trackball.cc

/*
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 * Unpublished-- rights reserved under the copyright laws of the
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/*
 * 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) {
  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) {
  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;
}