+++ /dev/null
-/*
- * Trackball code:
- *
- * Implementation of a virtual trackball.
- * Implemented by Gavin Bell, lots of ideas from Thant Tessman and
- * the August '88 issue of Siggraph's "Computer Graphics," pp. 121-129.
- *
- * Vector manip code:
- *
- * Original code from:
- * David M. Ciemiewicz, Mark Grossman, Henry Moreton, and Paul Haeberli
- *
- * Much mucking with by:
- * Gavin Bell
- */
-
-#if defined(_WIN32) && !defined( __CYGWIN32__ )
-#pragma warning (disable:4244) /* disable bogus conversion warnings */
-#endif
-#include <math.h>
-#include <stdio.h>
-#include "trackball.h"
-
-/*
- * This size should really be based on the distance from the center of
- * rotation to the point on the object underneath the mouse. That
- * point would then track the mouse as closely as possible. This is a
- * simple example, though, so that is left as an Exercise for the
- * Programmer.
- */
-#define TRACKBALLSIZE (0.8f)
-#define SQRT(x) sqrt(x)
-
-/*
- * Local function prototypes (not defined in trackball.h)
- */
-static float tb_project_to_sphere(float, float, float);
-static void normalize_quat(float [4]);
-
-static void
- vzero(float *v)
-{
- v[0] = 0.0;
- v[1] = 0.0;
- v[2] = 0.0;
-}
-
-static void
- vset(float *v, float x, float y, float z)
-{
- v[0] = x;
- v[1] = y;
- v[2] = z;
-}
-
-static void
- vsub(const float *src1, const float *src2, float *dst)
-{
- dst[0] = src1[0] - src2[0];
- dst[1] = src1[1] - src2[1];
- dst[2] = src1[2] - src2[2];
-}
-
-static void
- vcopy(const float *v1, float *v2)
-{
- register int i;
- for (i = 0 ; i < 3 ; i++)
- v2[i] = v1[i];
-}
-
-static void
- vcross(const float *v1, const float *v2, float *cross)
-{
- float temp[3];
-
- temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
- temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
- temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
- vcopy(temp, cross);
-}
-
-static float
- vlength(const float *v)
-{
- float tmp = v[0] * v[0] + v[1] * v[1] + v[2] * v[2];
- return SQRT(tmp);
-}
-
-static void
- vscale(float *v, float div)
-{
- v[0] *= div;
- v[1] *= div;
- v[2] *= div;
-}
-
-static void
- vnormal(float *v)
-{
- vscale(v,1.0/vlength(v));
-}
-
-static float
- vdot(const float *v1, const float *v2)
-{
- return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
-}
-
-static void
- vadd(const float *src1, const float *src2, float *dst)
-{
- dst[0] = src1[0] + src2[0];
- dst[1] = src1[1] + src2[1];
- dst[2] = src1[2] + src2[2];
-}
-
-/*
- * Given an axis and angle, compute quaternion.
- */
-void
- axis_to_quat(float a[3], float phi, float q[4])
-{
- double sinphi2, cosphi2;
- double phi2 = phi/2.0;
- sinphi2 = sin(phi2);
- cosphi2 = cos(phi2);
- vnormal(a);
- vcopy(a,q);
- vscale(q,sinphi2);
- q[3] = cosphi2;
-}
-
-/*
- * Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
- * if we are away from the center of the sphere.
- */
-static float
- tb_project_to_sphere(float r, float x, float y)
-{
- float d, t, z, tmp;
-
- tmp = x*x + y*y;
- d = SQRT(tmp);
- if (d < r * 0.70710678118654752440) { /* Inside sphere */
- tmp = r*r - d*d;
- z = SQRT(tmp);
- } else { /* On hyperbola */
- t = r / 1.41421356237309504880;
- z = t*t / d;
- }
- return z;
-}
-
-/*
- * Quaternions always obey: a^2 + b^2 + c^2 + d^2 = 1.0
- * If they don't add up to 1.0, dividing by their magnitued will
- * renormalize them.
- *
- * Note: See the following for more information on quaternions:
- *
- * - Shoemake, K., Animating rotation with quaternion curves, Computer
- * Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
- * - Pletinckx, D., Quaternion calculus as a basic tool in computer
- * graphics, The Visual Computer 5, 2-13, 1989.
- */
-static void
- normalize_quat(float q[4])
-{
- int i;
- float mag, tmp;
-
- tmp = q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3];
- mag = 1.0 / SQRT(tmp);
- for (i = 0; i < 4; i++)
- q[i] *= mag;
-}
-
-/*
- * Ok, simulate a track-ball. Project the points onto the virtual
- * trackball, then figure out the axis of rotation, which is the cross
- * product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
- * Note: This is a deformed trackball-- is a trackball in the center,
- * but is deformed into a hyperbolic sheet of rotation away from the
- * center. This particular function was chosen after trying out
- * several variations.
- *
- * It is assumed that the arguments to this routine are in the range
- * (-1.0 ... 1.0)
- */
-void
- trackball(float q[4], float p1x, float p1y, float p2x, float p2y)
-{
- float a[3]; /* Axis of rotation */
- float phi; /* how much to rotate about axis */
- float p1[3], p2[3], d[3];
- float t;
-
- if (p1x == p2x && p1y == p2y) {
- /* Zero rotation */
- vzero(q);
- q[3] = 1.0;
- return;
- }
-
- /*
- * First, figure out z-coordinates for projection of P1 and P2 to
- * deformed sphere
- */
- vset(p1,p1x,p1y,tb_project_to_sphere(TRACKBALLSIZE,p1x,p1y));
- vset(p2,p2x,p2y,tb_project_to_sphere(TRACKBALLSIZE,p2x,p2y));
-
- /*
- * Now, we want the cross product of P1 and P2
- */
- vcross(p2,p1,a);
-
- /*
- * Figure out how much to rotate around that axis.
- */
- vsub(p1,p2,d);
- t = vlength(d) / (2.0*TRACKBALLSIZE);
-
- /*
- * Avoid problems with out-of-control values...
- */
- if (t > 1.0) t = 1.0;
- if (t < -1.0) t = -1.0;
- phi = 2.0 * asin(t);
-
- axis_to_quat(a,phi,q);
-}
-
-/*
- * Given two rotations, e1 and e2, expressed as quaternion rotations,
- * figure out the equivalent single rotation and stuff it into dest.
- *
- * This routine also normalizes the result every RENORMCOUNT times it is
- * called, to keep error from creeping in.
- *
- * NOTE: This routine is written so that q1 or q2 may be the same
- * as dest (or each other).
- */
-
-#define RENORMCOUNT 97
-
-void
- add_quats(float q1[4], float q2[4], float dest[4])
-{
- static int count=0;
- float t1[4], t2[4], t3[4];
- float tf[4];
-
-#if 0
- printf("q1 = %f %f %f %f\n", q1[0], q1[1], q1[2], q1[3]);
- printf("q2 = %f %f %f %f\n", q2[0], q2[1], q2[2], q2[3]);
-#endif
-
- vcopy(q1,t1);
- vscale(t1,q2[3]);
-
- vcopy(q2,t2);
- vscale(t2,q1[3]);
-
- vcross(q2,q1,t3);
- vadd(t1,t2,tf);
- vadd(t3,tf,tf);
- tf[3] = q1[3] * q2[3] - vdot(q1,q2);
-
-#if 0
- printf("tf = %f %f %f %f\n", tf[0], tf[1], tf[2], tf[3]);
-#endif
-
- dest[0] = tf[0];
- dest[1] = tf[1];
- dest[2] = tf[2];
- dest[3] = tf[3];
-
- if (++count > RENORMCOUNT) {
- count = 0;
- normalize_quat(dest);
- }
-}
-
-/*
- * Build a rotation matrix, given a quaternion rotation.
- *
- */
-void build_rotmatrix(float m[4][4], float q[4])
-{
- m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
- m[0][1] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
- m[0][2] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
- m[0][3] = 0.0;
-
- m[1][0] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
- m[1][1]= 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
- m[1][2] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
- m[1][3] = 0.0;
-
- m[2][0] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
- m[2][1] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
- m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);
-
- m[2][3] = 0.0;
- m[3][0] = 0.0;
- m[3][1] = 0.0;
- m[3][2] = 0.0;
- m[3][3] = 1.0;
-}
-
-void build_transposed_rotmatrix(float m[4][4], float q[4])
-{
- m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
- m[0][1] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
- m[0][2] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
- m[0][3] = 0.0;
-
- m[1][0] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
- m[1][1] = 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
- m[1][2] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
- m[1][3] = 0.0;
-
- m[2][0] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
- m[2][1] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
- m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);
- m[2][3] = 0.0;
-
- m[3][0] = 0.0;
- m[3][1] = 0.0;
- m[3][2] = 0.0;
- m[3][3] = 1.0;
-}
-
-
+++ /dev/null
-/*
- * trackball.h
- * A virtual trackball implementation
- * Written by Gavin Bell for Silicon Graphics, November 1988.
- */
-
-#ifndef _TRACKBALL_H
-#define _TRACKBALL_H
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-/*
- * Pass the x and y coordinates of the last and current positions of
- * the mouse, scaled so they are from (-1.0 ... 1.0).
- *
- * The resulting rotation is returned as a quaternion rotation in the
- * first paramater.
- */
-void
- trackball(float q[4], float p1x, float p1y, float p2x, float p2y);
-
-/*
- * Given two quaternions, add them together to get a third quaternion.
- * Adding quaternions to get a compound rotation is analagous to adding
- * translations to get a compound translation. When incrementally
- * adding rotations, the first argument here should be the new
-
- * rotation, the second and third the total rotation (which will be
- * over-written with the resulting new total rotation).
- */
-void add_quats(float *q1, float *q2, float *dest);
-
-/*
- * A useful function, builds a rotation matrix in Matrix based on
- * given quaternion.
- */
-void build_rotmatrix(float m[4][4], float q[4]);
-void build_transposed_rotmatrix(float m[4][4], float q[4]);
-
-/*
- * This function computes a quaternion based on an axis (defined by
- * the given vector) and an angle about which to rotate. The angle is
- * expressed in radians. The result is put into the third argument.
- */
-void axis_to_quat(float a[3], float phi, float q[4]);
-
-
-#ifdef __cplusplus
-}
-#endif
-
-
-#endif /* _TRACKBALL_H */
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