text: /*
   * (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   * Unpublished-- rights reserved under the copyright laws of the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  (0.8f)
  
  /*
   * Local function prototypes (not defined in trackball.h)
   */
  static float tb_project_to_sphere(float, float, float);
  static void normalize_quat(float [4]);
  
  void
  vzero(float *v)
  {
      v[0] = 0.0;
      v[1] = 0.0;
      v[2] = 0.0;
  }
  
  void
  vset(float *v, float x, float y, float z)
  {
      v[0] = x;
      v[1] = y;
      v[2] = z;
  }
  
  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];
  }
  
  void
  vcopy(const float *v1, float *v2)
  {
      register int i;
      for (i = 0 ; i < 3 ; i++)
          v2[i] = v1[i];
  }
  
  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);
  }
  
  float
  vlength(const float *v)
  {
      return (float) sqrt((double)(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]));
  }
  
  void
  vscale(float *v, float div)
  {
      v[0] *= div;
      v[1] *= div;
      v[2] *= div;
  }
  
  void
  vnormal(float *v)
  {
      vscale(v, 1.0f/vlength(v));
  }
  
  float
  vdot(const float *v1, const float *v2)
  {
      return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
  }
  
  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) / (2.0f*TRACKBALLSIZE);
  
      /*
       * Avoid problems with out-of-control values...
       */
      if (t > 1) t = 1;
      if (t < -1) t = -1;
      phi = 2 * (float) asin((double)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, (float) sin((double)phi / 2));
      q[3] = (float) cos((double)phi / 2);
  }
  
  /*
   * 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 = (float) sqrt((double)(x*x + y*y));
      if (d < r * 0.70710678118654752440f) {    /* Inside sphere */
          z = (float) sqrt((double)(r*r - d*d));
      } else {           /* On hyperbola */
          t = r / 1.41421356237309504880f;
          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], float q[4])
  {
      m[0][0] = 1.0f - 2.0f * (q[1] * q[1] + q[2] * q[2]);
      m[0][1] = 2.0f * (q[0] * q[1] - q[2] * q[3]);
      m[0][2] = 2.0f * (q[2] * q[0] + q[1] * q[3]);
      m[0][3] = 0.0f;
  
      m[1][0] = 2.0f * (q[0] * q[1] + q[2] * q[3]);
      m[1][1]= 1.0f - 2.0f * (q[2] * q[2] + q[0] * q[0]);
      m[1][2] = 2.0f * (q[1] * q[2] - q[0] * q[3]);
      m[1][3] = 0.0f;
  
      m[2][0] = 2.0f * (q[2] * q[0] - q[1] * q[3]);
      m[2][1] = 2.0f * (q[1] * q[2] + q[0] * q[3]);
      m[2][2] = 1.0f - 2.0f * (q[1] * q[1] + q[0] * q[0]);
      m[2][3] = 0.0f;
  
      m[3][0] = 0.0f;
      m[3][1] = 0.0f;
      m[3][2] = 0.0f;
      m[3][3] = 1.0f;
  }
  
  