deletes files that may require special tools to rebuild."
+
+.PHONY: mostlyclean-binPROGRAMS distclean-binPROGRAMS clean-binPROGRAMS \
+maintainer-clean-binPROGRAMS uninstall-binPROGRAMS install-binPROGRAMS \
+mostlyclean-compile distclean-compile clean-compile \
+maintainer-clean-compile mostlyclean-libtool distclean-libtool \
+clean-libtool maintainer-clean-libtool tags mostlyclean-tags \
+distclean-tags clean-tags maintainer-clean-tags distdir \
+mostlyclean-depend distclean-depend clean-depend \
+maintainer-clean-depend info dvi installcheck install-exec install-data \
+install uninstall all installdirs mostlyclean-generic distclean-generic \
+clean-generic maintainer-clean-generic clean mostlyclean distclean \
+maintainer-clean
+
+
+INCLUDES += -I../../Simulator
+
+#---------------------------------------------------------------------------
+# $Log$
+# Revision 1.1 1998/04/08 23:21:11 curt
+# Adopted Gnu automake/autoconf system.
+#
+# Revision 1.3 1998/01/21 02:55:55 curt
+# Incorporated new make system from Bob Kuehne <rpk@sgi.com>.
+#
+# Revision 1.2 1998/01/14 15:54:42 curt
+# Initial revision completed.
+#
+# Revision 1.1 1998/01/14 02:11:30 curt
+# Initial revision.
+#
+
+# Tell versions [3.59,3.63) of GNU make to not export all variables.
+# Otherwise a system limit (for SysV at least) may be exceeded.
+.NOEXPORT:
--- /dev/null
+/**************************************************************************
+ * fg_geodesy.c -- routines to convert between geodetic and geocentric
+ * coordinate systems.
+ *
+ * Copied and adapted directly from LaRCsim/ls_geodesy.c
+ *
+ * See below for the complete original LaRCsim comments.
+ *
+ * $Id$
+ * (Log is kept at end of this file)
+ **************************************************************************/
+
+
+#include <math.h>
+
+#include <Include/fg_constants.h>
+
+#include "fg_geodesy.h"
+
+
+/* ONE_SECOND is pi/180/60/60, or about 100 feet at earths' equator */
+#define ONE_SECOND 4.848136811E-6
+
+
+/* fgGeocToGeod(lat_geoc, radius, *lat_geod, *alt, *sea_level_r)
+ * INPUTS:
+ * lat_geoc Geocentric latitude, radians, + = North
+ * radius C.G. radius to earth center, ft
+ *
+ * OUTPUTS:
+ * lat_geod Geodetic latitude, radians, + = North
+ * alt C.G. altitude above mean sea level, ft
+ * sea_level_r radius from earth center to sea level at
+ * local vertical (surface normal) of C.G.
+ */
+
+void fgGeocToGeod( double lat_geoc, double radius, double
+ *lat_geod, double *alt, double *sea_level_r )
+{
+ double t_lat, x_alpha, mu_alpha, delt_mu, r_alpha, l_point, rho_alpha;
+ double sin_mu_a, denom,delt_lambda, lambda_sl, sin_lambda_sl;
+
+ if( ( (FG_PI_2 - lat_geoc) < ONE_SECOND ) /* near North pole */
+ || ( (FG_PI_2 + lat_geoc) < ONE_SECOND ) ) /* near South pole */
+ {
+ *lat_geod = lat_geoc;
+ *sea_level_r = EQUATORIAL_RADIUS_KM*E;
+ *alt = radius - *sea_level_r;
+ } else {
+ t_lat = tan(lat_geoc);
+ x_alpha = E*EQUATORIAL_RADIUS_KM/sqrt(t_lat*t_lat + E*E);
+ mu_alpha = atan2(sqrt(RESQ_KM - x_alpha*x_alpha),E*x_alpha);
+ if (lat_geoc < 0) mu_alpha = - mu_alpha;
+ sin_mu_a = sin(mu_alpha);
+ delt_lambda = mu_alpha - lat_geoc;
+ r_alpha = x_alpha/cos(lat_geoc);
+ l_point = radius - r_alpha;
+ *alt = l_point*cos(delt_lambda);
+ denom = sqrt(1-EPS*EPS*sin_mu_a*sin_mu_a);
+ rho_alpha = EQUATORIAL_RADIUS_KM*(1-EPS)/
+ (denom*denom*denom);
+ delt_mu = atan2(l_point*sin(delt_lambda),rho_alpha + *alt);
+ *lat_geod = mu_alpha - delt_mu;
+ lambda_sl = atan( E*E * tan(*lat_geod) ); /* SL geoc. latitude */
+ sin_lambda_sl = sin( lambda_sl );
+ *sea_level_r =
+ sqrt(RESQ_KM / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl));
+ }
+}
+
+
+/* fgGeodToGeoc( lat_geod, alt, *sl_radius, *lat_geoc )
+ * INPUTS:
+ * lat_geod Geodetic latitude, radians, + = North
+ * alt C.G. altitude above mean sea level, ft
+ *
+ * OUTPUTS:
+ * sl_radius SEA LEVEL radius to earth center, ft (add Altitude to
+ * get true distance from earth center.
+ * lat_geoc Geocentric latitude, radians, + = North
+ *
+ */
+
+void fgGeodToGeoc( double lat_geod, double alt, double *sl_radius,
+ double *lat_geoc )
+{
+ double lambda_sl, sin_lambda_sl, cos_lambda_sl, sin_mu, cos_mu, px, py;
+
+ lambda_sl = atan( E*E * tan(lat_geod) ); /* sea level geocentric latitude */
+ sin_lambda_sl = sin( lambda_sl );
+ cos_lambda_sl = cos( lambda_sl );
+ sin_mu = sin(lat_geod); /* Geodetic (map makers') latitude */
+ cos_mu = cos(lat_geod);
+ *sl_radius =
+ sqrt(RESQ_KM / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl));
+ py = *sl_radius*sin_lambda_sl + alt*sin_mu;
+ px = *sl_radius*cos_lambda_sl + alt*cos_mu;
+ *lat_geoc = atan2( py, px );
+}
+
+
+/***************************************************************************
+
+ TITLE: ls_geodesy
+
+----------------------------------------------------------------------------
+
+ FUNCTION: Converts geocentric coordinates to geodetic positions
+
+----------------------------------------------------------------------------
+
+ MODULE STATUS: developmental
+
+----------------------------------------------------------------------------
+
+ GENEALOGY: Written as part of LaRCSim project by E. B. Jackson
+
+----------------------------------------------------------------------------
+
+ DESIGNED BY: E. B. Jackson
+
+ CODED BY: E. B. Jackson
+
+ MAINTAINED BY: E. B. Jackson
+
+----------------------------------------------------------------------------
+
+ MODIFICATION HISTORY:
+
+ DATE PURPOSE BY
+
+ 930208 Modified to avoid singularity near polar region. EBJ
+ 930602 Moved backwards calcs here from ls_step. EBJ
+ 931214 Changed erroneous Latitude and Altitude variables to
+ *lat_geod and *alt in routine ls_geoc_to_geod. EBJ
+ 940111 Changed header files from old ls_eom.h style to ls_types,
+ and ls_constants. Also replaced old DATA type with new
+ SCALAR type. EBJ
+
+ CURRENT RCS HEADER:
+
+$Header$
+$Log$
+Revision 1.1 1998/04/08 23:21:11 curt
+Adopted Gnu automake/autoconf system.
+
+Revision 1.4 1998/01/27 00:47:59 curt
+Incorporated Paul Bleisch's <bleisch@chromatic.com> new debug message
+system and commandline/config file processing code.
+
+Revision 1.3 1998/01/19 19:27:12 curt
+Merged in make system changes from Bob Kuehne <rpk@sgi.com>
+This should simplify things tremendously.
+
+Revision 1.2 1997/12/15 23:54:54 curt
+Add xgl wrappers for debugging.
+Generate terrain normals on the fly.
+
+Revision 1.1 1997/07/31 23:13:14 curt
+Initial revision.
+
+Revision 1.1 1997/05/29 00:09:56 curt
+Initial Flight Gear revision.
+
+ * Revision 1.5 1994/01/11 18:47:05 bjax
+ * Changed include files to use types and constants, not ls_eom.h
+ * Also changed DATA type to SCALAR type.
+ *
+ * Revision 1.4 1993/12/14 21:06:47 bjax
+ * Removed global variable references Altitude and Latitude. EBJ
+ *
+ * Revision 1.3 1993/06/02 15:03:40 bjax
+ * Made new subroutine for calculating geodetic to geocentric; changed name
+ * of forward conversion routine from ls_geodesy to ls_geoc_to_geod.
+ *
+
+----------------------------------------------------------------------------
+
+ REFERENCES:
+
+ [ 1] Stevens, Brian L.; and Lewis, Frank L.: "Aircraft
+ Control and Simulation", Wiley and Sons, 1992.
+ ISBN 0-471-61397-5
+
+
+----------------------------------------------------------------------------
+
+ CALLED BY: ls_aux
+
+----------------------------------------------------------------------------
+
+ CALLS TO:
+
+----------------------------------------------------------------------------
+
+ INPUTS:
+ lat_geoc Geocentric latitude, radians, + = North
+ radius C.G. radius to earth center, ft
+
+----------------------------------------------------------------------------
+
+ OUTPUTS:
+ lat_geod Geodetic latitude, radians, + = North
+ alt C.G. altitude above mean sea level, ft
+ sea_level_r radius from earth center to sea level at
+ local vertical (surface normal) of C.G.
+
+--------------------------------------------------------------------------*/
+
+
+/* $Log$
+/* Revision 1.1 1998/04/08 23:21:11 curt
+/* Adopted Gnu automake/autoconf system.
+/*
+ * Revision 1.4 1998/01/27 00:47:59 curt
+ * Incorporated Paul Bleisch's <bleisch@chromatic.com> new debug message
+ * system and commandline/config file processing code.
+ *
+ * Revision 1.3 1998/01/19 19:27:12 curt
+ * Merged in make system changes from Bob Kuehne <rpk@sgi.com>
+ * This should simplify things tremendously.
+ *
+ * Revision 1.2 1997/12/15 23:54:54 curt
+ * Add xgl wrappers for debugging.
+ * Generate terrain normals on the fly.
+ *
+ * Revision 1.1 1997/07/31 23:13:14 curt
+ * Initial revision.
+ *
+ */
--- /dev/null
+/**************************************************************************
+ * fg_geodesy.h -- routines to convert between geodetic and geocentric
+ * coordinate systems.
+ *
+ * Copied and adapted directly from LaRCsim/ls_geodesy.c
+ *
+ * See below for the complete original LaRCsim comments.
+ *
+ * $Id$
+ * (Log is kept at end of this file)
+ **************************************************************************/
+
+
+#ifndef _FG_GEODESY_H
+#define _FG_GEODESY_H
+
+
+/* fgGeocToGeod(lat_geoc, radius, *lat_geod, *alt, *sea_level_r)
+ * INPUTS:
+ * lat_geoc Geocentric latitude, radians, + = North
+ * radius C.G. radius to earth center, ft
+ *
+ * OUTPUTS:
+ * lat_geod Geodetic latitude, radians, + = North
+ * alt C.G. altitude above mean sea level, ft
+ * sea_level_r radius from earth center to sea level at
+ * local vertical (surface normal) of C.G.
+ */
+
+void fgGeocToGeod( double lat_geoc, double radius, double
+ *lat_geod, double *alt, double *sea_level_r );
+
+/* fgGeodToGeoc( lat_geod, alt, *sl_radius, *lat_geoc )
+ * INPUTS:
+ * lat_geod Geodetic latitude, radians, + = North
+ * alt C.G. altitude above mean sea level, ft
+ *
+ * OUTPUTS:
+ * sl_radius SEA LEVEL radius to earth center, ft (add Altitude to
+ * get true distance from earth center.
+ * lat_geoc Geocentric latitude, radians, + = North
+ *
+ */
+
+void fgGeodToGeoc( double lat_geod, double alt, double *sl_radius,
+ double *lat_geoc );
+
+
+
+/***************************************************************************
+
+ TITLE: ls_geodesy
+
+----------------------------------------------------------------------------
+
+ FUNCTION: Converts geocentric coordinates to geodetic positions
+
+----------------------------------------------------------------------------
+
+ MODULE STATUS: developmental
+
+----------------------------------------------------------------------------
+
+ GENEALOGY: Written as part of LaRCSim project by E. B. Jackson
+
+----------------------------------------------------------------------------
+
+ DESIGNED BY: E. B. Jackson
+
+ CODED BY: E. B. Jackson
+
+ MAINTAINED BY: E. B. Jackson
+
+----------------------------------------------------------------------------
+
+ MODIFICATION HISTORY:
+
+ DATE PURPOSE BY
+
+ 930208 Modified to avoid singularity near polar region. EBJ
+ 930602 Moved backwards calcs here from ls_step. EBJ
+ 931214 Changed erroneous Latitude and Altitude variables to
+ *lat_geod and *alt in routine ls_geoc_to_geod. EBJ
+ 940111 Changed header files from old ls_eom.h style to ls_types,
+ and ls_constants. Also replaced old DATA type with new
+ SCALAR type. EBJ
+
+ CURRENT RCS HEADER:
+
+$Header$
+$Log$
+Revision 1.1 1998/04/08 23:21:12 curt
+Adopted Gnu automake/autoconf system.
+
+Revision 1.2 1998/01/22 02:59:38 curt
+Changed #ifdef FILE_H to #ifdef _FILE_H
+
+Revision 1.1 1997/07/31 23:13:14 curt
+Initial revision.
+
+Revision 1.1 1997/05/29 00:09:56 curt
+Initial Flight Gear revision.
+
+ * Revision 1.5 1994/01/11 18:47:05 bjax
+ * Changed include files to use types and constants, not ls_eom.h
+ * Also changed DATA type to SCALAR type.
+ *
+ * Revision 1.4 1993/12/14 21:06:47 bjax
+ * Removed global variable references Altitude and Latitude. EBJ
+ *
+ * Revision 1.3 1993/06/02 15:03:40 bjax
+ * Made new subroutine for calculating geodetic to geocentric; changed name
+ * of forward conversion routine from ls_geodesy to ls_geoc_to_geod.
+ *
+
+----------------------------------------------------------------------------
+
+ REFERENCES:
+
+ [ 1] Stevens, Brian L.; and Lewis, Frank L.: "Aircraft
+ Control and Simulation", Wiley and Sons, 1992.
+ ISBN 0-471-61397-5
+
+
+----------------------------------------------------------------------------
+
+ CALLED BY: ls_aux
+
+----------------------------------------------------------------------------
+
+ CALLS TO:
+
+----------------------------------------------------------------------------
+
+ INPUTS:
+ lat_geoc Geocentric latitude, radians, + = North
+ radius C.G. radius to earth center, ft
+
+----------------------------------------------------------------------------
+
+ OUTPUTS:
+ lat_geod Geodetic latitude, radians, + = North
+ alt C.G. altitude above mean sea level, ft
+ sea_level_r radius from earth center to sea level at
+ local vertical (surface normal) of C.G.
+
+--------------------------------------------------------------------------*/
+
+
+#endif /* _FG_GEODESY_H */
+
+
+/* $Log$
+/* Revision 1.1 1998/04/08 23:21:12 curt
+/* Adopted Gnu automake/autoconf system.
+/*
+ * Revision 1.2 1998/01/22 02:59:38 curt
+ * Changed #ifdef FILE_H to #ifdef _FILE_H
+ *
+ * Revision 1.1 1997/07/31 23:13:14 curt
+ * Initial revision.
+ *
+ */
--- /dev/null
+/* Copyright 1988, Brown Computer Graphics Group. All Rights Reserved. */
+
+/* -------------------------------------------------------------------------
+ Public MAT3 include file
+ ------------------------------------------------------------------------- */
+
+#ifndef MAT3_HAS_BEEN_INCLUDED
+#define MAT3_HAS_BEEN_INCLUDED
+
+/* ----------------------------- Constants ------------------------------ */
+
+/*
+ * Make sure the math library .h file is included, in case it wasn't.
+ */
+
+#ifndef HUGE
+#include <math.h>
+#endif
+#include <stdio.h>
+
+
+#define MAT3_DET0 -1 /* Indicates singular mat */
+#define MAT3_EPSILON 1e-12 /* Close enough to zero */
+#define MAT3_PI 3.141592653589793 /* Pi */
+
+/* ------------------------------ Types --------------------------------- */
+
+typedef double MAT3mat[4][4]; /* 4x4 matrix */
+typedef double MAT3vec[3]; /* Vector */
+typedef double MAT3hvec[4]; /* Vector with homogeneous coord */
+
+/* ------------------------------ Macros -------------------------------- */
+
+/* Tests if a number is within EPSILON of zero */
+#define MAT3_IS_ZERO(N) ((N) < MAT3_EPSILON && (N) > -MAT3_EPSILON)
+
+/* Sets a vector to the three given values */
+#define MAT3_SET_VEC(V,X,Y,Z) ((V)[0]=(X), (V)[1]=(Y), (V)[2]=(Z))
+
+/* Tests a vector for all components close to zero */
+#define MAT3_IS_ZERO_VEC(V) (MAT3_IS_ZERO((V)[0]) && \
+ MAT3_IS_ZERO((V)[1]) && \
+ MAT3_IS_ZERO((V)[2]))
+
+/* Dot product of two vectors */
+#define MAT3_DOT_PRODUCT(V1,V2) \
+ ((V1)[0]*(V2)[0] + (V1)[1]*(V2)[1] + (V1)[2]*(V2)[2])
+
+/* Copy one vector to other */
+#define MAT3_COPY_VEC(TO,FROM) ((TO)[0] = (FROM)[0], \
+ (TO)[1] = (FROM)[1], \
+ (TO)[2] = (FROM)[2])
+
+/* Normalize vector to unit length, using TEMP as temporary variable.
+ * TEMP will be zero if vector has zero length */
+#define MAT3_NORMALIZE_VEC(V,TEMP) \
+ if ((TEMP = sqrt(MAT3_DOT_PRODUCT(V,V))) > MAT3_EPSILON) { \
+ TEMP = 1.0 / TEMP; \
+ MAT3_SCALE_VEC(V,V,TEMP); \
+ } else TEMP = 0.0
+
+/* Scale vector by given factor, storing result vector in RESULT_V */
+#define MAT3_SCALE_VEC(RESULT_V,V,SCALE) \
+ MAT3_SET_VEC(RESULT_V, (V)[0]*(SCALE), (V)[1]*(SCALE), (V)[2]*(SCALE))
+
+/* Adds vectors V1 and V2, storing result in RESULT_V */
+#define MAT3_ADD_VEC(RESULT_V,V1,V2) \
+ MAT3_SET_VEC(RESULT_V, (V1)[0]+(V2)[0], (V1)[1]+(V2)[1], \
+ (V1)[2]+(V2)[2])
+
+/* Subtracts vector V2 from V1, storing result in RESULT_V */
+#define MAT3_SUB_VEC(RESULT_V,V1,V2) \
+ MAT3_SET_VEC(RESULT_V, (V1)[0]-(V2)[0], (V1)[1]-(V2)[1], \
+ (V1)[2]-(V2)[2])
+
+/* Multiplies vectors V1 and V2, storing result in RESULT_V */
+#define MAT3_MULT_VEC(RESULT_V,V1,V2) \
+ MAT3_SET_VEC(RESULT_V, (V1)[0]*(V2)[0], (V1)[1]*(V2)[1], \
+ (V1)[2]*(V2)[2])
+
+/* Sets RESULT_V to the linear combination of V1 and V2, scaled by
+ * SCALE1 and SCALE2, respectively */
+#define MAT3_LINEAR_COMB(RESULT_V,SCALE1,V1,SCALE2,V2) \
+ MAT3_SET_VEC(RESULT_V, (SCALE1)*(V1)[0] + (SCALE2)*(V2)[0], \
+ (SCALE1)*(V1)[1] + (SCALE2)*(V2)[1], \
+ (SCALE1)*(V1)[2] + (SCALE2)*(V2)[2])
+
+/* Several of the vector macros are useful for homogeneous-coord vectors */
+#define MAT3_SET_HVEC(V,X,Y,Z,W) ((V)[0]=(X), (V)[1]=(Y), \
+ (V)[2]=(Z), (V)[3]=(W))
+
+#define MAT3_COPY_HVEC(TO,FROM) ((TO)[0] = (FROM)[0], \
+ (TO)[1] = (FROM)[1], \
+ (TO)[2] = (FROM)[2], \
+ (TO)[3] = (FROM)[3])
+
+#define MAT3_SCALE_HVEC(RESULT_V,V,SCALE) \
+ MAT3_SET_HVEC(RESULT_V, (V)[0]*(SCALE), (V)[1]*(SCALE), \
+ (V)[2]*(SCALE), (V)[3]*(SCALE))
+
+#define MAT3_ADD_HVEC(RESULT_V,V1,V2) \
+ MAT3_SET_HVEC(RESULT_V, (V1)[0]+(V2)[0], (V1)[1]+(V2)[1], \
+ (V1)[2]+(V2)[2], (V1)[3]+(V2)[3])
+
+#define MAT3_SUB_HVEC(RESULT_V,V1,V2) \
+ MAT3_SET_HVEC(RESULT_V, (V1)[0]-(V2)[0], (V1)[1]-(V2)[1], \
+ (V1)[2]-(V2)[2], (V1)[3]-(V2)[3])
+
+#define MAT3_MULT_HVEC(RESULT_V,V1,V2) \
+ MAT3_SET_HVEC(RESULT_V, (V1)[0]*(V2)[0], (V1)[1]*(V2)[1], \
+ (V1)[2]*(V2)[2], (V1)[3]*(V2)[3])
+
+/* ------------------------------ Entries ------------------------------- */
+
+
+/* In MAT3geom.c */
+void MAT3direction_matrix (MAT3mat result_mat, MAT3mat mat);
+int MAT3normal_matrix (MAT3mat result_mat, MAT3mat mat);
+void MAT3rotate (MAT3mat result_mat, MAT3vec axis, double angle_in_radians);
+void MAT3translate (MAT3mat result_mat, MAT3vec trans);
+void MAT3scale (MAT3mat result_mat, MAT3vec scale);
+void MAT3shear(MAT3mat result_mat, double xshear, double yshear);
+
+/* In MAT3mat.c */
+void MAT3identity(MAT3mat);
+void MAT3zero(MAT3mat);
+void MAT3copy (MAT3mat to, MAT3mat from);
+void MAT3mult (MAT3mat result, MAT3mat, MAT3mat);
+void MAT3transpose (MAT3mat result, MAT3mat);
+int MAT3invert (MAT3mat result, MAT3mat);
+void MAT3print (MAT3mat, FILE *fp);
+void MAT3print_formatted (MAT3mat, FILE *fp,
+ char *title, char *head, char *format, char *tail);
+extern int MAT3equal( void );
+extern double MAT3trace( void );
+extern int MAT3power( void );
+extern int MAT3column_reduce( void );
+extern int MAT3kernel_basis( void );
+
+/* In MAT3vec.c */
+void MAT3mult_vec(MAT3vec result_vec, MAT3vec vec, MAT3mat mat);
+int MAT3mult_hvec (MAT3hvec result_vec, MAT3hvec vec, MAT3mat mat, int normalize);
+void MAT3cross_product(MAT3vec result,MAT3vec,MAT3vec);
+void MAT3perp_vec(MAT3vec result_vec, MAT3vec vec, int is_unit);
+
+#endif /* MAT3_HAS_BEEN_INCLUDED */
+
--- /dev/null
+/**************************************************************************
+ * polar.c -- routines to deal with polar math and transformations
+ *
+ * Written by Curtis Olson, started June 1997.
+ *
+ * Copyright (C) 1997 Curtis L. Olson - curt@infoplane.com
+ *
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+ *
+ * $Id$
+ * (Log is kept at end of this file)
+ **************************************************************************/
+
+
+#include <math.h>
+#include <stdio.h>
+
+#include <Math/polar.h>
+#include <Include/fg_constants.h>
+
+
+/* we can save these values between calls for efficiency */
+static double st, ct, sp, cp;
+
+
+/* Convert a polar coordinate to a cartesian coordinate. Lon and Lat
+ * must be specified in radians. The FG convention is for distances
+ * to be specified in meters */
+struct fgCartesianPoint fgPolarToCart(double lon, double lat, double radius) {
+ struct fgCartesianPoint pnew;
+
+ pnew.x = cos(lon) * cos(lat) * radius;
+ pnew.y = sin(lon) * cos(lat) * radius;
+ pnew.z = sin(lat) * radius;
+
+ return(pnew);
+}
+
+
+/* Precalculate as much as possible so we can do a batch of transforms
+ * through the same angles, will rotates a cartesian point about the
+ * center of the earth by Theta (longitude axis) and Phi (latitude
+ * axis) */
+
+/* Here are the unoptimized transformation equations
+
+ x' = cos(Phi) * cos(Theta) * x + cos(Phi) * sin(Theta) * y +
+ sin(Phi) * z
+ y' = -sin(Theta) * x + cos(Theta) * y
+ z' = -sin(Phi) * sin(Theta) * y - sin(Phi) * cos(Theta) * x +
+ cos(Phi) * z;
+
+ */
+void fgRotateBatchInit(double Theta, double Phi) {
+ printf("Theta = %.3f, Phi = %.3f\n", Theta, Phi);
+
+ st = sin(Theta);
+ ct = cos(Theta);
+ sp = sin(-Phi);
+ cp = cos(-Phi);
+}
+
+/* Rotates a cartesian point about the center of the earth by Theta
+ * (longitude axis) and Phi (latitude axis) */
+struct fgCartesianPoint fgRotateCartesianPoint(struct fgCartesianPoint p) {
+ struct fgCartesianPoint p1, p2;
+
+ /* printf("start = %.3f %.3f %.3f\n", p.x, p.y, p.z); */
+
+ /* rotate about the z axis */
+ p1.x = ct * p.x - st * p.y;
+ p1.y = st * p.x + ct * p.y;
+ p1.z = p.z;
+
+ /* printf("step 1 = %.3f %.3f %.3f\n", p1.x, p1.y, p1.z); */
+
+ /* rotate new point about y axis */
+ p2.x = cp * p1.x + sp * p1.z;
+ p2.y = p1.y;
+ p2.z = cp * p1.z - sp * p1.x;
+
+ /* printf("cp = %.5f, sp = %.5f\n", cp, sp); */
+ /* printf("(1) = %.5f, (2) = %.5f\n", cp * p1.z, sp * p1.x); */
+
+ /* printf("step 2 = %.3f %.3f %.3f\n", p2.x, p2.y, p2.z); */
+
+ return(p2);
+}
+
+
+/* $Log$
+/* Revision 1.1 1998/04/08 23:21:12 curt
+/* Adopted Gnu automake/autoconf system.
+/*
+ * Revision 1.5 1998/01/27 00:48:00 curt
+ * Incorporated Paul Bleisch's <bleisch@chromatic.com> new debug message
+ * system and commandline/config file processing code.
+ *
+ * Revision 1.4 1998/01/19 19:27:12 curt
+ * Merged in make system changes from Bob Kuehne <rpk@sgi.com>
+ * This should simplify things tremendously.
+ *
+ * Revision 1.3 1997/12/15 23:54:54 curt
+ * Add xgl wrappers for debugging.
+ * Generate terrain normals on the fly.
+ *
+ * Revision 1.2 1997/07/31 22:52:27 curt
+ * Working on redoing internal coordinate systems & scenery transformations.
+ *
+ * Revision 1.1 1997/07/07 21:02:36 curt
+ * Initial revision.
+ * */
--- /dev/null
+/**************************************************************************
+ * polar.h -- routines to deal with polar math and transformations
+ *
+ * Written by Curtis Olson, started June 1997.
+ *
+ * Copyright (C) 1997 Curtis L. Olson - curt@infoplane.com
+ *
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+ *
+ * $Id$
+ * (Log is kept at end of this file)
+ **************************************************************************/
+
+
+#ifndef _POLAR_H
+#define _POLAR_H
+
+
+#include <Include/fg_types.h>
+
+
+/* Convert a polar coordinate to a cartesian coordinate. Lon and Lat
+ * must be specified in radians. The FG convention is for distances
+ * to be specified in meters */
+struct fgCartesianPoint fgPolarToCart(double lon, double lat, double radius);
+
+
+/* Precalculate as much as possible so we can do a batch of transforms
+ * through the same angles, will rotates a cartesian point about the
+ * center of the earth by Theta (longitude axis) and Phi (latitude
+ * axis) */
+
+/* Here are the unoptimized transformation equations
+
+ x' = cos(Phi) * cos(Theta) * x + cos(Phi) * sin(Theta) * y +
+ sin(Phi) * z
+ y' = -sin(Theta) * x + cos(Theta) * y
+ z' = -sin(Phi) * sin(Theta) * y - sin(Phi) * cos(Theta) * x +
+ cos(Phi) * z;
+
+ */
+void fgRotateBatchInit(double Theta, double Phi);
+
+
+/* Rotates a cartesian point about the center of the earth by Theta
+ * (longitude axis) and Phi (latitude axis) */
+struct fgCartesianPoint fgRotateCartesianPoint(struct fgCartesianPoint p);
+
+
+#endif /* _POLAR_H */
+
+
+/* $Log$
+/* Revision 1.1 1998/04/08 23:21:13 curt
+/* Adopted Gnu automake/autoconf system.
+/*
+ * Revision 1.7 1998/01/27 00:48:00 curt
+ * Incorporated Paul Bleisch's <bleisch@chromatic.com> new debug message
+ * system and commandline/config file processing code.
+ *
+ * Revision 1.6 1998/01/22 02:59:39 curt
+ * Changed #ifdef FILE_H to #ifdef _FILE_H
+ *
+ * Revision 1.5 1998/01/19 19:27:13 curt
+ * Merged in make system changes from Bob Kuehne <rpk@sgi.com>
+ * This should simplify things tremendously.
+ *
+ * Revision 1.4 1997/12/15 23:54:55 curt
+ * Add xgl wrappers for debugging.
+ * Generate terrain normals on the fly.
+ *
+ * Revision 1.3 1997/07/31 22:52:28 curt
+ * Working on redoing internal coordinate systems & scenery transformations.
+ *
+ * Revision 1.2 1997/07/23 21:52:21 curt
+ * Put comments around the text after an #endif for increased portability.
+ *
+ * Revision 1.1 1997/07/07 21:02:37 curt
+ * Initial revision.
+ *
+ */
#include <Include/fg_constants.h>
#include <Include/fg_types.h>
-#include <Math/fg_geodesy.h>
-#include <Math/mat3.h>
-#include <Math/polar.h>
-#include <Scenery/bucketutils.h>
+#include <Scenery/Bucket/bucketutils.h>
+#include "fg_geodesy.h"
+#include "mat3.h"
+#include "polar.h"
int nodecount, tricount;
double xmin, xmax, ymin, ymax;
/* $Log$
-/* Revision 1.6 1998/03/03 15:36:13 curt
-/* Tweaks for compiling with g++
+/* Revision 1.7 1998/04/08 23:21:13 curt
+/* Adopted Gnu automake/autoconf system.
/*
+ * Revision 1.6 1998/03/03 15:36:13 curt
+ * Tweaks for compiling with g++
+ *
* Revision 1.5 1998/03/03 03:37:04 curt
* Cumulative tweaks.
*
+++ /dev/null
-#---------------------------------------------------------------------------
-# Toplevel FGTools Makefile
-#
-# Written by Curtis Olson, started October 1997.
-#
-# Copyright (C) 1997 Curtis L. Olson - curt@infoplane.com
-#
-# This program is free software; you can redistribute it and/or modify
-# it under the terms of the GNU General Public License as published by
-# the Free Software Foundation; either version 2 of the License, or
-# (at your option) any later version.
-#
-# This program is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-# GNU General Public License for more details.
-#
-# You should have received a copy of the GNU General Public License
-# along with this program; if not, write to the Free Software
-# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
-#
-# $Id$
-# (Log is kept at end of this file)
-#---------------------------------------------------------------------------
-
-
-include $(FG_ROOT_SRC)/commondefs
-
-
-LIBDIRS = DEM gpc2.01
-SUBDIRS = Areas AssemTris Dem2node DemRaw2Ascii FixNode FixObj \
- SplitTris Stripe_u Tri2obj Triangle
-ORDEREDDIRS = $(LIBDIRS) $(SUBDIRS)
-
-
-all:
- for dir in $(ORDEREDDIRS); do \
- ( cd $$dir; $(MAKE) ) ; \
- done
-
-depend:
- for dir in $(ORDEREDDIRS); do \
- ( echo "Making depend in $$dir"; \
- cd $$dir; $(CC) $(CFLAGS) -M *.c > depend ) ; \
- done
-
-Makefile-os2:
- cat Makefile | perl mkmfos2.pl > Makefile.os2; \
- for dir in $(ORDEREDDIRS); do \
- ( echo "Making Makefile.os2 in $$dir"; \
- cat $$dir/Makefile | perl mkmfos2.pl > $$dir/Makefile.os2; \
- cat $$dir/depend | perl mkmfos2.pl > $$dir/depend.os2) ; \
- done
-
-clean:
- -rm -f *.os2 *~
- for dir in $(ORDEREDDIRS); do \
- (cd $$dir; $(MAKE) clean) ; \
- done
-
-
-source-tar: clean
- (cd ..; \
- tar cvzf demtools-$(FG_VERSION).tar.gz Tools/Makefile Tools/README \
- Tools/Todo Tools/make.inc Tools/process-dem.pl Tools/AssemTris \
- Tools/DEM Tools/gpc2.01 Tools/Dem2node Tools/DemRaw2Ascii \
- Tools/FixNode Tools/FixObj Tools/SplitTris Tools/Stripe_u \
- Tools/Tri2obj Tools/Triangle)
-
-source-zip: clean
- (cd ..; \
- zip -r demtools-$(FG_VERSION).zip Tools/Makefile Tools/README \
- Tools/Todo Tools/make.inc Tools/process-dem.pl Tools/AssemTris \
- Tools/DEM Tools/gpc2.01 Tools/Dem2node Tools/DemRaw2Ascii \
- Tools/FixNode Tools/FixObj Tools/SplitTris Tools/Stripe_u \
- Tools/Tri2obj Tools/Triangle)
-
-bin-tar: all
- echo "need to fix this"
-# cp GLUT/fg0 GLUT/runfg ..
-# (cd ../..; \
-# tar cvzf bin-$(FG_VERSION).tar.gz FlightGear/fgtop FlightGear/fg0 \
-# FlightGear/runfg FlightGear/COPYING FlightGear/Docs FlightGear/Thanks)
-
-bin-zip:
- echo "need to fix this"
-# cp GLUT/fg0.exe GLUT/runfg.bat GLUT/cygwin.dll ..
-# (cd ../..; \
-# zip -r bin-$(FG_VERSION).zip FlightGear/fgtop FlightGear/fg0.exe \
-# FlightGear/runfg.bat FlightGear/cygwin.dll FlightGear/COPYING \
-# FlightGear/Docs FlightGear/Thanks)
-
-
-#---------------------------------------------------------------------------
-# $Log$
-# Revision 1.14 1998/04/06 21:09:37 curt
-# Additional win32 support.
-# Fixed a bad bug in dem file parsing that was causing the output to be
-# flipped about x = y.
-#
-# Revision 1.13 1998/03/19 02:52:51 curt
-# Updated to reflect some minor tool reorganization and the creation of class
-# to handle DEM processing needs.
-#
-# Revision 1.12 1998/03/19 01:48:34 curt
-# Added gpc-2.01 (generic polygon clipping library)
-#
-# Revision 1.11 1998/03/03 21:54:43 curt
-# Changes to process 30 arcsec binary DEM files.
-#
-# Revision 1.10 1998/03/03 15:36:11 curt
-# Tweaks for compiling with g++
-#
-# Revision 1.9 1998/03/03 01:21:17 curt
-# Added DemRaw2Ascii
-#
-# Revision 1.8 1998/01/31 00:41:19 curt
-# Made a few changes converting floats to doubles.
-#
-# Revision 1.7 1998/01/27 18:36:53 curt
-# Lots of updates to get back in sync with changes made over in .../Src/
-#
-# Revision 1.6 1998/01/21 02:55:42 curt
-# Incorporated new make system from Bob Kuehne <rpk@sgi.com>.
-#
-# Revision 1.5 1998/01/14 15:55:34 curt
-# Finished splittris, started assemtris.
-#
-# Revision 1.4 1997/12/10 01:18:25 curt
-# Initial revision.
-#
-# Revision 1.3 1997/11/27 00:18:26 curt
-# Added FixNode
-#
-# Revision 1.2 1997/11/14 00:31:06 curt
-# Abandon Tri2terrain ... replace with Tri2obj so we can use an existing
-# tri-stripper.
-#
-# Revision 1.1 1997/10/20 19:52:18 curt
-# Initial revision.
-#
--- /dev/null
+EXTRA_DIST = process-dem.pl
+
+SUBDIRS = \
+ AssemTris \
+ DEM \
+ Dem2node \
+ FixNode \
+ FixObj \
+ SplitTris \
+ Stripe_u \
+ Tri2obj \
+ Triangle
+
+bin_SCRIPTS = process-dem.pl
--- /dev/null
+# Makefile.in generated automatically by automake 1.2h from Makefile.am
+
+# Copyright (C) 1994, 1995, 1996, 1997, 1998 Free Software Foundation, Inc.
+# This Makefile.in is free software; the Free Software Foundation
+# gives unlimited permission to copy and/or distribute it,
+# with or without modifications, as long as this notice is preserved.
+
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY, to the extent permitted by law; without
+# even the implied warranty of MERCHANTABILITY or FITNESS FOR A
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+
+
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+
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+ FixNode \
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+ SplitTris \
+ Stripe_u \
+ Tri2obj \
+ Triangle
+
+bin_SCRIPTS = process-dem.pl
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+CONFIG_HEADER = ../Simulator/Include/config.h
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+
+# This directory's subdirectories are mostly independent; you can cd
+# into them and run `make' without going through this Makefile.
+# To change the values of `make' variables: instead of editing Makefiles,
+# (1) if the variable is set in `config.status', edit `config.status'
+# (which will cause the Makefiles to be regenerated when you run `make');
+# (2) otherwise, pass the desired values on the `make' command line.
+
+@SET_MAKE@
+
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+
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+ -rm -f config.cache config.log stamp-h stamp-h[0-9]*
+ -test -z "$(CONFIG_CLEAN_FILES)" || rm -f $(CONFIG_CLEAN_FILES)
+
+maintainer-clean-generic:
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+mostlyclean-am: mostlyclean-tags mostlyclean-generic
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+clean-am: clean-tags clean-generic mostlyclean-am
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+clean: clean-recursive clean-am
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+distclean: distclean-recursive distclean-am
+ -rm -f config.status
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+
+maintainer-clean: maintainer-clean-recursive maintainer-clean-am
+ @echo "This command is intended for maintainers to use;"
+ @echo "it deletes files that may require special tools to rebuild."
+
+.PHONY: uninstall-binSCRIPTS install-binSCRIPTS install-data-recursive \
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+# Otherwise a system limit (for SysV at least) may be exceeded.
+.NOEXPORT:
+++ /dev/null
-# Hey Emacs, this is a Makefile. -*- Mode: Makefile -*-
-#
-# Common FGTools Makefile section
-#
-# Written by Curtis Olson, started October 1997.
-#
-# Copyright (C) 1997 Curtis L. Olson - curt@infoplane.com
-#
-# This program is free software; you can redistribute it and/or modify
-# it under the terms of the GNU General Public License as published by
-# the Free Software Foundation; either version 2 of the License, or
-# (at your option) any later version.
-#
-# This program is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-# GNU General Public License for more details.
-#
-# You should have received a copy of the GNU General Public License
-# along with this program; if not, write to the Free Software
-# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
-#
-# $Id$
-# (Log is kept at end of this file)
-#---------------------------------------------------------------------------
-
-
-VERSION = 0.02
-
-#---------------------------------------------------------------------------
-# Choose your weapons
-#---------------------------------------------------------------------------
-
-CC = gcc
-FLEX = flex -f -L
-BISON = bison -v --no-lines
-AR = ar
-RANLIB = ranlib
-
-
-#---------------------------------------------------------------------------
-# Global Compile Options
-#
-# You may set FG_CFLAGS to include any of the following options depending on
-# your environment:
-#
-# -g - Compile with debugging symbols
-#
-# -Wall - Enable full compiler warnings
-#
-# -O2 - Enable compiler optimization
-#
-#---------------------------------------------------------------------------
-
-GLOBAL_CFLAGS = -g -Wall -DVERSION=\"$(VERSION)\"
-
-
-#---------------------------------------------------------------------------
-# Platform specific compile options, these should be set with FG_CFLAGS
-# below. These have been predefined for the supported platforms below.
-#
-# -DNO_PRINTF - Disable all printf()'s. Works by replacing the printf
-# fuction with an empty function.
-#
-# -DUSE_ITIMER - Use setitimer(), getitimer(), and signal() to mimic
-# a real time system and call the flight model routines
-# at a regular interval, rather than between screen updates
-# which can be highly variable. This can make the flight
-# model calculations much smoother.
-#
-# -DUSE_FTIME - Use ftime() to get an accurate current time instead of
-# gettimeofday()
-#
-# -DUSE_RAND - Use rand() instead of random()
-#
-#---------------------------------------------------------------------------
-
-
-#---------------------------------------------------------------------------
-# Uncomment one of the following sections depending on your system
-#
-# You may set FG_GRAPHICS to include any of the following options depending
-# on your environment:
-#---------------------------------------------------------------------------
-
-#---------------------------------------------------------------------------
-# SGI IRIX with the GLUT toolkit
-# (Surprisingly, this also works on our SunOS 4.x machine with the
-# way we have Mesa & Glut installed.)
-#
-# INTERFACE_FLAGS = -DGLUT
-# INTERFACE_LIBS = -lglut
-# INTERFACE_FILES = GLUTmain.c GLUTkey.c
-# GRAPHICS_LIBS = -lGLU -lGL -lXmu -lX11
-# FG_CFLAGS = $(GLOBAL_CFLAGS)
-#---------------------------------------------------------------------------
-
-#---------------------------------------------------------------------------
-# Linux/Mesa with the GLUT toolkit
-#
-INTERFACE_FLAGS = -DGLUT
-INTERFACE_LIBS = -lglut
-INTERFACE_FILES = GLUTmain.c GLUTkey.c
-MESA_LIBS = -L/usr/lib/mesa -lMesatk -lMesaaux -lMesaGLU -lMesaGL
-X11_LIBS = -L/usr/X11R6/lib -lXext -lXmu -lXi -lX11
-GRAPHICS_LIBS = $(MESA_LIBS) $(X11_LIBS)
-FG_CFLAGS = $(GLOBAL_CFLAGS)
-#---------------------------------------------------------------------------
-
-#---------------------------------------------------------------------------
-# Cygnus Win32 (gcc based) with a static version of the GLUT toolkit
-#
-# INTERFACE_FLAGS = -DGLUT
-# INTERFACE_LIBS = ../Win32/libglut.a
-# INTERFACE_FILES = GLUTmain.c GLUTkey.c
-# GRAPHICS_LIBS = -lglu32 -lopengl32 -luser32 -lgdi32
-# FG_CFLAGS = $(GLOBAL_CFLAGS) -DWIN32 -DUSE_RAND
-#---------------------------------------------------------------------------
-
-
-#---------------------------------------------------------------------------
-# $Log$
-# Revision 1.2 1997/12/10 01:18:26 curt
-# Initial revision.
-#
-# Revision 1.1 1997/10/20 19:52:18 curt
-# Initial revision.
-#
$| = 1; # flush buffers after every write
-$do_demfit = 1;
+$do_dem2node = 1;
$do_triangle_1 = 1;
$do_fixnode = 1;
$do_splittris = 1;
}
- if ( $do_demfit ) {
- demfit() ;
+ if ( $do_dem2node ) {
+ dem2node() ;
} else {
$subdir = "../Scenery/w100n040/w093n045";
print "WARNING: Hardcoding subdir = $subdir\n";
# splits dem file into 64 file.node's which contain the
# irregularly fitted vertices
-sub demfit {
+sub dem2node {
if ( $dem_file =~ m/.gz$/ ) {
$command = "gzip -dc $dem_file | Dem2node/dem2node $ENV{FG_ROOT} - $error";
} else {
#---------------------------------------------------------------------------
# $Log$
+# Revision 1.15 1998/04/08 23:24:07 curt
+# Adopted Gnu automake/autoconf system.
+#
# Revision 1.14 1998/04/06 21:09:38 curt
# Additional win32 support.
# Fixed a bad bug in dem file parsing that was causing the output to be
--- /dev/null
+/* Copyright 1988, Brown Computer Graphics Group. All Rights Reserved. */
+
+/* --------------------------------------------------------------------------
+ * This file contains routines that operate on matrices and vectors, or
+ * vectors and vectors.
+ * -------------------------------------------------------------------------*/
+
+/* #include "sphigslocal.h" */
+
+/* -------------------------- Static Routines ---------------------------- */
+
+/* ------------------------- Internal Routines --------------------------- */
+
+/* -------------------------- Public Routines ---------------------------- */
+
+/*
+ * Multiplies a vector by a matrix, setting the result vector.
+ * It assumes all homogeneous coordinates are 1.
+ * The two vectors involved may be the same.
+ */
+
+#include <Math/mat3.h>
+
+#ifndef TRUE
+# define TRUE 1
+#endif
+
+#ifndef FALSE
+# define FALSE 0
+#endif
+
+
+void
+MAT3mult_vec(double *result_vec, register double *vec, register double (*mat)[4])
+{
+ MAT3vec tempvec;
+ register double *temp = tempvec;
+
+ temp[0] = vec[0] * mat[0][0] + vec[1] * mat[1][0] +
+ vec[2] * mat[2][0] + mat[3][0];
+ temp[1] = vec[0] * mat[0][1] + vec[1] * mat[1][1] +
+ vec[2] * mat[2][1] + mat[3][1];
+ temp[2] = vec[0] * mat[0][2] + vec[1] * mat[1][2] +
+ vec[2] * mat[2][2] + mat[3][2];
+
+ MAT3_COPY_VEC(result_vec, temp);
+}
+
+/*
+ * Multiplies a vector of size 4 by a matrix, setting the result vector.
+ * The fourth element of the vector is the homogeneous coordinate, which
+ * may or may not be 1. If the "normalize" parameter is TRUE, then the
+ * result vector will be normalized so that the homogeneous coordinate is 1.
+ * The two vectors involved may be the same.
+ * This returns zero if the vector was to be normalized, but couldn't be.
+ */
+
+int
+MAT3mult_hvec(double *result_vec, register double *vec, register double (*mat)[4], int normalize)
+{
+ MAT3hvec tempvec;
+ double norm_fac;
+ register double *temp = tempvec;
+ register int ret = TRUE;
+
+ temp[0] = vec[0] * mat[0][0] + vec[1] * mat[1][0] +
+ vec[2] * mat[2][0] + vec[3] * mat[3][0];
+ temp[1] = vec[0] * mat[0][1] + vec[1] * mat[1][1] +
+ vec[2] * mat[2][1] + vec[3] * mat[3][1];
+ temp[2] = vec[0] * mat[0][2] + vec[1] * mat[1][2] +
+ vec[2] * mat[2][2] + vec[3] * mat[3][2];
+ temp[3] = vec[0] * mat[0][3] + vec[1] * mat[1][3] +
+ vec[2] * mat[2][3] + vec[3] * mat[3][3];
+
+ /* Normalize if asked for, possible, and necessary */
+ if (normalize) {
+ if (MAT3_IS_ZERO(temp[3])) {
+#ifndef THINK_C
+ fprintf (stderr,
+ "Can't normalize vector: homogeneous coordinate is 0");
+#endif
+ ret = FALSE;
+ }
+ else {
+ norm_fac = 1.0 / temp[3];
+ MAT3_SCALE_VEC(result_vec, temp, norm_fac);
+ result_vec[3] = 1.0;
+ }
+ }
+ else MAT3_COPY_HVEC(result_vec, temp);
+
+ return(ret);
+}
+
+/*
+ * Sets the first vector to be the cross-product of the last two vectors.
+ */
+
+void
+MAT3cross_product(double *result_vec, register double *vec1, register double *vec2)
+{
+ MAT3vec tempvec;
+ register double *temp = tempvec;
+
+ temp[0] = vec1[1] * vec2[2] - vec1[2] * vec2[1];
+ temp[1] = vec1[2] * vec2[0] - vec1[0] * vec2[2];
+ temp[2] = vec1[0] * vec2[1] - vec1[1] * vec2[0];
+
+ MAT3_COPY_VEC(result_vec, temp);
+}
+
+/*
+ * Finds a vector perpendicular to vec and stores it in result_vec.
+ * Method: take any vector (we use <0,1,0>) and subtract the
+ * portion of it pointing in the vec direction. This doesn't
+ * work if vec IS <0,1,0> or is very near it. So if this is
+ * the case, use <0,0,1> instead.
+ * If "is_unit" is TRUE, the given vector is assumed to be unit length.
+ */
+
+#define SELECT .7071 /* selection constant (roughly .5*sqrt(2) */
+
+void
+MAT3perp_vec(double *result_vec, double *vec, int is_unit)
+{
+ MAT3vec norm;
+ double dot;
+
+ MAT3_SET_VEC(result_vec, 0.0, 1.0, 0.0);
+
+ MAT3_COPY_VEC(norm, vec);
+
+ if (! is_unit) MAT3_NORMALIZE_VEC(norm, dot);
+
+ /* See if vector is too close to <0,1,0>. If so, use <0,0,1> */
+ if ((dot = MAT3_DOT_PRODUCT(norm, result_vec)) > SELECT || dot < -SELECT) {
+ result_vec[1] = 0.0;
+ result_vec[2] = 1.0;
+ dot = MAT3_DOT_PRODUCT(norm, result_vec);
+ }
+
+ /* Subtract off non-perpendicular part */
+ result_vec[0] -= dot * norm[0];
+ result_vec[1] -= dot * norm[1];
+ result_vec[2] -= dot * norm[2];
+
+ /* Make result unit length */
+ MAT3_NORMALIZE_VEC(result_vec, dot);
+}
+++ /dev/null
-#---------------------------------------------------------------------------
-# Makefile
-#
-# Written by Curtis Olson, started October 1997.
-#
-# Copyright (C) 1997 Curtis L. Olson - curt@infoplane.com
-#
-# This program is free software; you can redistribute it and/or modify
-# it under the terms of the GNU General Public License as published by
-# the Free Software Foundation; either version 2 of the License, or
-# (at your option) any later version.
-#
-# This program is distributed in the hope that it will be useful,
-# but WITHOUT ANY WARRANTY; without even the implied warranty of
-# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-# GNU General Public License for more details.
-#
-# You should have received a copy of the GNU General Public License
-# along with this program; if not, write to the Free Software
-# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
-#
-# $Id$
-# (Log is kept at end of this file)
-#---------------------------------------------------------------------------
-
-
-TARGET = tri2obj
-
-CFILES = tri2obj.c
-LDLIBS = -lMath -lScenery -lm
-
-
-include $(FG_ROOT_SRC)/commondefs
-
-
-#---------------------------------------------------------------------------
-# Primary Targets
-#---------------------------------------------------------------------------
-
-$(TARGET): $(OBJECTS)
- $(CC) -o $(TARGET) $(OBJECTS) $(LDFLAGS) $(LDLIBS)
-
-
-include $(COMMONRULES)
-
-
-#---------------------------------------------------------------------------
-# $Log$
-# Revision 1.5 1998/01/21 02:55:56 curt
-# Incorporated new make system from Bob Kuehne <rpk@sgi.com>.
-#
-# Revision 1.4 1998/01/17 01:25:39 curt
-# Added support for shared normals.
-#
-# Revision 1.3 1997/12/02 13:13:32 curt
-# Fixed problem with averaged vertex normals.
-#
-# Revision 1.2 1997/11/14 00:29:13 curt
-# Transform scenery coordinates at this point in pipeline when scenery is
-# being translated to .obj format, not when it is being loaded into the end
-# renderer. Precalculate normals for each node as average of the normals
-# of each containing polygon so Garoude shading is now supportable.
-#
-# Revision 1.1 1997/10/29 23:05:14 curt
-# Initial revision.
-#
-# Revision 1.1 1997/10/23 23:12:09 curt
-# Initial revision.
-#
--- /dev/null
+#---------------------------------------------------------------------------
+# Makefile
+#
+# Written by Curtis Olson, started January 1998.
+#
+# Copyright (C) 1998 Curtis L. Olson - curt@me.umn.edu
+#
+# This program is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 2 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program; if not, write to the Free Software
+# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+#
+# $Id$
+# (Log is kept at end of this file)
+#---------------------------------------------------------------------------
+
+
+bin_PROGRAMS = tri2obj
+
+tri2obj_SOURCES = \
+ tri2obj.c tri2obj.h \
+ MAT3vec.c \
+ fg_geodesy.c fg_geodesy.h \
+ mat3.h \
+ polar.c polar.h
+
+tri2obj_LDADD = \
+ $(top_builddir)/Simulator/Scenery/Bucket/libBucket.la
+
+INCLUDES += -I../../Simulator
+
+
+#---------------------------------------------------------------------------
+# $Log$
+# Revision 1.1 1998/04/08 23:22:13 curt
+# Adopted Gnu automake/autoconf system.
+#
+# Revision 1.2 1998/01/21 02:55:46 curt
+# Incorporated new make system from Bob Kuehne <rpk@sgi.com>.
+#
+# Revision 1.1 1998/01/15 02:45:25 curt
+# Initial revision.
+#
+
--- /dev/null
+# Makefile.in generated automatically by automake 1.2h from Makefile.am
+
+# Copyright (C) 1994, 1995, 1996, 1997, 1998 Free Software Foundation, Inc.
+# This Makefile.in is free software; the Free Software Foundation
+# gives unlimited permission to copy and/or distribute it,
+# with or without modifications, as long as this notice is preserved.
+
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY, to the extent permitted by law; without
+# even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+# PARTICULAR PURPOSE.
+
+#---------------------------------------------------------------------------
+# Makefile
+#
+# Written by Curtis Olson, started January 1998.
+#
+# Copyright (C) 1998 Curtis L. Olson - curt@me.umn.edu
+#
+# This program is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 2 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program; if not, write to the Free Software
+# Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+#
+# $Id$
+# (Log is kept at end of this file)
+#---------------------------------------------------------------------------
+
+
+SHELL = /bin/sh
+
+srcdir = @srcdir@
+top_srcdir = @top_srcdir@
+VPATH = @srcdir@
+prefix = @prefix@
+exec_prefix = @exec_prefix@
+
+bindir = @bindir@
+sbindir = @sbindir@
+libexecdir = @libexecdir@
+datadir = @datadir@
+sysconfdir = @sysconfdir@
+sharedstatedir = @sharedstatedir@
+localstatedir = @localstatedir@
+libdir = @libdir@
+infodir = @infodir@
+mandir = @mandir@
+includedir = @includedir@
+oldincludedir = /usr/include
+
+DISTDIR =
+
+pkgdatadir = $(datadir)/@PACKAGE@
+pkglibdir = $(libdir)/@PACKAGE@
+pkgincludedir = $(includedir)/@PACKAGE@
+
+top_builddir = ../..
+
+ACLOCAL = @ACLOCAL@
+AUTOCONF = @AUTOCONF@
+AUTOMAKE = @AUTOMAKE@
+AUTOHEADER = @AUTOHEADER@
+
+INSTALL = @INSTALL@
+INSTALL_PROGRAM = @INSTALL_PROGRAM@
+INSTALL_DATA = @INSTALL_DATA@
+INSTALL_SCRIPT = @INSTALL_SCRIPT@
+transform = @program_transform_name@
+
+NORMAL_INSTALL = :
+PRE_INSTALL = :
+POST_INSTALL = :
+NORMAL_UNINSTALL = :
+PRE_UNINSTALL = :
+POST_UNINSTALL = :
+host_alias = @host_alias@
+host_triplet = @host@
+CC = @CC@
+CXX = @CXX@
+LD = @LD@
+LIBTOOL = @LIBTOOL@
+LN_S = @LN_S@
+MAINT = @MAINT@
+MAKEINFO = @MAKEINFO@
+NM = @NM@
+PACKAGE = @PACKAGE@
+RANLIB = @RANLIB@
+VERSION = @VERSION@
+
+bin_PROGRAMS = tri2obj
+
+tri2obj_SOURCES = \
+ tri2obj.c tri2obj.h \
+ MAT3vec.c \
+ fg_geodesy.c fg_geodesy.h \
+ mat3.h \
+ polar.c polar.h
+
+tri2obj_LDADD = \
+ $(top_builddir)/Simulator/Scenery/Bucket/libBucket.la
+mkinstalldirs = $(SHELL) $(top_srcdir)/mkinstalldirs
+CONFIG_HEADER = ../../Simulator/Include/config.h
+CONFIG_CLEAN_FILES =
+PROGRAMS = $(bin_PROGRAMS)
+
+
+DEFS = @DEFS@ -I. -I$(srcdir) -I../../Simulator/Include
+CPPFLAGS = @CPPFLAGS@
+LDFLAGS = @LDFLAGS@
+LIBS = @LIBS@
+X_CFLAGS = @X_CFLAGS@
+X_LIBS = @X_LIBS@
+X_EXTRA_LIBS = @X_EXTRA_LIBS@
+X_PRE_LIBS = @X_PRE_LIBS@
+tri2obj_OBJECTS = tri2obj.o MAT3vec.o fg_geodesy.o polar.o
+tri2obj_DEPENDENCIES = \
+$(top_builddir)/Simulator/Scenery/Bucket/libBucket.la
+tri2obj_LDFLAGS =
+CFLAGS = @CFLAGS@
+COMPILE = $(CC) $(DEFS) $(INCLUDES) $(CPPFLAGS) $(CFLAGS)
+LTCOMPILE = $(LIBTOOL) --mode=compile $(CC) $(DEFS) $(INCLUDES) $(CPPFLAGS) $(CFLAGS)
+LINK = $(LIBTOOL) --mode=link $(CC) $(CFLAGS) $(LDFLAGS) -o $@
+DIST_COMMON = Makefile.am Makefile.in
+
+
+DISTFILES = $(DIST_COMMON) $(SOURCES) $(HEADERS) $(TEXINFOS) $(EXTRA_DIST)
+
+TAR = tar
+GZIP = --best
+DEP_FILES = .deps/MAT3vec.P .deps/fg_geodesy.P .deps/polar.P \
+.deps/tri2obj.P
+SOURCES = $(tri2obj_SOURCES)
+OBJECTS = $(tri2obj_OBJECTS)
+
+all: Makefile $(PROGRAMS)
+
+.SUFFIXES:
+.SUFFIXES: .S .c .lo .o .s
+$(srcdir)/Makefile.in: @MAINT@ Makefile.am $(top_srcdir)/configure.in $(ACLOCAL_M4)
+ cd $(top_srcdir) && $(AUTOMAKE) --gnu Tools/Tri2obj/Makefile
+
+Makefile: $(srcdir)/Makefile.in $(top_builddir)/config.status $(BUILT_SOURCES)
+ cd $(top_builddir) \
+ && CONFIG_FILES=$(subdir)/$@ CONFIG_HEADERS= $(SHELL) ./config.status
+
+
+mostlyclean-binPROGRAMS:
+
+clean-binPROGRAMS:
+ -test -z "$(bin_PROGRAMS)" || rm -f $(bin_PROGRAMS)
+
+distclean-binPROGRAMS:
+
+maintainer-clean-binPROGRAMS:
+
+install-binPROGRAMS: $(bin_PROGRAMS)
+ @$(NORMAL_INSTALL)
+ $(mkinstalldirs) $(DESTDIR)$(bindir)
+ @list='$(bin_PROGRAMS)'; for p in $$list; do \
+ if test -f $$p; then \
+ echo " $(LIBTOOL) --mode=install $(INSTALL_PROGRAM) $$p $(DESTDIR)$(bindir)/`echo $$p|sed '$(transform)'`"; \
+ $(LIBTOOL) --mode=install $(INSTALL_PROGRAM) $$p $(DESTDIR)$(bindir)/`echo $$p|sed '$(transform)'`; \
+ else :; fi; \
+ done
+
+uninstall-binPROGRAMS:
+ @$(NORMAL_UNINSTALL)
+ list='$(bin_PROGRAMS)'; for p in $$list; do \
+ rm -f $(DESTDIR)$(bindir)/`echo $$p|sed '$(transform)'`; \
+ done
+
+.s.o:
+ $(COMPILE) -c $<
+
+.S.o:
+ $(COMPILE) -c $<
+
+mostlyclean-compile:
+ -rm -f *.o core *.core
+
+clean-compile:
+
+distclean-compile:
+ -rm -f *.tab.c
+
+maintainer-clean-compile:
+
+.s.lo:
+ $(LIBTOOL) --mode=compile $(COMPILE) -c $<
+
+.S.lo:
+ $(LIBTOOL) --mode=compile $(COMPILE) -c $<
+
+mostlyclean-libtool:
+ -rm -f *.lo
+
+clean-libtool:
+ -rm -rf .libs _libs
+
+distclean-libtool:
+
+maintainer-clean-libtool:
+
+tri2obj: $(tri2obj_OBJECTS) $(tri2obj_DEPENDENCIES)
+ @rm -f tri2obj
+ $(LINK) $(tri2obj_LDFLAGS) $(tri2obj_OBJECTS) $(tri2obj_LDADD) $(LIBS)
+
+tags: TAGS
+
+ID: $(HEADERS) $(SOURCES) $(LISP)
+ here=`pwd` && cd $(srcdir) \
+ && mkid -f$$here/ID $(SOURCES) $(HEADERS) $(LISP)
+
+TAGS: $(HEADERS) $(SOURCES) $(TAGS_DEPENDENCIES) $(LISP)
+ tags=; \
+ here=`pwd`; \
+ list='$(SOURCES) $(HEADERS)'; \
+ unique=`for i in $$list; do echo $$i; done | \
+ awk ' { files[$$0] = 1; } \
+ END { for (i in files) print i; }'`; \
+ test -z "$(ETAGS_ARGS)$$unique$(LISP)$$tags" \
+ || (cd $(srcdir) && etags $(ETAGS_ARGS) $$tags $$unique $(LISP) -o $$here/TAGS)
+
+mostlyclean-tags:
+
+clean-tags:
+
+distclean-tags:
+ -rm -f TAGS ID
+
+maintainer-clean-tags:
+
+distdir = $(top_builddir)/$(PACKAGE)-$(VERSION)/$(subdir)
+
+subdir = Tools/Tri2obj
+
+distdir: $(DISTFILES)
+ here=`cd $(top_builddir) && pwd`; \
+ top_distdir=`cd $(top_distdir) && pwd`; \
+ distdir=`cd $(distdir) && pwd`; \
+ cd $(top_srcdir) \
+ && $(AUTOMAKE) --include-deps --build-dir=$$here --srcdir-name=$(top_srcdir) --output-dir=$$top_distdir --gnu Tools/Tri2obj/Makefile
+ @for file in $(DISTFILES); do \
+ d=$(srcdir); \
+ test -f $(distdir)/$$file \
+ || ln $$d/$$file $(distdir)/$$file 2> /dev/null \
+ || cp -p $$d/$$file $(distdir)/$$file; \
+ done
+
+DEPS_MAGIC := $(shell mkdir .deps > /dev/null 2>&1 || :)
+
+-include $(DEP_FILES)
+
+mostlyclean-depend:
+
+clean-depend:
+
+distclean-depend:
+
+maintainer-clean-depend:
+ -rm -rf .deps
+
+%.o: %.c
+ @echo '$(COMPILE) -c $<'; \
+ $(COMPILE) -Wp,-MD,.deps/$(*F).P -c $<
+
+%.lo: %.c
+ @echo '$(LTCOMPILE) -c $<'; \
+ $(LTCOMPILE) -Wp,-MD,.deps/$(*F).p -c $<
+ @-sed -e 's/^\([^:]*\)\.o:/\1.lo \1.o:/' \
+ < .deps/$(*F).p > .deps/$(*F).P
+ @-rm -f .deps/$(*F).p
+info:
+dvi:
+check: all
+ $(MAKE)
+installcheck:
+install-exec: install-binPROGRAMS
+ @$(NORMAL_INSTALL)
+
+install-data:
+ @$(NORMAL_INSTALL)
+
+install: install-exec install-data all
+ @:
+
+uninstall: uninstall-binPROGRAMS
+
+install-strip:
+ $(MAKE) INSTALL_PROGRAM='$(INSTALL_PROGRAM) -s' INSTALL_SCRIPT='$(INSTALL_PROGRAM)' install
+installdirs:
+ $(mkinstalldirs) $(DATADIR)$(bindir)
+
+
+mostlyclean-generic:
+ -test -z "$(MOSTLYCLEANFILES)" || rm -f $(MOSTLYCLEANFILES)
+
+clean-generic:
+ -test -z "$(CLEANFILES)" || rm -f $(CLEANFILES)
+
+distclean-generic:
+ -rm -f Makefile $(DISTCLEANFILES)
+ -rm -f config.cache config.log stamp-h stamp-h[0-9]*
+ -test -z "$(CONFIG_CLEAN_FILES)" || rm -f $(CONFIG_CLEAN_FILES)
+
+maintainer-clean-generic:
+ -test -z "$(MAINTAINERCLEANFILES)" || rm -f $(MAINTAINERCLEANFILES)
+ -test -z "$(BUILT_SOURCES)" || rm -f $(BUILT_SOURCES)
+mostlyclean: mostlyclean-binPROGRAMS mostlyclean-compile \
+ mostlyclean-libtool mostlyclean-tags mostlyclean-depend \
+ mostlyclean-generic
+
+clean: clean-binPROGRAMS clean-compile clean-libtool clean-tags \
+ clean-depend clean-generic mostlyclean
+
+distclean: distclean-binPROGRAMS distclean-compile distclean-libtool \
+ distclean-tags distclean-depend distclean-generic clean
+ -rm -f config.status
+ -rm -f libtool
+
+maintainer-clean: maintainer-clean-binPROGRAMS maintainer-clean-compile \
+ maintainer-clean-libtool maintainer-clean-tags \
+ maintainer-clean-depend maintainer-clean-generic \
+ distclean
+ @echo "This command is intended for maintainers to use;"
+ @echo "it deletes files that may require special tools to rebuild."
+
+.PHONY: mostlyclean-binPROGRAMS distclean-binPROGRAMS clean-binPROGRAMS \
+maintainer-clean-binPROGRAMS uninstall-binPROGRAMS install-binPROGRAMS \
+mostlyclean-compile distclean-compile clean-compile \
+maintainer-clean-compile mostlyclean-libtool distclean-libtool \
+clean-libtool maintainer-clean-libtool tags mostlyclean-tags \
+distclean-tags clean-tags maintainer-clean-tags distdir \
+mostlyclean-depend distclean-depend clean-depend \
+maintainer-clean-depend info dvi installcheck install-exec install-data \
+install uninstall all installdirs mostlyclean-generic distclean-generic \
+clean-generic maintainer-clean-generic clean mostlyclean distclean \
+maintainer-clean
+
+
+INCLUDES += -I../../Simulator
+
+#---------------------------------------------------------------------------
+# $Log$
+# Revision 1.1 1998/04/08 23:22:14 curt
+# Adopted Gnu automake/autoconf system.
+#
+# Revision 1.2 1998/01/21 02:55:46 curt
+# Incorporated new make system from Bob Kuehne <rpk@sgi.com>.
+#
+# Revision 1.1 1998/01/15 02:45:25 curt
+# Initial revision.
+#
+
+# Tell versions [3.59,3.63) of GNU make to not export all variables.
+# Otherwise a system limit (for SysV at least) may be exceeded.
+.NOEXPORT:
--- /dev/null
+/**************************************************************************
+ * fg_geodesy.c -- routines to convert between geodetic and geocentric
+ * coordinate systems.
+ *
+ * Copied and adapted directly from LaRCsim/ls_geodesy.c
+ *
+ * See below for the complete original LaRCsim comments.
+ *
+ * $Id$
+ * (Log is kept at end of this file)
+ **************************************************************************/
+
+
+#include <math.h>
+
+#include <Include/fg_constants.h>
+
+#include "fg_geodesy.h"
+
+
+/* ONE_SECOND is pi/180/60/60, or about 100 feet at earths' equator */
+#define ONE_SECOND 4.848136811E-6
+
+
+/* fgGeocToGeod(lat_geoc, radius, *lat_geod, *alt, *sea_level_r)
+ * INPUTS:
+ * lat_geoc Geocentric latitude, radians, + = North
+ * radius C.G. radius to earth center, ft
+ *
+ * OUTPUTS:
+ * lat_geod Geodetic latitude, radians, + = North
+ * alt C.G. altitude above mean sea level, ft
+ * sea_level_r radius from earth center to sea level at
+ * local vertical (surface normal) of C.G.
+ */
+
+void fgGeocToGeod( double lat_geoc, double radius, double
+ *lat_geod, double *alt, double *sea_level_r )
+{
+ double t_lat, x_alpha, mu_alpha, delt_mu, r_alpha, l_point, rho_alpha;
+ double sin_mu_a, denom,delt_lambda, lambda_sl, sin_lambda_sl;
+
+ if( ( (FG_PI_2 - lat_geoc) < ONE_SECOND ) /* near North pole */
+ || ( (FG_PI_2 + lat_geoc) < ONE_SECOND ) ) /* near South pole */
+ {
+ *lat_geod = lat_geoc;
+ *sea_level_r = EQUATORIAL_RADIUS_KM*E;
+ *alt = radius - *sea_level_r;
+ } else {
+ t_lat = tan(lat_geoc);
+ x_alpha = E*EQUATORIAL_RADIUS_KM/sqrt(t_lat*t_lat + E*E);
+ mu_alpha = atan2(sqrt(RESQ_KM - x_alpha*x_alpha),E*x_alpha);
+ if (lat_geoc < 0) mu_alpha = - mu_alpha;
+ sin_mu_a = sin(mu_alpha);
+ delt_lambda = mu_alpha - lat_geoc;
+ r_alpha = x_alpha/cos(lat_geoc);
+ l_point = radius - r_alpha;
+ *alt = l_point*cos(delt_lambda);
+ denom = sqrt(1-EPS*EPS*sin_mu_a*sin_mu_a);
+ rho_alpha = EQUATORIAL_RADIUS_KM*(1-EPS)/
+ (denom*denom*denom);
+ delt_mu = atan2(l_point*sin(delt_lambda),rho_alpha + *alt);
+ *lat_geod = mu_alpha - delt_mu;
+ lambda_sl = atan( E*E * tan(*lat_geod) ); /* SL geoc. latitude */
+ sin_lambda_sl = sin( lambda_sl );
+ *sea_level_r =
+ sqrt(RESQ_KM / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl));
+ }
+}
+
+
+/* fgGeodToGeoc( lat_geod, alt, *sl_radius, *lat_geoc )
+ * INPUTS:
+ * lat_geod Geodetic latitude, radians, + = North
+ * alt C.G. altitude above mean sea level, ft
+ *
+ * OUTPUTS:
+ * sl_radius SEA LEVEL radius to earth center, ft (add Altitude to
+ * get true distance from earth center.
+ * lat_geoc Geocentric latitude, radians, + = North
+ *
+ */
+
+void fgGeodToGeoc( double lat_geod, double alt, double *sl_radius,
+ double *lat_geoc )
+{
+ double lambda_sl, sin_lambda_sl, cos_lambda_sl, sin_mu, cos_mu, px, py;
+
+ lambda_sl = atan( E*E * tan(lat_geod) ); /* sea level geocentric latitude */
+ sin_lambda_sl = sin( lambda_sl );
+ cos_lambda_sl = cos( lambda_sl );
+ sin_mu = sin(lat_geod); /* Geodetic (map makers') latitude */
+ cos_mu = cos(lat_geod);
+ *sl_radius =
+ sqrt(RESQ_KM / (1 + ((1/(E*E))-1)*sin_lambda_sl*sin_lambda_sl));
+ py = *sl_radius*sin_lambda_sl + alt*sin_mu;
+ px = *sl_radius*cos_lambda_sl + alt*cos_mu;
+ *lat_geoc = atan2( py, px );
+}
+
+
+/***************************************************************************
+
+ TITLE: ls_geodesy
+
+----------------------------------------------------------------------------
+
+ FUNCTION: Converts geocentric coordinates to geodetic positions
+
+----------------------------------------------------------------------------
+
+ MODULE STATUS: developmental
+
+----------------------------------------------------------------------------
+
+ GENEALOGY: Written as part of LaRCSim project by E. B. Jackson
+
+----------------------------------------------------------------------------
+
+ DESIGNED BY: E. B. Jackson
+
+ CODED BY: E. B. Jackson
+
+ MAINTAINED BY: E. B. Jackson
+
+----------------------------------------------------------------------------
+
+ MODIFICATION HISTORY:
+
+ DATE PURPOSE BY
+
+ 930208 Modified to avoid singularity near polar region. EBJ
+ 930602 Moved backwards calcs here from ls_step. EBJ
+ 931214 Changed erroneous Latitude and Altitude variables to
+ *lat_geod and *alt in routine ls_geoc_to_geod. EBJ
+ 940111 Changed header files from old ls_eom.h style to ls_types,
+ and ls_constants. Also replaced old DATA type with new
+ SCALAR type. EBJ
+
+ CURRENT RCS HEADER:
+
+$Header$
+$Log$
+Revision 1.1 1998/04/08 23:22:14 curt
+Adopted Gnu automake/autoconf system.
+
+Revision 1.4 1998/01/27 00:47:59 curt
+Incorporated Paul Bleisch's <bleisch@chromatic.com> new debug message
+system and commandline/config file processing code.
+
+Revision 1.3 1998/01/19 19:27:12 curt
+Merged in make system changes from Bob Kuehne <rpk@sgi.com>
+This should simplify things tremendously.
+
+Revision 1.2 1997/12/15 23:54:54 curt
+Add xgl wrappers for debugging.
+Generate terrain normals on the fly.
+
+Revision 1.1 1997/07/31 23:13:14 curt
+Initial revision.
+
+Revision 1.1 1997/05/29 00:09:56 curt
+Initial Flight Gear revision.
+
+ * Revision 1.5 1994/01/11 18:47:05 bjax
+ * Changed include files to use types and constants, not ls_eom.h
+ * Also changed DATA type to SCALAR type.
+ *
+ * Revision 1.4 1993/12/14 21:06:47 bjax
+ * Removed global variable references Altitude and Latitude. EBJ
+ *
+ * Revision 1.3 1993/06/02 15:03:40 bjax
+ * Made new subroutine for calculating geodetic to geocentric; changed name
+ * of forward conversion routine from ls_geodesy to ls_geoc_to_geod.
+ *
+
+----------------------------------------------------------------------------
+
+ REFERENCES:
+
+ [ 1] Stevens, Brian L.; and Lewis, Frank L.: "Aircraft
+ Control and Simulation", Wiley and Sons, 1992.
+ ISBN 0-471-61397-5
+
+
+----------------------------------------------------------------------------
+
+ CALLED BY: ls_aux
+
+----------------------------------------------------------------------------
+
+ CALLS TO:
+
+----------------------------------------------------------------------------
+
+ INPUTS:
+ lat_geoc Geocentric latitude, radians, + = North
+ radius C.G. radius to earth center, ft
+
+----------------------------------------------------------------------------
+
+ OUTPUTS:
+ lat_geod Geodetic latitude, radians, + = North
+ alt C.G. altitude above mean sea level, ft
+ sea_level_r radius from earth center to sea level at
+ local vertical (surface normal) of C.G.
+
+--------------------------------------------------------------------------*/
+
+
+/* $Log$
+/* Revision 1.1 1998/04/08 23:22:14 curt
+/* Adopted Gnu automake/autoconf system.
+/*
+ * Revision 1.4 1998/01/27 00:47:59 curt
+ * Incorporated Paul Bleisch's <bleisch@chromatic.com> new debug message
+ * system and commandline/config file processing code.
+ *
+ * Revision 1.3 1998/01/19 19:27:12 curt
+ * Merged in make system changes from Bob Kuehne <rpk@sgi.com>
+ * This should simplify things tremendously.
+ *
+ * Revision 1.2 1997/12/15 23:54:54 curt
+ * Add xgl wrappers for debugging.
+ * Generate terrain normals on the fly.
+ *
+ * Revision 1.1 1997/07/31 23:13:14 curt
+ * Initial revision.
+ *
+ */
--- /dev/null
+/**************************************************************************
+ * fg_geodesy.h -- routines to convert between geodetic and geocentric
+ * coordinate systems.
+ *
+ * Copied and adapted directly from LaRCsim/ls_geodesy.c
+ *
+ * See below for the complete original LaRCsim comments.
+ *
+ * $Id$
+ * (Log is kept at end of this file)
+ **************************************************************************/
+
+
+#ifndef _FG_GEODESY_H
+#define _FG_GEODESY_H
+
+
+/* fgGeocToGeod(lat_geoc, radius, *lat_geod, *alt, *sea_level_r)
+ * INPUTS:
+ * lat_geoc Geocentric latitude, radians, + = North
+ * radius C.G. radius to earth center, ft
+ *
+ * OUTPUTS:
+ * lat_geod Geodetic latitude, radians, + = North
+ * alt C.G. altitude above mean sea level, ft
+ * sea_level_r radius from earth center to sea level at
+ * local vertical (surface normal) of C.G.
+ */
+
+void fgGeocToGeod( double lat_geoc, double radius, double
+ *lat_geod, double *alt, double *sea_level_r );
+
+/* fgGeodToGeoc( lat_geod, alt, *sl_radius, *lat_geoc )
+ * INPUTS:
+ * lat_geod Geodetic latitude, radians, + = North
+ * alt C.G. altitude above mean sea level, ft
+ *
+ * OUTPUTS:
+ * sl_radius SEA LEVEL radius to earth center, ft (add Altitude to
+ * get true distance from earth center.
+ * lat_geoc Geocentric latitude, radians, + = North
+ *
+ */
+
+void fgGeodToGeoc( double lat_geod, double alt, double *sl_radius,
+ double *lat_geoc );
+
+
+
+/***************************************************************************
+
+ TITLE: ls_geodesy
+
+----------------------------------------------------------------------------
+
+ FUNCTION: Converts geocentric coordinates to geodetic positions
+
+----------------------------------------------------------------------------
+
+ MODULE STATUS: developmental
+
+----------------------------------------------------------------------------
+
+ GENEALOGY: Written as part of LaRCSim project by E. B. Jackson
+
+----------------------------------------------------------------------------
+
+ DESIGNED BY: E. B. Jackson
+
+ CODED BY: E. B. Jackson
+
+ MAINTAINED BY: E. B. Jackson
+
+----------------------------------------------------------------------------
+
+ MODIFICATION HISTORY:
+
+ DATE PURPOSE BY
+
+ 930208 Modified to avoid singularity near polar region. EBJ
+ 930602 Moved backwards calcs here from ls_step. EBJ
+ 931214 Changed erroneous Latitude and Altitude variables to
+ *lat_geod and *alt in routine ls_geoc_to_geod. EBJ
+ 940111 Changed header files from old ls_eom.h style to ls_types,
+ and ls_constants. Also replaced old DATA type with new
+ SCALAR type. EBJ
+
+ CURRENT RCS HEADER:
+
+$Header$
+$Log$
+Revision 1.1 1998/04/08 23:22:15 curt
+Adopted Gnu automake/autoconf system.
+
+Revision 1.2 1998/01/22 02:59:38 curt
+Changed #ifdef FILE_H to #ifdef _FILE_H
+
+Revision 1.1 1997/07/31 23:13:14 curt
+Initial revision.
+
+Revision 1.1 1997/05/29 00:09:56 curt
+Initial Flight Gear revision.
+
+ * Revision 1.5 1994/01/11 18:47:05 bjax
+ * Changed include files to use types and constants, not ls_eom.h
+ * Also changed DATA type to SCALAR type.
+ *
+ * Revision 1.4 1993/12/14 21:06:47 bjax
+ * Removed global variable references Altitude and Latitude. EBJ
+ *
+ * Revision 1.3 1993/06/02 15:03:40 bjax
+ * Made new subroutine for calculating geodetic to geocentric; changed name
+ * of forward conversion routine from ls_geodesy to ls_geoc_to_geod.
+ *
+
+----------------------------------------------------------------------------
+
+ REFERENCES:
+
+ [ 1] Stevens, Brian L.; and Lewis, Frank L.: "Aircraft
+ Control and Simulation", Wiley and Sons, 1992.
+ ISBN 0-471-61397-5
+
+
+----------------------------------------------------------------------------
+
+ CALLED BY: ls_aux
+
+----------------------------------------------------------------------------
+
+ CALLS TO:
+
+----------------------------------------------------------------------------
+
+ INPUTS:
+ lat_geoc Geocentric latitude, radians, + = North
+ radius C.G. radius to earth center, ft
+
+----------------------------------------------------------------------------
+
+ OUTPUTS:
+ lat_geod Geodetic latitude, radians, + = North
+ alt C.G. altitude above mean sea level, ft
+ sea_level_r radius from earth center to sea level at
+ local vertical (surface normal) of C.G.
+
+--------------------------------------------------------------------------*/
+
+
+#endif /* _FG_GEODESY_H */
+
+
+/* $Log$
+/* Revision 1.1 1998/04/08 23:22:15 curt
+/* Adopted Gnu automake/autoconf system.
+/*
+ * Revision 1.2 1998/01/22 02:59:38 curt
+ * Changed #ifdef FILE_H to #ifdef _FILE_H
+ *
+ * Revision 1.1 1997/07/31 23:13:14 curt
+ * Initial revision.
+ *
+ */
--- /dev/null
+/* Copyright 1988, Brown Computer Graphics Group. All Rights Reserved. */
+
+/* -------------------------------------------------------------------------
+ Public MAT3 include file
+ ------------------------------------------------------------------------- */
+
+#ifndef MAT3_HAS_BEEN_INCLUDED
+#define MAT3_HAS_BEEN_INCLUDED
+
+/* ----------------------------- Constants ------------------------------ */
+
+/*
+ * Make sure the math library .h file is included, in case it wasn't.
+ */
+
+#ifndef HUGE
+#include <math.h>
+#endif
+#include <stdio.h>
+
+
+#define MAT3_DET0 -1 /* Indicates singular mat */
+#define MAT3_EPSILON 1e-12 /* Close enough to zero */
+#define MAT3_PI 3.141592653589793 /* Pi */
+
+/* ------------------------------ Types --------------------------------- */
+
+typedef double MAT3mat[4][4]; /* 4x4 matrix */
+typedef double MAT3vec[3]; /* Vector */
+typedef double MAT3hvec[4]; /* Vector with homogeneous coord */
+
+/* ------------------------------ Macros -------------------------------- */
+
+/* Tests if a number is within EPSILON of zero */
+#define MAT3_IS_ZERO(N) ((N) < MAT3_EPSILON && (N) > -MAT3_EPSILON)
+
+/* Sets a vector to the three given values */
+#define MAT3_SET_VEC(V,X,Y,Z) ((V)[0]=(X), (V)[1]=(Y), (V)[2]=(Z))
+
+/* Tests a vector for all components close to zero */
+#define MAT3_IS_ZERO_VEC(V) (MAT3_IS_ZERO((V)[0]) && \
+ MAT3_IS_ZERO((V)[1]) && \
+ MAT3_IS_ZERO((V)[2]))
+
+/* Dot product of two vectors */
+#define MAT3_DOT_PRODUCT(V1,V2) \
+ ((V1)[0]*(V2)[0] + (V1)[1]*(V2)[1] + (V1)[2]*(V2)[2])
+
+/* Copy one vector to other */
+#define MAT3_COPY_VEC(TO,FROM) ((TO)[0] = (FROM)[0], \
+ (TO)[1] = (FROM)[1], \
+ (TO)[2] = (FROM)[2])
+
+/* Normalize vector to unit length, using TEMP as temporary variable.
+ * TEMP will be zero if vector has zero length */
+#define MAT3_NORMALIZE_VEC(V,TEMP) \
+ if ((TEMP = sqrt(MAT3_DOT_PRODUCT(V,V))) > MAT3_EPSILON) { \
+ TEMP = 1.0 / TEMP; \
+ MAT3_SCALE_VEC(V,V,TEMP); \
+ } else TEMP = 0.0
+
+/* Scale vector by given factor, storing result vector in RESULT_V */
+#define MAT3_SCALE_VEC(RESULT_V,V,SCALE) \
+ MAT3_SET_VEC(RESULT_V, (V)[0]*(SCALE), (V)[1]*(SCALE), (V)[2]*(SCALE))
+
+/* Adds vectors V1 and V2, storing result in RESULT_V */
+#define MAT3_ADD_VEC(RESULT_V,V1,V2) \
+ MAT3_SET_VEC(RESULT_V, (V1)[0]+(V2)[0], (V1)[1]+(V2)[1], \
+ (V1)[2]+(V2)[2])
+
+/* Subtracts vector V2 from V1, storing result in RESULT_V */
+#define MAT3_SUB_VEC(RESULT_V,V1,V2) \
+ MAT3_SET_VEC(RESULT_V, (V1)[0]-(V2)[0], (V1)[1]-(V2)[1], \
+ (V1)[2]-(V2)[2])
+
+/* Multiplies vectors V1 and V2, storing result in RESULT_V */
+#define MAT3_MULT_VEC(RESULT_V,V1,V2) \
+ MAT3_SET_VEC(RESULT_V, (V1)[0]*(V2)[0], (V1)[1]*(V2)[1], \
+ (V1)[2]*(V2)[2])
+
+/* Sets RESULT_V to the linear combination of V1 and V2, scaled by
+ * SCALE1 and SCALE2, respectively */
+#define MAT3_LINEAR_COMB(RESULT_V,SCALE1,V1,SCALE2,V2) \
+ MAT3_SET_VEC(RESULT_V, (SCALE1)*(V1)[0] + (SCALE2)*(V2)[0], \
+ (SCALE1)*(V1)[1] + (SCALE2)*(V2)[1], \
+ (SCALE1)*(V1)[2] + (SCALE2)*(V2)[2])
+
+/* Several of the vector macros are useful for homogeneous-coord vectors */
+#define MAT3_SET_HVEC(V,X,Y,Z,W) ((V)[0]=(X), (V)[1]=(Y), \
+ (V)[2]=(Z), (V)[3]=(W))
+
+#define MAT3_COPY_HVEC(TO,FROM) ((TO)[0] = (FROM)[0], \
+ (TO)[1] = (FROM)[1], \
+ (TO)[2] = (FROM)[2], \
+ (TO)[3] = (FROM)[3])
+
+#define MAT3_SCALE_HVEC(RESULT_V,V,SCALE) \
+ MAT3_SET_HVEC(RESULT_V, (V)[0]*(SCALE), (V)[1]*(SCALE), \
+ (V)[2]*(SCALE), (V)[3]*(SCALE))
+
+#define MAT3_ADD_HVEC(RESULT_V,V1,V2) \
+ MAT3_SET_HVEC(RESULT_V, (V1)[0]+(V2)[0], (V1)[1]+(V2)[1], \
+ (V1)[2]+(V2)[2], (V1)[3]+(V2)[3])
+
+#define MAT3_SUB_HVEC(RESULT_V,V1,V2) \
+ MAT3_SET_HVEC(RESULT_V, (V1)[0]-(V2)[0], (V1)[1]-(V2)[1], \
+ (V1)[2]-(V2)[2], (V1)[3]-(V2)[3])
+
+#define MAT3_MULT_HVEC(RESULT_V,V1,V2) \
+ MAT3_SET_HVEC(RESULT_V, (V1)[0]*(V2)[0], (V1)[1]*(V2)[1], \
+ (V1)[2]*(V2)[2], (V1)[3]*(V2)[3])
+
+/* ------------------------------ Entries ------------------------------- */
+
+
+/* In MAT3geom.c */
+void MAT3direction_matrix (MAT3mat result_mat, MAT3mat mat);
+int MAT3normal_matrix (MAT3mat result_mat, MAT3mat mat);
+void MAT3rotate (MAT3mat result_mat, MAT3vec axis, double angle_in_radians);
+void MAT3translate (MAT3mat result_mat, MAT3vec trans);
+void MAT3scale (MAT3mat result_mat, MAT3vec scale);
+void MAT3shear(MAT3mat result_mat, double xshear, double yshear);
+
+/* In MAT3mat.c */
+void MAT3identity(MAT3mat);
+void MAT3zero(MAT3mat);
+void MAT3copy (MAT3mat to, MAT3mat from);
+void MAT3mult (MAT3mat result, MAT3mat, MAT3mat);
+void MAT3transpose (MAT3mat result, MAT3mat);
+int MAT3invert (MAT3mat result, MAT3mat);
+void MAT3print (MAT3mat, FILE *fp);
+void MAT3print_formatted (MAT3mat, FILE *fp,
+ char *title, char *head, char *format, char *tail);
+extern int MAT3equal( void );
+extern double MAT3trace( void );
+extern int MAT3power( void );
+extern int MAT3column_reduce( void );
+extern int MAT3kernel_basis( void );
+
+/* In MAT3vec.c */
+void MAT3mult_vec(MAT3vec result_vec, MAT3vec vec, MAT3mat mat);
+int MAT3mult_hvec (MAT3hvec result_vec, MAT3hvec vec, MAT3mat mat, int normalize);
+void MAT3cross_product(MAT3vec result,MAT3vec,MAT3vec);
+void MAT3perp_vec(MAT3vec result_vec, MAT3vec vec, int is_unit);
+
+#endif /* MAT3_HAS_BEEN_INCLUDED */
+
--- /dev/null
+/**************************************************************************
+ * polar.c -- routines to deal with polar math and transformations
+ *
+ * Written by Curtis Olson, started June 1997.
+ *
+ * Copyright (C) 1997 Curtis L. Olson - curt@infoplane.com
+ *
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+ *
+ * $Id$
+ * (Log is kept at end of this file)
+ **************************************************************************/
+
+
+#include <math.h>
+#include <stdio.h>
+
+#include <Math/polar.h>
+#include <Include/fg_constants.h>
+
+
+/* we can save these values between calls for efficiency */
+static double st, ct, sp, cp;
+
+
+/* Convert a polar coordinate to a cartesian coordinate. Lon and Lat
+ * must be specified in radians. The FG convention is for distances
+ * to be specified in meters */
+struct fgCartesianPoint fgPolarToCart(double lon, double lat, double radius) {
+ struct fgCartesianPoint pnew;
+
+ pnew.x = cos(lon) * cos(lat) * radius;
+ pnew.y = sin(lon) * cos(lat) * radius;
+ pnew.z = sin(lat) * radius;
+
+ return(pnew);
+}
+
+
+/* Precalculate as much as possible so we can do a batch of transforms
+ * through the same angles, will rotates a cartesian point about the
+ * center of the earth by Theta (longitude axis) and Phi (latitude
+ * axis) */
+
+/* Here are the unoptimized transformation equations
+
+ x' = cos(Phi) * cos(Theta) * x + cos(Phi) * sin(Theta) * y +
+ sin(Phi) * z
+ y' = -sin(Theta) * x + cos(Theta) * y
+ z' = -sin(Phi) * sin(Theta) * y - sin(Phi) * cos(Theta) * x +
+ cos(Phi) * z;
+
+ */
+void fgRotateBatchInit(double Theta, double Phi) {
+ printf("Theta = %.3f, Phi = %.3f\n", Theta, Phi);
+
+ st = sin(Theta);
+ ct = cos(Theta);
+ sp = sin(-Phi);
+ cp = cos(-Phi);
+}
+
+/* Rotates a cartesian point about the center of the earth by Theta
+ * (longitude axis) and Phi (latitude axis) */
+struct fgCartesianPoint fgRotateCartesianPoint(struct fgCartesianPoint p) {
+ struct fgCartesianPoint p1, p2;
+
+ /* printf("start = %.3f %.3f %.3f\n", p.x, p.y, p.z); */
+
+ /* rotate about the z axis */
+ p1.x = ct * p.x - st * p.y;
+ p1.y = st * p.x + ct * p.y;
+ p1.z = p.z;
+
+ /* printf("step 1 = %.3f %.3f %.3f\n", p1.x, p1.y, p1.z); */
+
+ /* rotate new point about y axis */
+ p2.x = cp * p1.x + sp * p1.z;
+ p2.y = p1.y;
+ p2.z = cp * p1.z - sp * p1.x;
+
+ /* printf("cp = %.5f, sp = %.5f\n", cp, sp); */
+ /* printf("(1) = %.5f, (2) = %.5f\n", cp * p1.z, sp * p1.x); */
+
+ /* printf("step 2 = %.3f %.3f %.3f\n", p2.x, p2.y, p2.z); */
+
+ return(p2);
+}
+
+
+/* $Log$
+/* Revision 1.1 1998/04/08 23:22:16 curt
+/* Adopted Gnu automake/autoconf system.
+/*
+ * Revision 1.5 1998/01/27 00:48:00 curt
+ * Incorporated Paul Bleisch's <bleisch@chromatic.com> new debug message
+ * system and commandline/config file processing code.
+ *
+ * Revision 1.4 1998/01/19 19:27:12 curt
+ * Merged in make system changes from Bob Kuehne <rpk@sgi.com>
+ * This should simplify things tremendously.
+ *
+ * Revision 1.3 1997/12/15 23:54:54 curt
+ * Add xgl wrappers for debugging.
+ * Generate terrain normals on the fly.
+ *
+ * Revision 1.2 1997/07/31 22:52:27 curt
+ * Working on redoing internal coordinate systems & scenery transformations.
+ *
+ * Revision 1.1 1997/07/07 21:02:36 curt
+ * Initial revision.
+ * */
--- /dev/null
+/**************************************************************************
+ * polar.h -- routines to deal with polar math and transformations
+ *
+ * Written by Curtis Olson, started June 1997.
+ *
+ * Copyright (C) 1997 Curtis L. Olson - curt@infoplane.com
+ *
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License as
+ * published by the Free Software Foundation; either version 2 of the
+ * License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
+ *
+ * $Id$
+ * (Log is kept at end of this file)
+ **************************************************************************/
+
+
+#ifndef _POLAR_H
+#define _POLAR_H
+
+
+#include <Include/fg_types.h>
+
+
+/* Convert a polar coordinate to a cartesian coordinate. Lon and Lat
+ * must be specified in radians. The FG convention is for distances
+ * to be specified in meters */
+struct fgCartesianPoint fgPolarToCart(double lon, double lat, double radius);
+
+
+/* Precalculate as much as possible so we can do a batch of transforms
+ * through the same angles, will rotates a cartesian point about the
+ * center of the earth by Theta (longitude axis) and Phi (latitude
+ * axis) */
+
+/* Here are the unoptimized transformation equations
+
+ x' = cos(Phi) * cos(Theta) * x + cos(Phi) * sin(Theta) * y +
+ sin(Phi) * z
+ y' = -sin(Theta) * x + cos(Theta) * y
+ z' = -sin(Phi) * sin(Theta) * y - sin(Phi) * cos(Theta) * x +
+ cos(Phi) * z;
+
+ */
+void fgRotateBatchInit(double Theta, double Phi);
+
+
+/* Rotates a cartesian point about the center of the earth by Theta
+ * (longitude axis) and Phi (latitude axis) */
+struct fgCartesianPoint fgRotateCartesianPoint(struct fgCartesianPoint p);
+
+
+#endif /* _POLAR_H */
+
+
+/* $Log$
+/* Revision 1.1 1998/04/08 23:22:17 curt
+/* Adopted Gnu automake/autoconf system.
+/*
+ * Revision 1.7 1998/01/27 00:48:00 curt
+ * Incorporated Paul Bleisch's <bleisch@chromatic.com> new debug message
+ * system and commandline/config file processing code.
+ *
+ * Revision 1.6 1998/01/22 02:59:39 curt
+ * Changed #ifdef FILE_H to #ifdef _FILE_H
+ *
+ * Revision 1.5 1998/01/19 19:27:13 curt
+ * Merged in make system changes from Bob Kuehne <rpk@sgi.com>
+ * This should simplify things tremendously.
+ *
+ * Revision 1.4 1997/12/15 23:54:55 curt
+ * Add xgl wrappers for debugging.
+ * Generate terrain normals on the fly.
+ *
+ * Revision 1.3 1997/07/31 22:52:28 curt
+ * Working on redoing internal coordinate systems & scenery transformations.
+ *
+ * Revision 1.2 1997/07/23 21:52:21 curt
+ * Put comments around the text after an #endif for increased portability.
+ *
+ * Revision 1.1 1997/07/07 21:02:37 curt
+ * Initial revision.
+ *
+ */
#include <Include/fg_constants.h>
#include <Include/fg_types.h>
-#include <Math/fg_geodesy.h>
-#include <Math/mat3.h>
-#include <Math/polar.h>
-#include <Scenery/bucketutils.h>
+#include <Scenery/Bucket/bucketutils.h>
+
+#include "fg_geodesy.h"
+#include "mat3.h"
+#include "polar.h"
int nodecount, tricount;
/* $Log$
-/* Revision 1.11 1998/03/03 16:01:00 curt
-/* More c++ compile tweaks.
+/* Revision 1.12 1998/04/08 23:22:18 curt
+/* Adopted Gnu automake/autoconf system.
/*
+ * Revision 1.11 1998/03/03 16:01:00 curt
+ * More c++ compile tweaks.
+ *
* Revision 1.10 1998/01/31 00:41:27 curt
* Made a few changes converting floats to doubles.
*
+++ /dev/null
-# makefile for Triangle and Show Me
-#
-# Type "make" to compile Triangle and Show Me.
-#
-# After compiling, type "triangle -h" and "showme -h" to read instructions
-# for using each of these programs.
-#
-# Type "make trilibrary" to compile Triangle as an object file (triangle.o).
-#
-# Type "make distclean" to delete all executable files.
-
-# SRC is the directory in which the C source files are, and BIN is the
-# directory where you want to put the executable programs. By default,
-# both are the current directory.
-
-SRC = ./
-BIN = ./
-
-# CC should be set to the name of your favorite C compiler.
-
-CC = cc
-
-# CSWITCHES is a list of all switches passed to the C compiler. I strongly
-# recommend using the best level of optimization. I also strongly
-# recommend timing each level of optimization to see which is the
-# best. For instance, on my DEC Alpha using DEC's optimizing compiler,
-# the -O2 switch generates a notably faster version of Triangle than the
-# -O3 switch. Go figure.
-#
-# By default, Triangle and Show Me use double precision floating point
-# numbers. If you prefer single precision, use the -DSINGLE switch.
-# Double precision uses more memory, but improves the resolution of
-# the meshes you can generate with Triangle. It also reduces the
-# likelihood of a floating exception due to overflow. Also, it is
-# much faster than single precision on 64-bit architectures like the
-# DEC Alpha. I recommend double precision unless you want to generate
-# a mesh for which you do not have enough memory to use double precision.
-#
-# If yours is not a Unix system, use the -DNO_TIMER switch to eliminate the
-# Unix-specific timer code.
-#
-# If you are modifying Triangle, I recommend using the -DSELF_CHECK switch
-# while you are debugging. Defining the SELF_CHECK symbol causes
-# Triangle to include self-checking code. Triangle will execute more
-# slowly, however, so be sure to remove this switch before compiling a
-# production version.
-#
-# If the size of the Triangle binary is important to you, you may wish to
-# generate a reduced version of Triangle. The -DREDUCED switch gets rid
-# of all features that are primarily of research interest. Specifically,
-# defining the REDUCED symbol eliminates the -i, -F, -s, and -C switches.
-# The -DCDT_ONLY switch gets rid of all meshing algorithms above and beyond
-# constrained Delaunay triangulation. Specifically, defining the CDT_ONLY
-# symbol eliminates the -r, -q, -a, -S, and -s switches. The REDUCED and
-# CDT_ONLY symbols may be particularly attractive when Triangle is called
-# by another program that does not need all of Triangle's features; in
-# this case, these switches should appear as part of "TRILIBDEFS" below.
-#
-# On some systems, you may need to include -I/usr/local/include and/or
-# -L/usr/local/lib in the compiler options to ensure that the X include
-# files and libraries that Show Me needs are found. If you get errors
-# like "Can't find include file X11/Xlib.h", you need the former switch.
-# Try compiling without them first; add them if that fails.
-#
-# An example CSWITCHES line is:
-#
-# CSWITCHES = -O -DNO_TIMER -I/usr/local/include -L/usr/local/lib
-
-CSWITCHES = -O
-
-# TRILIBDEFS is a list of definitions used to compile an object code version
-# of Triangle (triangle.o) to be called by another program. The file
-# "triangle.h" contains detailed information on how to call triangle.o.
-#
-# The -DTRILIBRARY should always be used when compiling Triangle into an
-# object file.
-#
-# An example TRILIBDEFS line is:
-#
-# TRILIBDEFS = -DTRILIBRARY -DREDUCED -DCDT_ONLY
-
-TRILIBDEFS = -DTRILIBRARY
-
-# RM should be set to the name of your favorite rm (file deletion program).
-
-RM = /bin/rm -f
-
-# The action starts here.
-
-all: $(BIN)triangle $(BIN)showme
-
-trilibrary: $(BIN)triangle.o $(BIN)tricall
-
-$(BIN)triangle: $(SRC)triangle.c
- $(CC) $(CSWITCHES) -o $(BIN)triangle $(SRC)triangle.c -lm
-
-$(BIN)tricall: $(BIN)tricall.c $(BIN)triangle.o
- $(CC) $(CSWITCHES) -o $(BIN)tricall $(SRC)tricall.c \
- $(BIN)triangle.o -lm
-
-$(BIN)triangle.o: $(SRC)triangle.c $(SRC)triangle.h
- $(CC) $(CSWITCHES) $(TRILIBDEFS) -c -o $(BIN)triangle.o \
- $(SRC)triangle.c
-
-$(BIN)showme: $(SRC)showme.c
- $(CC) $(CSWITCHES) -o $(BIN)showme $(SRC)showme.c -L/usr/X11R6/lib -lX11
-
-clean: distclean
-
-distclean:
- $(RM) $(BIN)triangle $(BIN)triangle.o $(BIN)showme
--- /dev/null
+# DEFS is a list of definitions used to compile an object code version
+# of Triangle (triangle.o) to be called by another program. The file
+# "triangle.h" contains detailed information on how to call triangle.o.
+#
+# The -DTRILIBRARY should always be used when compiling Triangle into an
+# object file.
+#
+# An example DEFS line is:
+#
+# DEFS = -DTRILIBRARY -DREDUCED -DCDT_ONLY
+
+DEFS +=
+
+bin_PROGRAMS = triangle # showme
+
+triangle_SOURCES = triangle.c triangle.h
+
+# showme_SOURCES = showme.c
--- /dev/null
+# Makefile.in generated automatically by automake 1.2h from Makefile.am
+
+# Copyright (C) 1994, 1995, 1996, 1997, 1998 Free Software Foundation, Inc.
+# This Makefile.in is free software; the Free Software Foundation
+# gives unlimited permission to copy and/or distribute it,
+# with or without modifications, as long as this notice is preserved.
+
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY, to the extent permitted by law; without
+# even the implied warranty of MERCHANTABILITY or FITNESS FOR A
+# PARTICULAR PURPOSE.
+
+# DEFS is a list of definitions used to compile an object code version
+# of Triangle (triangle.o) to be called by another program. The file
+# "triangle.h" contains detailed information on how to call triangle.o.
+#
+# The -DTRILIBRARY should always be used when compiling Triangle into an
+# object file.
+#
+# An example DEFS line is:
+#
+# DEFS = -DTRILIBRARY -DREDUCED -DCDT_ONLY
+
+
+SHELL = /bin/sh
+
+srcdir = @srcdir@
+top_srcdir = @top_srcdir@
+VPATH = @srcdir@
+prefix = @prefix@
+exec_prefix = @exec_prefix@
+
+bindir = @bindir@
+sbindir = @sbindir@
+libexecdir = @libexecdir@
+datadir = @datadir@
+sysconfdir = @sysconfdir@
+sharedstatedir = @sharedstatedir@
+localstatedir = @localstatedir@
+libdir = @libdir@
+infodir = @infodir@
+mandir = @mandir@
+includedir = @includedir@
+oldincludedir = /usr/include
+
+DISTDIR =
+
+pkgdatadir = $(datadir)/@PACKAGE@
+pkglibdir = $(libdir)/@PACKAGE@
+pkgincludedir = $(includedir)/@PACKAGE@
+
+top_builddir = ../..
+
+ACLOCAL = @ACLOCAL@
+AUTOCONF = @AUTOCONF@
+AUTOMAKE = @AUTOMAKE@
+AUTOHEADER = @AUTOHEADER@
+
+INSTALL = @INSTALL@
+INSTALL_PROGRAM = @INSTALL_PROGRAM@
+INSTALL_DATA = @INSTALL_DATA@
+INSTALL_SCRIPT = @INSTALL_SCRIPT@
+transform = @program_transform_name@
+
+NORMAL_INSTALL = :
+PRE_INSTALL = :
+POST_INSTALL = :
+NORMAL_UNINSTALL = :
+PRE_UNINSTALL = :
+POST_UNINSTALL = :
+host_alias = @host_alias@
+host_triplet = @host@
+CC = @CC@
+CXX = @CXX@
+LD = @LD@
+LIBTOOL = @LIBTOOL@
+LN_S = @LN_S@
+MAINT = @MAINT@
+MAKEINFO = @MAKEINFO@
+NM = @NM@
+PACKAGE = @PACKAGE@
+RANLIB = @RANLIB@
+VERSION = @VERSION@
+
+bin_PROGRAMS = triangle # showme
+
+triangle_SOURCES = triangle.c triangle.h
+mkinstalldirs = $(SHELL) $(top_srcdir)/mkinstalldirs
+CONFIG_HEADER = ../../Simulator/Include/config.h
+CONFIG_CLEAN_FILES =
+PROGRAMS = $(bin_PROGRAMS)
+
+
+DEFS = @DEFS@ -I. -I$(srcdir) -I../../Simulator/Include
+CPPFLAGS = @CPPFLAGS@
+LDFLAGS = @LDFLAGS@
+LIBS = @LIBS@
+X_CFLAGS = @X_CFLAGS@
+X_LIBS = @X_LIBS@
+X_EXTRA_LIBS = @X_EXTRA_LIBS@
+X_PRE_LIBS = @X_PRE_LIBS@
+triangle_OBJECTS = triangle.o
+triangle_LDADD = $(LDADD)
+triangle_DEPENDENCIES =
+triangle_LDFLAGS =
+CFLAGS = @CFLAGS@
+COMPILE = $(CC) $(DEFS) $(INCLUDES) $(CPPFLAGS) $(CFLAGS)
+LTCOMPILE = $(LIBTOOL) --mode=compile $(CC) $(DEFS) $(INCLUDES) $(CPPFLAGS) $(CFLAGS)
+LINK = $(LIBTOOL) --mode=link $(CC) $(CFLAGS) $(LDFLAGS) -o $@
+DIST_COMMON = README Makefile.am Makefile.in
+
+
+DISTFILES = $(DIST_COMMON) $(SOURCES) $(HEADERS) $(TEXINFOS) $(EXTRA_DIST)
+
+TAR = tar
+GZIP = --best
+DEP_FILES = .deps/triangle.P
+SOURCES = $(triangle_SOURCES)
+OBJECTS = $(triangle_OBJECTS)
+
+all: Makefile $(PROGRAMS)
+
+.SUFFIXES:
+.SUFFIXES: .S .c .lo .o .s
+$(srcdir)/Makefile.in: @MAINT@ Makefile.am $(top_srcdir)/configure.in $(ACLOCAL_M4)
+ cd $(top_srcdir) && $(AUTOMAKE) --gnu Tools/Triangle/Makefile
+
+Makefile: $(srcdir)/Makefile.in $(top_builddir)/config.status $(BUILT_SOURCES)
+ cd $(top_builddir) \
+ && CONFIG_FILES=$(subdir)/$@ CONFIG_HEADERS= $(SHELL) ./config.status
+
+
+mostlyclean-binPROGRAMS:
+
+clean-binPROGRAMS:
+ -test -z "$(bin_PROGRAMS)" || rm -f $(bin_PROGRAMS)
+
+distclean-binPROGRAMS:
+
+maintainer-clean-binPROGRAMS:
+
+install-binPROGRAMS: $(bin_PROGRAMS)
+ @$(NORMAL_INSTALL)
+ $(mkinstalldirs) $(DESTDIR)$(bindir)
+ @list='$(bin_PROGRAMS)'; for p in $$list; do \
+ if test -f $$p; then \
+ echo " $(LIBTOOL) --mode=install $(INSTALL_PROGRAM) $$p $(DESTDIR)$(bindir)/`echo $$p|sed '$(transform)'`"; \
+ $(LIBTOOL) --mode=install $(INSTALL_PROGRAM) $$p $(DESTDIR)$(bindir)/`echo $$p|sed '$(transform)'`; \
+ else :; fi; \
+ done
+
+uninstall-binPROGRAMS:
+ @$(NORMAL_UNINSTALL)
+ list='$(bin_PROGRAMS)'; for p in $$list; do \
+ rm -f $(DESTDIR)$(bindir)/`echo $$p|sed '$(transform)'`; \
+ done
+
+.s.o:
+ $(COMPILE) -c $<
+
+.S.o:
+ $(COMPILE) -c $<
+
+mostlyclean-compile:
+ -rm -f *.o core *.core
+
+clean-compile:
+
+distclean-compile:
+ -rm -f *.tab.c
+
+maintainer-clean-compile:
+
+.s.lo:
+ $(LIBTOOL) --mode=compile $(COMPILE) -c $<
+
+.S.lo:
+ $(LIBTOOL) --mode=compile $(COMPILE) -c $<
+
+mostlyclean-libtool:
+ -rm -f *.lo
+
+clean-libtool:
+ -rm -rf .libs _libs
+
+distclean-libtool:
+
+maintainer-clean-libtool:
+
+triangle: $(triangle_OBJECTS) $(triangle_DEPENDENCIES)
+ @rm -f triangle
+ $(LINK) $(triangle_LDFLAGS) $(triangle_OBJECTS) $(triangle_LDADD) $(LIBS)
+
+tags: TAGS
+
+ID: $(HEADERS) $(SOURCES) $(LISP)
+ here=`pwd` && cd $(srcdir) \
+ && mkid -f$$here/ID $(SOURCES) $(HEADERS) $(LISP)
+
+TAGS: $(HEADERS) $(SOURCES) $(TAGS_DEPENDENCIES) $(LISP)
+ tags=; \
+ here=`pwd`; \
+ list='$(SOURCES) $(HEADERS)'; \
+ unique=`for i in $$list; do echo $$i; done | \
+ awk ' { files[$$0] = 1; } \
+ END { for (i in files) print i; }'`; \
+ test -z "$(ETAGS_ARGS)$$unique$(LISP)$$tags" \
+ || (cd $(srcdir) && etags $(ETAGS_ARGS) $$tags $$unique $(LISP) -o $$here/TAGS)
+
+mostlyclean-tags:
+
+clean-tags:
+
+distclean-tags:
+ -rm -f TAGS ID
+
+maintainer-clean-tags:
+
+distdir = $(top_builddir)/$(PACKAGE)-$(VERSION)/$(subdir)
+
+subdir = Tools/Triangle
+
+distdir: $(DISTFILES)
+ here=`cd $(top_builddir) && pwd`; \
+ top_distdir=`cd $(top_distdir) && pwd`; \
+ distdir=`cd $(distdir) && pwd`; \
+ cd $(top_srcdir) \
+ && $(AUTOMAKE) --include-deps --build-dir=$$here --srcdir-name=$(top_srcdir) --output-dir=$$top_distdir --gnu Tools/Triangle/Makefile
+ @for file in $(DISTFILES); do \
+ d=$(srcdir); \
+ test -f $(distdir)/$$file \
+ || ln $$d/$$file $(distdir)/$$file 2> /dev/null \
+ || cp -p $$d/$$file $(distdir)/$$file; \
+ done
+
+DEPS_MAGIC := $(shell mkdir .deps > /dev/null 2>&1 || :)
+
+-include $(DEP_FILES)
+
+mostlyclean-depend:
+
+clean-depend:
+
+distclean-depend:
+
+maintainer-clean-depend:
+ -rm -rf .deps
+
+%.o: %.c
+ @echo '$(COMPILE) -c $<'; \
+ $(COMPILE) -Wp,-MD,.deps/$(*F).P -c $<
+
+%.lo: %.c
+ @echo '$(LTCOMPILE) -c $<'; \
+ $(LTCOMPILE) -Wp,-MD,.deps/$(*F).p -c $<
+ @-sed -e 's/^\([^:]*\)\.o:/\1.lo \1.o:/' \
+ < .deps/$(*F).p > .deps/$(*F).P
+ @-rm -f .deps/$(*F).p
+info:
+dvi:
+check: all
+ $(MAKE)
+installcheck:
+install-exec: install-binPROGRAMS
+ @$(NORMAL_INSTALL)
+
+install-data:
+ @$(NORMAL_INSTALL)
+
+install: install-exec install-data all
+ @:
+
+uninstall: uninstall-binPROGRAMS
+
+install-strip:
+ $(MAKE) INSTALL_PROGRAM='$(INSTALL_PROGRAM) -s' INSTALL_SCRIPT='$(INSTALL_PROGRAM)' install
+installdirs:
+ $(mkinstalldirs) $(DATADIR)$(bindir)
+
+
+mostlyclean-generic:
+ -test -z "$(MOSTLYCLEANFILES)" || rm -f $(MOSTLYCLEANFILES)
+
+clean-generic:
+ -test -z "$(CLEANFILES)" || rm -f $(CLEANFILES)
+
+distclean-generic:
+ -rm -f Makefile $(DISTCLEANFILES)
+ -rm -f config.cache config.log stamp-h stamp-h[0-9]*
+ -test -z "$(CONFIG_CLEAN_FILES)" || rm -f $(CONFIG_CLEAN_FILES)
+
+maintainer-clean-generic:
+ -test -z "$(MAINTAINERCLEANFILES)" || rm -f $(MAINTAINERCLEANFILES)
+ -test -z "$(BUILT_SOURCES)" || rm -f $(BUILT_SOURCES)
+mostlyclean: mostlyclean-binPROGRAMS mostlyclean-compile \
+ mostlyclean-libtool mostlyclean-tags mostlyclean-depend \
+ mostlyclean-generic
+
+clean: clean-binPROGRAMS clean-compile clean-libtool clean-tags \
+ clean-depend clean-generic mostlyclean
+
+distclean: distclean-binPROGRAMS distclean-compile distclean-libtool \
+ distclean-tags distclean-depend distclean-generic clean
+ -rm -f config.status
+ -rm -f libtool
+
+maintainer-clean: maintainer-clean-binPROGRAMS maintainer-clean-compile \
+ maintainer-clean-libtool maintainer-clean-tags \
+ maintainer-clean-depend maintainer-clean-generic \
+ distclean
+ @echo "This command is intended for maintainers to use;"
+ @echo "it deletes files that may require special tools to rebuild."
+
+.PHONY: mostlyclean-binPROGRAMS distclean-binPROGRAMS clean-binPROGRAMS \
+maintainer-clean-binPROGRAMS uninstall-binPROGRAMS install-binPROGRAMS \
+mostlyclean-compile distclean-compile clean-compile \
+maintainer-clean-compile mostlyclean-libtool distclean-libtool \
+clean-libtool maintainer-clean-libtool tags mostlyclean-tags \
+distclean-tags clean-tags maintainer-clean-tags distdir \
+mostlyclean-depend distclean-depend clean-depend \
+maintainer-clean-depend info dvi installcheck install-exec install-data \
+install uninstall all installdirs mostlyclean-generic distclean-generic \
+clean-generic maintainer-clean-generic clean mostlyclean distclean \
+maintainer-clean
+
+
+DEFS +=
+
+# showme_SOURCES = showme.c
+
+# Tell versions [3.59,3.63) of GNU make to not export all variables.
+# Otherwise a system limit (for SysV at least) may be exceeded.
+.NOEXPORT:
+++ /dev/null
-showme.o: showme.c /usr/include/stdio.h /usr/include/features.h \
- /usr/include/sys/cdefs.h /usr/include/libio.h \
- /usr/include/_G_config.h /usr/include/string.h \
- /usr/lib/gcc-lib/i486-linux/2.7.2.1/include/stddef.h \
- /usr/include/X11/Xlib.h /usr/include/sys/types.h \
- /usr/include/linux/types.h /usr/include/linux/posix_types.h \
- /usr/include/asm/posix_types.h /usr/include/asm/types.h \
- /usr/include/sys/bitypes.h /usr/include/X11/X.h \
- /usr/include/X11/Xfuncproto.h /usr/include/X11/Xosdefs.h \
- /usr/include/X11/Xutil.h /usr/include/X11/Xatom.h
-triangle.o: triangle.c /usr/include/stdio.h /usr/include/features.h \
- /usr/include/sys/cdefs.h /usr/include/libio.h \
- /usr/include/_G_config.h /usr/include/string.h \
- /usr/lib/gcc-lib/i486-linux/2.7.2.1/include/stddef.h \
- /usr/include/math.h /usr/include/huge_val.h /usr/include/endian.h \
- /usr/include/bytesex.h /usr/include/nan.h \
- /usr/lib/gcc-lib/i486-linux/2.7.2.1/include/float.h \
- /usr/include/values.h /usr/include/ieee754.h \
- /usr/include/i386/ieeefp.h /usr/include/ieee854.h \
- /usr/include/sys/time.h /usr/include/linux/types.h \
- /usr/include/linux/posix_types.h /usr/include/asm/posix_types.h \
- /usr/include/asm/types.h /usr/include/linux/time.h \
- /usr/include/time.h /usr/include/sys/types.h \
- /usr/include/sys/bitypes.h
-tricall.o: tricall.c /usr/include/stdio.h /usr/include/features.h \
- /usr/include/sys/cdefs.h /usr/include/libio.h \
- /usr/include/_G_config.h triangle.h
--- /dev/null
+Triangle
+A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.
+Version 1.3
+
+Copyright 1996 Jonathan Richard Shewchuk (bugs/comments to jrs@cs.cmu.edu)
+School of Computer Science / Carnegie Mellon University
+5000 Forbes Avenue / Pittsburgh, Pennsylvania 15213-3891
+Created as part of the Archimedes project (tools for parallel FEM).
+Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.
+There is no warranty whatsoever. Use at your own risk.
+This executable is compiled for double precision arithmetic.
+
+
+Triangle generates exact Delaunay triangulations, constrained Delaunay
+triangulations, and quality conforming Delaunay triangulations. The latter
+can be generated with no small angles, and are thus suitable for finite
+element analysis. If no command line switches are specified, your .node
+input file will be read, and the Delaunay triangulation will be returned in
+.node and .ele output files. The command syntax is:
+
+triangle [-prq__a__AcevngBPNEIOXzo_YS__iFlsCQVh] input_file
+
+Underscores indicate that numbers may optionally follow certain switches;
+do not leave any space between a switch and its numeric parameter.
+input_file must be a file with extension .node, or extension .poly if the
+-p switch is used. If -r is used, you must supply .node and .ele files,
+and possibly a .poly file and .area file as well. The formats of these
+files are described below.
+
+Command Line Switches:
+
+ -p Reads a Planar Straight Line Graph (.poly file), which can specify
+ points, segments, holes, and regional attributes and area
+ constraints. Will generate a constrained Delaunay triangulation
+ fitting the input; or, if -s, -q, or -a is used, a conforming
+ Delaunay triangulation. If -p is not used, Triangle reads a .node
+ file by default.
+ -r Refines a previously generated mesh. The mesh is read from a .node
+ file and an .ele file. If -p is also used, a .poly file is read
+ and used to constrain edges in the mesh. Further details on
+ refinement are given below.
+ -q Quality mesh generation by Jim Ruppert's Delaunay refinement
+ algorithm. Adds points to the mesh to ensure that no angles
+ smaller than 20 degrees occur. An alternative minimum angle may be
+ specified after the `q'. If the minimum angle is 20.7 degrees or
+ smaller, the triangulation algorithm is theoretically guaranteed to
+ terminate (assuming infinite precision arithmetic - Triangle may
+ fail to terminate if you run out of precision). In practice, the
+ algorithm often succeeds for minimum angles up to 33.8 degrees.
+ For highly refined meshes, however, it may be necessary to reduce
+ the minimum angle to well below 20 to avoid problems associated
+ with insufficient floating-point precision. The specified angle
+ may include a decimal point.
+ -a Imposes a maximum triangle area. If a number follows the `a', no
+ triangle will be generated whose area is larger than that number.
+ If no number is specified, an .area file (if -r is used) or .poly
+ file (if -r is not used) specifies a number of maximum area
+ constraints. An .area file contains a separate area constraint for
+ each triangle, and is useful for refining a finite element mesh
+ based on a posteriori error estimates. A .poly file can optionally
+ contain an area constraint for each segment-bounded region, thereby
+ enforcing triangle densities in a first triangulation. You can
+ impose both a fixed area constraint and a varying area constraint
+ by invoking the -a switch twice, once with and once without a
+ number following. Each area specified may include a decimal point.
+ -A Assigns an additional attribute to each triangle that identifies
+ what segment-bounded region each triangle belongs to. Attributes
+ are assigned to regions by the .poly file. If a region is not
+ explicitly marked by the .poly file, triangles in that region are
+ assigned an attribute of zero. The -A switch has an effect only
+ when the -p switch is used and the -r switch is not.
+ -c Creates segments on the convex hull of the triangulation. If you
+ are triangulating a point set, this switch causes a .poly file to
+ be written, containing all edges in the convex hull. (By default,
+ a .poly file is written only if a .poly file is read.) If you are
+ triangulating a PSLG, this switch specifies that the interior of
+ the convex hull of the PSLG should be triangulated. If you do not
+ use this switch when triangulating a PSLG, it is assumed that you
+ have identified the region to be triangulated by surrounding it
+ with segments of the input PSLG. Beware: if you are not careful,
+ this switch can cause the introduction of an extremely thin angle
+ between a PSLG segment and a convex hull segment, which can cause
+ overrefinement or failure if Triangle runs out of precision. If
+ you are refining a mesh, the -c switch works differently; it
+ generates the set of boundary edges of the mesh, rather than the
+ convex hull.
+ -e Outputs (to an .edge file) a list of edges of the triangulation.
+ -v Outputs the Voronoi diagram associated with the triangulation.
+ Does not attempt to detect degeneracies.
+ -n Outputs (to a .neigh file) a list of triangles neighboring each
+ triangle.
+ -g Outputs the mesh to an Object File Format (.off) file, suitable for
+ viewing with the Geometry Center's Geomview package.
+ -B No boundary markers in the output .node, .poly, and .edge output
+ files. See the detailed discussion of boundary markers below.
+ -P No output .poly file. Saves disk space, but you lose the ability
+ to impose segment constraints on later refinements of the mesh.
+ -N No output .node file.
+ -E No output .ele file.
+ -I No iteration numbers. Suppresses the output of .node and .poly
+ files, so your input files won't be overwritten. (If your input is
+ a .poly file only, a .node file will be written.) Cannot be used
+ with the -r switch, because that would overwrite your input .ele
+ file. Shouldn't be used with the -s, -q, or -a switch if you are
+ using a .node file for input, because no .node file will be
+ written, so there will be no record of any added points.
+ -O No holes. Ignores the holes in the .poly file.
+ -X No exact arithmetic. Normally, Triangle uses exact floating-point
+ arithmetic for certain tests if it thinks the inexact tests are not
+ accurate enough. Exact arithmetic ensures the robustness of the
+ triangulation algorithms, despite floating-point roundoff error.
+ Disabling exact arithmetic with the -X switch will cause a small
+ improvement in speed and create the possibility (albeit small) that
+ Triangle will fail to produce a valid mesh. Not recommended.
+ -z Numbers all items starting from zero (rather than one). Note that
+ this switch is normally overrided by the value used to number the
+ first point of the input .node or .poly file. However, this switch
+ is useful when calling Triangle from another program.
+ -o2 Generates second-order subparametric elements with six nodes each.
+ -Y No new points on the boundary. This switch is useful when the mesh
+ boundary must be preserved so that it conforms to some adjacent
+ mesh. Be forewarned that you will probably sacrifice some of the
+ quality of the mesh; Triangle will try, but the resulting mesh may
+ contain triangles of poor aspect ratio. Works well if all the
+ boundary points are closely spaced. Specify this switch twice
+ (`-YY') to prevent all segment splitting, including internal
+ boundaries.
+ -S Specifies the maximum number of Steiner points (points that are not
+ in the input, but are added to meet the constraints of minimum
+ angle and maximum area). The default is to allow an unlimited
+ number. If you specify this switch with no number after it,
+ the limit is set to zero. Triangle always adds points at segment
+ intersections, even if it needs to use more points than the limit
+ you set. When Triangle inserts segments by splitting (-s), it
+ always adds enough points to ensure that all the segments appear in
+ the triangulation, again ignoring the limit. Be forewarned that
+ the -S switch may result in a conforming triangulation that is not
+ truly Delaunay, because Triangle may be forced to stop adding
+ points when the mesh is in a state where a segment is non-Delaunay
+ and needs to be split. If so, Triangle will print a warning.
+ -i Uses an incremental rather than divide-and-conquer algorithm to
+ form a Delaunay triangulation. Try it if the divide-and-conquer
+ algorithm fails.
+ -F Uses Steven Fortune's sweepline algorithm to form a Delaunay
+ triangulation. Warning: does not use exact arithmetic for all
+ calculations. An exact result is not guaranteed.
+ -l Uses only vertical cuts in the divide-and-conquer algorithm. By
+ default, Triangle uses alternating vertical and horizontal cuts,
+ which usually improve the speed except with point sets that are
+ small or short and wide. This switch is primarily of theoretical
+ interest.
+ -s Specifies that segments should be forced into the triangulation by
+ recursively splitting them at their midpoints, rather than by
+ generating a constrained Delaunay triangulation. Segment splitting
+ is true to Ruppert's original algorithm, but can create needlessly
+ small triangles near external small features.
+ -C Check the consistency of the final mesh. Uses exact arithmetic for
+ checking, even if the -X switch is used. Useful if you suspect
+ Triangle is buggy.
+ -Q Quiet: Suppresses all explanation of what Triangle is doing, unless
+ an error occurs.
+ -V Verbose: Gives detailed information about what Triangle is doing.
+ Add more `V's for increasing amount of detail. `-V' gives
+ information on algorithmic progress and more detailed statistics.
+ `-VV' gives point-by-point details, and will print so much that
+ Triangle will run much more slowly. `-VVV' gives information only
+ a debugger could love.
+ -h Help: Displays these instructions.
+
+Definitions:
+
+ A Delaunay triangulation of a point set is a triangulation whose vertices
+ are the point set, having the property that no point in the point set
+ falls in the interior of the circumcircle (circle that passes through all
+ three vertices) of any triangle in the triangulation.
+
+ A Voronoi diagram of a point set is a subdivision of the plane into
+ polygonal regions (some of which may be infinite), where each region is
+ the set of points in the plane that are closer to some input point than
+ to any other input point. (The Voronoi diagram is the geometric dual of
+ the Delaunay triangulation.)
+
+ A Planar Straight Line Graph (PSLG) is a collection of points and
+ segments. Segments are simply edges, whose endpoints are points in the
+ PSLG. The file format for PSLGs (.poly files) is described below.
+
+ A constrained Delaunay triangulation of a PSLG is similar to a Delaunay
+ triangulation, but each PSLG segment is present as a single edge in the
+ triangulation. (A constrained Delaunay triangulation is not truly a
+ Delaunay triangulation.)
+
+ A conforming Delaunay triangulation of a PSLG is a true Delaunay
+ triangulation in which each PSLG segment may have been subdivided into
+ several edges by the insertion of additional points. These inserted
+ points are necessary to allow the segments to exist in the mesh while
+ maintaining the Delaunay property.
+
+File Formats:
+
+ All files may contain comments prefixed by the character '#'. Points,
+ triangles, edges, holes, and maximum area constraints must be numbered
+ consecutively, starting from either 1 or 0. Whichever you choose, all
+ input files must be consistent; if the nodes are numbered from 1, so must
+ be all other objects. Triangle automatically detects your choice while
+ reading the .node (or .poly) file. (When calling Triangle from another
+ program, use the -z switch if you wish to number objects from zero.)
+ Examples of these file formats are given below.
+
+ .node files:
+ First line: <# of points> <dimension (must be 2)> <# of attributes>
+ <# of boundary markers (0 or 1)>
+ Remaining lines: <point #> <x> <y> [attributes] [boundary marker]
+
+ The attributes, which are typically floating-point values of physical
+ quantities (such as mass or conductivity) associated with the nodes of
+ a finite element mesh, are copied unchanged to the output mesh. If -s,
+ -q, or -a is selected, each new Steiner point added to the mesh will
+ have attributes assigned to it by linear interpolation.
+
+ If the fourth entry of the first line is `1', the last column of the
+ remainder of the file is assumed to contain boundary markers. Boundary
+ markers are used to identify boundary points and points resting on PSLG
+ segments; a complete description appears in a section below. The .node
+ file produced by Triangle will contain boundary markers in the last
+ column unless they are suppressed by the -B switch.
+
+ .ele files:
+ First line: <# of triangles> <points per triangle> <# of attributes>
+ Remaining lines: <triangle #> <point> <point> <point> ... [attributes]
+
+ Points are indices into the corresponding .node file. The first three
+ points are the corners, and are listed in counterclockwise order around
+ each triangle. (The remaining points, if any, depend on the type of
+ finite element used.) The attributes are just like those of .node
+ files. Because there is no simple mapping from input to output
+ triangles, an attempt is made to interpolate attributes, which may
+ result in a good deal of diffusion of attributes among nearby triangles
+ as the triangulation is refined. Diffusion does not occur across
+ segments, so attributes used to identify segment-bounded regions remain
+ intact. In output .ele files, all triangles have three points each
+ unless the -o2 switch is used, in which case they have six, and the
+ fourth, fifth, and sixth points lie on the midpoints of the edges
+ opposite the first, second, and third corners.
+
+ .poly files:
+ First line: <# of points> <dimension (must be 2)> <# of attributes>
+ <# of boundary markers (0 or 1)>
+ Following lines: <point #> <x> <y> [attributes] [boundary marker]
+ One line: <# of segments> <# of boundary markers (0 or 1)>
+ Following lines: <segment #> <endpoint> <endpoint> [boundary marker]
+ One line: <# of holes>
+ Following lines: <hole #> <x> <y>
+ Optional line: <# of regional attributes and/or area constraints>
+ Optional following lines: <constraint #> <x> <y> <attrib> <max area>
+
+ A .poly file represents a PSLG, as well as some additional information.
+ The first section lists all the points, and is identical to the format
+ of .node files. <# of points> may be set to zero to indicate that the
+ points are listed in a separate .node file; .poly files produced by
+ Triangle always have this format. This has the advantage that a point
+ set may easily be triangulated with or without segments. (The same
+ effect can be achieved, albeit using more disk space, by making a copy
+ of the .poly file with the extension .node; all sections of the file
+ but the first are ignored.)
+
+ The second section lists the segments. Segments are edges whose
+ presence in the triangulation is enforced. Each segment is specified
+ by listing the indices of its two endpoints. This means that you must
+ include its endpoints in the point list. If -s, -q, and -a are not
+ selected, Triangle will produce a constrained Delaunay triangulation,
+ in which each segment appears as a single edge in the triangulation.
+ If -q or -a is selected, Triangle will produce a conforming Delaunay
+ triangulation, in which segments may be subdivided into smaller edges.
+ Each segment, like each point, may have a boundary marker.
+
+ The third section lists holes (and concavities, if -c is selected) in
+ the triangulation. Holes are specified by identifying a point inside
+ each hole. After the triangulation is formed, Triangle creates holes
+ by eating triangles, spreading out from each hole point until its
+ progress is blocked by PSLG segments; you must be careful to enclose
+ each hole in segments, or your whole triangulation may be eaten away.
+ If the two triangles abutting a segment are eaten, the segment itself
+ is also eaten. Do not place a hole directly on a segment; if you do,
+ Triangle will choose one side of the segment arbitrarily.
+
+ The optional fourth section lists regional attributes (to be assigned
+ to all triangles in a region) and regional constraints on the maximum
+ triangle area. Triangle will read this section only if the -A switch
+ is used or the -a switch is used without a number following it, and the
+ -r switch is not used. Regional attributes and area constraints are
+ propagated in the same manner as holes; you specify a point for each
+ attribute and/or constraint, and the attribute and/or constraint will
+ affect the whole region (bounded by segments) containing the point. If
+ two values are written on a line after the x and y coordinate, the
+ former is assumed to be a regional attribute (but will only be applied
+ if the -A switch is selected), and the latter is assumed to be a
+ regional area constraint (but will only be applied if the -a switch is
+ selected). You may also specify just one value after the coordinates,
+ which can serve as both an attribute and an area constraint, depending
+ on the choice of switches. If you are using the -A and -a switches
+ simultaneously and wish to assign an attribute to some region without
+ imposing an area constraint, use a negative maximum area.
+
+ When a triangulation is created from a .poly file, you must either
+ enclose the entire region to be triangulated in PSLG segments, or
+ use the -c switch, which encloses the convex hull of the input point
+ set. If you do not use the -c switch, Triangle will eat all triangles
+ on the outer boundary that are not protected by segments; if you are
+ not careful, your whole triangulation may be eaten away. If you do
+ use the -c switch, you can still produce concavities by appropriate
+ placement of holes just inside the convex hull.
+
+ An ideal PSLG has no intersecting segments, nor any points that lie
+ upon segments (except, of course, the endpoints of each segment.) You
+ aren't required to make your .poly files ideal, but you should be aware
+ of what can go wrong. Segment intersections are relatively safe -
+ Triangle will calculate the intersection points for you and add them to
+ the triangulation - as long as your machine's floating-point precision
+ doesn't become a problem. You are tempting the fates if you have three
+ segments that cross at the same location, and expect Triangle to figure
+ out where the intersection point is. Thanks to floating-point roundoff
+ error, Triangle will probably decide that the three segments intersect
+ at three different points, and you will find a minuscule triangle in
+ your output - unless Triangle tries to refine the tiny triangle, uses
+ up the last bit of machine precision, and fails to terminate at all.
+ You're better off putting the intersection point in the input files,
+ and manually breaking up each segment into two. Similarly, if you
+ place a point at the middle of a segment, and hope that Triangle will
+ break up the segment at that point, you might get lucky. On the other
+ hand, Triangle might decide that the point doesn't lie precisely on the
+ line, and you'll have a needle-sharp triangle in your output - or a lot
+ of tiny triangles if you're generating a quality mesh.
+
+ When Triangle reads a .poly file, it also writes a .poly file, which
+ includes all edges that are part of input segments. If the -c switch
+ is used, the output .poly file will also include all of the edges on
+ the convex hull. Hence, the output .poly file is useful for finding
+ edges associated with input segments and setting boundary conditions in
+ finite element simulations. More importantly, you will need it if you
+ plan to refine the output mesh, and don't want segments to be missing
+ in later triangulations.
+
+ .area files:
+ First line: <# of triangles>
+ Following lines: <triangle #> <maximum area>
+
+ An .area file associates with each triangle a maximum area that is used
+ for mesh refinement. As with other file formats, every triangle must
+ be represented, and they must be numbered consecutively. A triangle
+ may be left unconstrained by assigning it a negative maximum area.
+
+ .edge files:
+ First line: <# of edges> <# of boundary markers (0 or 1)>
+ Following lines: <edge #> <endpoint> <endpoint> [boundary marker]
+
+ Endpoints are indices into the corresponding .node file. Triangle can
+ produce .edge files (use the -e switch), but cannot read them. The
+ optional column of boundary markers is suppressed by the -B switch.
+
+ In Voronoi diagrams, one also finds a special kind of edge that is an
+ infinite ray with only one endpoint. For these edges, a different
+ format is used:
+
+ <edge #> <endpoint> -1 <direction x> <direction y>
+
+ The `direction' is a floating-point vector that indicates the direction
+ of the infinite ray.
+
+ .neigh files:
+ First line: <# of triangles> <# of neighbors per triangle (always 3)>
+ Following lines: <triangle #> <neighbor> <neighbor> <neighbor>
+
+ Neighbors are indices into the corresponding .ele file. An index of -1
+ indicates a mesh boundary, and therefore no neighbor. Triangle can
+ produce .neigh files (use the -n switch), but cannot read them.
+
+ The first neighbor of triangle i is opposite the first corner of
+ triangle i, and so on.
+
+Boundary Markers:
+
+ Boundary markers are tags used mainly to identify which output points and
+ edges are associated with which PSLG segment, and to identify which
+ points and edges occur on a boundary of the triangulation. A common use
+ is to determine where boundary conditions should be applied to a finite
+ element mesh. You can prevent boundary markers from being written into
+ files produced by Triangle by using the -B switch.
+
+ The boundary marker associated with each segment in an output .poly file
+ or edge in an output .edge file is chosen as follows:
+ - If an output edge is part or all of a PSLG segment with a nonzero
+ boundary marker, then the edge is assigned the same marker.
+ - Otherwise, if the edge occurs on a boundary of the triangulation
+ (including boundaries of holes), then the edge is assigned the marker
+ one (1).
+ - Otherwise, the edge is assigned the marker zero (0).
+ The boundary marker associated with each point in an output .node file is
+ chosen as follows:
+ - If a point is assigned a nonzero boundary marker in the input file,
+ then it is assigned the same marker in the output .node file.
+ - Otherwise, if the point lies on a PSLG segment (including the
+ segment's endpoints) with a nonzero boundary marker, then the point
+ is assigned the same marker. If the point lies on several such
+ segments, one of the markers is chosen arbitrarily.
+ - Otherwise, if the point occurs on a boundary of the triangulation,
+ then the point is assigned the marker one (1).
+ - Otherwise, the point is assigned the marker zero (0).
+
+ If you want Triangle to determine for you which points and edges are on
+ the boundary, assign them the boundary marker zero (or use no markers at
+ all) in your input files. Alternatively, you can mark some of them and
+ leave others marked zero, allowing Triangle to label them.
+
+Triangulation Iteration Numbers:
+
+ Because Triangle can read and refine its own triangulations, input
+ and output files have iteration numbers. For instance, Triangle might
+ read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the
+ triangulation, and output the files mesh.4.node, mesh.4.ele, and
+ mesh.4.poly. Files with no iteration number are treated as if
+ their iteration number is zero; hence, Triangle might read the file
+ points.node, triangulate it, and produce the files points.1.node and
+ points.1.ele.
+
+ Iteration numbers allow you to create a sequence of successively finer
+ meshes suitable for multigrid methods. They also allow you to produce a
+ sequence of meshes using error estimate-driven mesh refinement.
+
+ If you're not using refinement or quality meshing, and you don't like
+ iteration numbers, use the -I switch to disable them. This switch will
+ also disable output of .node and .poly files to prevent your input files
+ from being overwritten. (If the input is a .poly file that contains its
+ own points, a .node file will be written.)
+
+Examples of How to Use Triangle:
+
+ `triangle dots' will read points from dots.node, and write their Delaunay
+ triangulation to dots.1.node and dots.1.ele. (dots.1.node will be
+ identical to dots.node.) `triangle -I dots' writes the triangulation to
+ dots.ele instead. (No additional .node file is needed, so none is
+ written.)
+
+ `triangle -pe object.1' will read a PSLG from object.1.poly (and possibly
+ object.1.node, if the points are omitted from object.1.poly) and write
+ their constrained Delaunay triangulation to object.2.node and
+ object.2.ele. The segments will be copied to object.2.poly, and all
+ edges will be written to object.2.edge.
+
+ `triangle -pq31.5a.1 object' will read a PSLG from object.poly (and
+ possibly object.node), generate a mesh whose angles are all greater than
+ 31.5 degrees and whose triangles all have area smaller than 0.1, and
+ write the mesh to object.1.node and object.1.ele. Each segment may have
+ been broken up into multiple edges; the resulting constrained edges are
+ written to object.1.poly.
+
+ Here is a sample file `box.poly' describing a square with a square hole:
+
+ # A box with eight points in 2D, no attributes, one boundary marker.
+ 8 2 0 1
+ # Outer box has these vertices:
+ 1 0 0 0
+ 2 0 3 0
+ 3 3 0 0
+ 4 3 3 33 # A special marker for this point.
+ # Inner square has these vertices:
+ 5 1 1 0
+ 6 1 2 0
+ 7 2 1 0
+ 8 2 2 0
+ # Five segments with boundary markers.
+ 5 1
+ 1 1 2 5 # Left side of outer box.
+ 2 5 7 0 # Segments 2 through 5 enclose the hole.
+ 3 7 8 0
+ 4 8 6 10
+ 5 6 5 0
+ # One hole in the middle of the inner square.
+ 1
+ 1 1.5 1.5
+
+ Note that some segments are missing from the outer square, so one must
+ use the `-c' switch. After `triangle -pqc box.poly', here is the output
+ file `box.1.node', with twelve points. The last four points were added
+ to meet the angle constraint. Points 1, 2, and 9 have markers from
+ segment 1. Points 6 and 8 have markers from segment 4. All the other
+ points but 4 have been marked to indicate that they lie on a boundary.
+
+ 12 2 0 1
+ 1 0 0 5
+ 2 0 3 5
+ 3 3 0 1
+ 4 3 3 33
+ 5 1 1 1
+ 6 1 2 10
+ 7 2 1 1
+ 8 2 2 10
+ 9 0 1.5 5
+ 10 1.5 0 1
+ 11 3 1.5 1
+ 12 1.5 3 1
+ # Generated by triangle -pqc box.poly
+
+ Here is the output file `box.1.ele', with twelve triangles.
+
+ 12 3 0
+ 1 5 6 9
+ 2 10 3 7
+ 3 6 8 12
+ 4 9 1 5
+ 5 6 2 9
+ 6 7 3 11
+ 7 11 4 8
+ 8 7 5 10
+ 9 12 2 6
+ 10 8 7 11
+ 11 5 1 10
+ 12 8 4 12
+ # Generated by triangle -pqc box.poly
+
+ Here is the output file `box.1.poly'. Note that segments have been added
+ to represent the convex hull, and some segments have been split by newly
+ added points. Note also that <# of points> is set to zero to indicate
+ that the points should be read from the .node file.
+
+ 0 2 0 1
+ 12 1
+ 1 1 9 5
+ 2 5 7 1
+ 3 8 7 1
+ 4 6 8 10
+ 5 5 6 1
+ 6 3 10 1
+ 7 4 11 1
+ 8 2 12 1
+ 9 9 2 5
+ 10 10 1 1
+ 11 11 3 1
+ 12 12 4 1
+ 1
+ 1 1.5 1.5
+ # Generated by triangle -pqc box.poly
+
+Refinement and Area Constraints:
+
+ The -r switch causes a mesh (.node and .ele files) to be read and
+ refined. If the -p switch is also used, a .poly file is read and used to
+ specify edges that are constrained and cannot be eliminated (although
+ they can be divided into smaller edges) by the refinement process.
+
+ When you refine a mesh, you generally want to impose tighter quality
+ constraints. One way to accomplish this is to use -q with a larger
+ angle, or -a followed by a smaller area than you used to generate the
+ mesh you are refining. Another way to do this is to create an .area
+ file, which specifies a maximum area for each triangle, and use the -a
+ switch (without a number following). Each triangle's area constraint is
+ applied to that triangle. Area constraints tend to diffuse as the mesh
+ is refined, so if there are large variations in area constraint between
+ adjacent triangles, you may not get the results you want.
+
+ If you are refining a mesh composed of linear (three-node) elements, the
+ output mesh will contain all the nodes present in the input mesh, in the
+ same order, with new nodes added at the end of the .node file. However,
+ there is no guarantee that each output element is contained in a single
+ input element. Often, output elements will overlap two input elements,
+ and input edges are not present in the output mesh. Hence, a sequence of
+ refined meshes will form a hierarchy of nodes, but not a hierarchy of
+ elements. If you a refining a mesh of higher-order elements, the
+ hierarchical property applies only to the nodes at the corners of an
+ element; other nodes may not be present in the refined mesh.
+
+ It is important to understand that maximum area constraints in .poly
+ files are handled differently from those in .area files. A maximum area
+ in a .poly file applies to the whole (segment-bounded) region in which a
+ point falls, whereas a maximum area in an .area file applies to only one
+ triangle. Area constraints in .poly files are used only when a mesh is
+ first generated, whereas area constraints in .area files are used only to
+ refine an existing mesh, and are typically based on a posteriori error
+ estimates resulting from a finite element simulation on that mesh.
+
+ `triangle -rq25 object.1' will read object.1.node and object.1.ele, then
+ refine the triangulation to enforce a 25 degree minimum angle, and then
+ write the refined triangulation to object.2.node and object.2.ele.
+
+ `triangle -rpaa6.2 z.3' will read z.3.node, z.3.ele, z.3.poly, and
+ z.3.area. After reconstructing the mesh and its segments, Triangle will
+ refine the mesh so that no triangle has area greater than 6.2, and
+ furthermore the triangles satisfy the maximum area constraints in
+ z.3.area. The output is written to z.4.node, z.4.ele, and z.4.poly.
+
+ The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1
+ x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,
+ suitable for multigrid.
+
+Convex Hulls and Mesh Boundaries:
+
+ If the input is a point set (rather than a PSLG), Triangle produces its
+ convex hull as a by-product in the output .poly file if you use the -c
+ switch. There are faster algorithms for finding a two-dimensional convex
+ hull than triangulation, of course, but this one comes for free. If the
+ input is an unconstrained mesh (you are using the -r switch but not the
+ -p switch), Triangle produces a list of its boundary edges (including
+ hole boundaries) as a by-product if you use the -c switch.
+
+Voronoi Diagrams:
+
+ The -v switch produces a Voronoi diagram, in files suffixed .v.node and
+ .v.edge. For example, `triangle -v points' will read points.node,
+ produce its Delaunay triangulation in points.1.node and points.1.ele,
+ and produce its Voronoi diagram in points.1.v.node and points.1.v.edge.
+ The .v.node file contains a list of all Voronoi vertices, and the .v.edge
+ file contains a list of all Voronoi edges, some of which may be infinite
+ rays. (The choice of filenames makes it easy to run the set of Voronoi
+ vertices through Triangle, if so desired.)
+
+ This implementation does not use exact arithmetic to compute the Voronoi
+ vertices, and does not check whether neighboring vertices are identical.
+ Be forewarned that if the Delaunay triangulation is degenerate or
+ near-degenerate, the Voronoi diagram may have duplicate points, crossing
+ edges, or infinite rays whose direction vector is zero. Also, if you
+ generate a constrained (as opposed to conforming) Delaunay triangulation,
+ or if the triangulation has holes, the corresponding Voronoi diagram is
+ likely to have crossing edges and unlikely to make sense.
+
+Mesh Topology:
+
+ You may wish to know which triangles are adjacent to a certain Delaunay
+ edge in an .edge file, which Voronoi regions are adjacent to a certain
+ Voronoi edge in a .v.edge file, or which Voronoi regions are adjacent to
+ each other. All of this information can be found by cross-referencing
+ output files with the recollection that the Delaunay triangulation and
+ the Voronoi diagrams are planar duals.
+
+ Specifically, edge i of an .edge file is the dual of Voronoi edge i of
+ the corresponding .v.edge file, and is rotated 90 degrees counterclock-
+ wise from the Voronoi edge. Triangle j of an .ele file is the dual of
+ vertex j of the corresponding .v.node file; and Voronoi region k is the
+ dual of point k of the corresponding .node file.
+
+ Hence, to find the triangles adjacent to a Delaunay edge, look at the
+ vertices of the corresponding Voronoi edge; their dual triangles are on
+ the left and right of the Delaunay edge, respectively. To find the
+ Voronoi regions adjacent to a Voronoi edge, look at the endpoints of the
+ corresponding Delaunay edge; their dual regions are on the right and left
+ of the Voronoi edge, respectively. To find which Voronoi regions are
+ adjacent to each other, just read the list of Delaunay edges.
+
+Statistics:
+
+ After generating a mesh, Triangle prints a count of the number of points,
+ triangles, edges, boundary edges, and segments in the output mesh. If
+ you've forgotten the statistics for an existing mesh, the -rNEP switches
+ (or -rpNEP if you've got a .poly file for the existing mesh) will
+ regenerate these statistics without writing any output.
+
+ The -V switch produces extended statistics, including a rough estimate
+ of memory use and a histogram of triangle aspect ratios and angles in the
+ mesh.
+
+Exact Arithmetic:
+
+ Triangle uses adaptive exact arithmetic to perform what computational
+ geometers call the `orientation' and `incircle' tests. If the floating-
+ point arithmetic of your machine conforms to the IEEE 754 standard (as
+ most workstations do), and does not use extended precision internal
+ registers, then your output is guaranteed to be an absolutely true
+ Delaunay or conforming Delaunay triangulation, roundoff error
+ notwithstanding. The word `adaptive' implies that these arithmetic
+ routines compute the result only to the precision necessary to guarantee
+ correctness, so they are usually nearly as fast as their approximate
+ counterparts. The exact tests can be disabled with the -X switch. On
+ most inputs, this switch will reduce the computation time by about eight
+ percent - it's not worth the risk. There are rare difficult inputs
+ (having many collinear and cocircular points), however, for which the
+ difference could be a factor of two. These are precisely the inputs most
+ likely to cause errors if you use the -X switch.
+
+ Unfortunately, these routines don't solve every numerical problem. Exact
+ arithmetic is not used to compute the positions of points, because the
+ bit complexity of point coordinates would grow without bound. Hence,
+ segment intersections aren't computed exactly; in very unusual cases,
+ roundoff error in computing an intersection point might actually lead to
+ an inverted triangle and an invalid triangulation. (This is one reason
+ to compute your own intersection points in your .poly files.) Similarly,
+ exact arithmetic is not used to compute the vertices of the Voronoi
+ diagram.
+
+ Underflow and overflow can also cause difficulties; the exact arithmetic
+ routines do not ameliorate out-of-bounds exponents, which can arise
+ during the orientation and incircle tests. As a rule of thumb, you
+ should ensure that your input values are within a range such that their
+ third powers can be taken without underflow or overflow. Underflow can
+ silently prevent the tests from being performed exactly, while overflow
+ will typically cause a floating exception.
+
+Calling Triangle from Another Program:
+
+ Read the file triangle.h for details.
+
+Troubleshooting:
+
+ Please read this section before mailing me bugs.
+
+ `My output mesh has no triangles!'
+
+ If you're using a PSLG, you've probably failed to specify a proper set
+ of bounding segments, or forgotten to use the -c switch. Or you may
+ have placed a hole badly. To test these possibilities, try again with
+ the -c and -O switches. Alternatively, all your input points may be
+ collinear, in which case you can hardly expect to triangulate them.
+
+ `Triangle doesn't terminate, or just crashes.'
+
+ Bad things can happen when triangles get so small that the distance
+ between their vertices isn't much larger than the precision of your
+ machine's arithmetic. If you've compiled Triangle for single-precision
+ arithmetic, you might do better by recompiling it for double-precision.
+ Then again, you might just have to settle for more lenient constraints
+ on the minimum angle and the maximum area than you had planned.
+
+ You can minimize precision problems by ensuring that the origin lies
+ inside your point set, or even inside the densest part of your
+ mesh. On the other hand, if you're triangulating an object whose x
+ coordinates all fall between 6247133 and 6247134, you're not leaving
+ much floating-point precision for Triangle to work with.
+
+ Precision problems can occur covertly if the input PSLG contains two
+ segments that meet (or intersect) at a very small angle, or if such an
+ angle is introduced by the -c switch, which may occur if a point lies
+ ever-so-slightly inside the convex hull, and is connected by a PSLG
+ segment to a point on the convex hull. If you don't realize that a
+ small angle is being formed, you might never discover why Triangle is
+ crashing. To check for this possibility, use the -S switch (with an
+ appropriate limit on the number of Steiner points, found by trial-and-
+ error) to stop Triangle early, and view the output .poly file with
+ Show Me (described below). Look carefully for small angles between
+ segments; zoom in closely, as such segments might look like a single
+ segment from a distance.
+
+ If some of the input values are too large, Triangle may suffer a
+ floating exception due to overflow when attempting to perform an
+ orientation or incircle test. (Read the section on exact arithmetic
+ above.) Again, I recommend compiling Triangle for double (rather
+ than single) precision arithmetic.
+
+ `The numbering of the output points doesn't match the input points.'
+
+ You may have eaten some of your input points with a hole, or by placing
+ them outside the area enclosed by segments.
+
+ `Triangle executes without incident, but when I look at the resulting
+ mesh, it has overlapping triangles or other geometric inconsistencies.'
+
+ If you select the -X switch, Triangle's divide-and-conquer Delaunay
+ triangulation algorithm occasionally makes mistakes due to floating-
+ point roundoff error. Although these errors are rare, don't use the -X
+ switch. If you still have problems, please report the bug.
+
+ Strange things can happen if you've taken liberties with your PSLG. Do
+ you have a point lying in the middle of a segment? Triangle sometimes
+ copes poorly with that sort of thing. Do you want to lay out a collinear
+ row of evenly spaced, segment-connected points? Have you simply defined
+ one long segment connecting the leftmost point to the rightmost point,
+ and a bunch of points lying along it? This method occasionally works,
+ especially with horizontal and vertical lines, but often it doesn't, and
+ you'll have to connect each adjacent pair of points with a separate
+ segment. If you don't like it, tough.
+
+ Furthermore, if you have segments that intersect other than at their
+ endpoints, try not to let the intersections fall extremely close to PSLG
+ points or each other.
+
+ If you have problems refining a triangulation not produced by Triangle:
+ Are you sure the triangulation is geometrically valid? Is it formatted
+ correctly for Triangle? Are the triangles all listed so the first three
+ points are their corners in counterclockwise order?
+
+Show Me:
+
+ Triangle comes with a separate program named `Show Me', whose primary
+ purpose is to draw meshes on your screen or in PostScript. Its secondary
+ purpose is to check the validity of your input files, and do so more
+ thoroughly than Triangle does. Show Me requires that you have the X
+ Windows system. If you didn't receive Show Me with Triangle, complain to
+ whomever you obtained Triangle from, then send me mail.
+
+Triangle on the Web:
+
+ To see an illustrated, updated version of these instructions, check out
+
+ http://www.cs.cmu.edu/~quake/triangle.html
+
+A Brief Plea:
+
+ If you use Triangle, and especially if you use it to accomplish real
+ work, I would like very much to hear from you. A short letter or email
+ (to jrs@cs.cmu.edu) describing how you use Triangle will mean a lot to
+ me. The more people I know are using this program, the more easily I can
+ justify spending time on improvements and on the three-dimensional
+ successor to Triangle, which in turn will benefit you. Also, I can put
+ you on a list to receive email whenever a new version of Triangle is
+ available.
+
+ If you use a mesh generated by Triangle in a publication, please include
+ an acknowledgment as well.
+
+Research credit:
+
+ Of course, I can take credit for only a fraction of the ideas that made
+ this mesh generator possible. Triangle owes its existence to the efforts
+ of many fine computational geometers and other researchers, including
+ Marshall Bern, L. Paul Chew, Boris Delaunay, Rex A. Dwyer, David
+ Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E. Knuth, C. L.
+ Lawson, Der-Tsai Lee, Ernst P. Mucke, Douglas M. Priest, Jim Ruppert,
+ Isaac Saias, Bruce J. Schachter, Micha Sharir, Jorge Stolfi, Christopher
+ J. Van Wyk, David F. Watson, and Binhai Zhu. See the comments at the
+ beginning of the source code for references.
+
projects / flightgear.git / commitdiff