+
+
+
+/*
+ * 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])
+{
+//#define TRANSPOSED_QUAT
+#ifndef TRANSPOSED_QUAT
+ 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;
+#else // TRANSPOSED_QUAT
+ 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;
+#endif // 0
+}
+