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+/*
+ * (c) Copyright 1993, 1994, Silicon Graphics, Inc.
+ * ALL RIGHTS RESERVED
+ * Permission to use, copy, modify, and distribute this software for
+ * any purpose and without fee is hereby granted, provided that the above
+ * copyright notice appear in all copies and that both the copyright notice
+ * and this permission notice appear in supporting documentation, and that
+ * the name of Silicon Graphics, Inc. not be used in advertising
+ * or publicity pertaining to distribution of the software without specific,
+ * written prior permission.
+ *
+ * THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "AS-IS"
+ * AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE,
+ * INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR
+ * FITNESS FOR A PARTICULAR PURPOSE.  IN NO EVENT SHALL SILICON
+ * GRAPHICS, INC.  BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT,
+ * SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY
+ * KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION,
+ * LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF
+ * THIRD PARTIES, WHETHER OR NOT SILICON GRAPHICS, INC.  HAS BEEN
+ * ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON
+ * ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE
+ * POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE.
+ *
+ * US Government Users Restricted Rights
+ * Use, duplication, or disclosure by the Government is subject to
+ * restrictions set forth in FAR 52.227.19(c)(2) or subparagraph
+ * (c)(1)(ii) of the Rights in Technical Data and Computer Software
+ * clause at DFARS 252.227-7013 and/or in similar or successor
+ * clauses in the FAR or the DOD or NASA FAR Supplement.
+ * Unpublished-- rights reserved under the copyright laws of the
+ * United States.  Contractor/manufacturer is Silicon Graphics,
+ * Inc., 2011 N.  Shoreline Blvd., Mountain View, CA 94039-7311.
+ *
+ * OpenGL(TM) is a trademark of Silicon Graphics, Inc.
+ */
+/*
+ * 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
+ */
+#include <math.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 (0.8)
+
+/*
+ * 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) {
+  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) {
+  return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
+}
+
+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];
+}
+
+/*
+ * 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 an axis and angle, compute quaternion.
+ */
+void axis_to_quat(float a[3], float phi, float q[4]) {
+  vnormal(a);
+  vcopy(a, q);
+  vscale(q, sin(phi / 2.0));
+  q[3] = cos(phi / 2.0);
+}
+
+/*
+ * 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;
+
+  d = sqrt(x * x + y * y);
+  if (d < r * 0.70710678118654752440) { /* Inside sphere */
+    z = sqrt(r * r - d * d);
+  } else { /* On hyperbola */
+    t = r / 1.41421356237309504880;
+    z = t * t / d;
+  }
+  return z;
+}
+
+/*
+ * 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];
+
+  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);
+
+  dest[0] = tf[0];
+  dest[1] = tf[1];
+  dest[2] = tf[2];
+  dest[3] = tf[3];
+
+  if (++count > RENORMCOUNT) {
+    count = 0;
+    normalize_quat(dest);
+  }
+}
+
+/*
+ * 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;
+
+  mag = (q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]);
+  for (i = 0; i < 4; i++)
+    q[i] /= mag;
+}
+
+/*
+ * Build a rotation matrix, given a quaternion rotation.
+ *
+ */
+void build_rotmatrix(float m[4][4], const 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;
+}