samples/opengl/penguin/trackball.c

   1 /*
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  13  * AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE,
  14  * INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR
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  18  * KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION,
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  24  *
  25  * US Government Users Restricted Rights
  26  * Use, duplication, or disclosure by the Government is subject to
  27  * restrictions set forth in FAR 52.227.19(c)(2) or subparagraph
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  29  * clause at DFARS 252.227-7013 and/or in similar or successor
  30  * clauses in the FAR or the DOD or NASA FAR Supplement.
  31  * Unpublished-- rights reserved under the copyright laws of the
  32  * United States.  Contractor/manufacturer is Silicon Graphics,
  33  * Inc., 2011 N.  Shoreline Blvd., Mountain View, CA 94039-7311.
  34  *
  35  * OpenGL(TM) is a trademark of Silicon Graphics, Inc.
  36  */
  37 /*
  38  * Trackball code:
  39  *
  40  * Implementation of a virtual trackball.
  41  * Implemented by Gavin Bell, lots of ideas from Thant Tessman and
  42  *   the August '88 issue of Siggraph's "Computer Graphics," pp. 121-129.
  43  *
  44  * Vector manip code:
  45  *
  46  * Original code from:
  47  * David M. Ciemiewicz, Mark Grossman, Henry Moreton, and Paul Haeberli
  48  *
  49  * Much mucking with by:
  50  * Gavin Bell
  51  */
  52 #include <math.h>
  53 #include "trackball.h"
  54
  55 /*
  56  * This size should really be based on the distance from the center of
  57  * rotation to the point on the object underneath the mouse.  That
  58  * point would then track the mouse as closely as possible.  This is a
  59  * simple example, though, so that is left as an Exercise for the
  60  * Programmer.
  61  */
  62 #define TRACKBALLSIZE  (0.8)
  63
  64 /*
  65  * Local function prototypes (not defined in trackball.h)
  66  */
  67 static float tb_project_to_sphere(float, float, float);
  68 static void normalize_quat(float [4]);
  69
  70 void
  71 vzero(float *v)
  72 {
  73     v[0] = 0.0;
  74     v[1] = 0.0;
  75     v[2] = 0.0;
  76 }
  77
  78 void
  79 vset(float *v, float x, float y, float z)
  80 {
  81     v[0] = x;
  82     v[1] = y;
  83     v[2] = z;
  84 }
  85
  86 void
  87 vsub(const float *src1, const float *src2, float *dst)
  88 {
  89     dst[0] = src1[0] - src2[0];
  90     dst[1] = src1[1] - src2[1];
  91     dst[2] = src1[2] - src2[2];
  92 }
  93
  94 void
  95 vcopy(const float *v1, float *v2)
  96 {
  97     register int i;
  98     for (i = 0 ; i < 3 ; i++)
  99         v2[i] = v1[i];
 100 }
 101
 102 void
 103 vcross(const float *v1, const float *v2, float *cross)
 104 {
 105     float temp[3];
 106
 107     temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
 108     temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
 109     temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
 110     vcopy(temp, cross);
 111 }
 112
 113 float
 114 vlength(const float *v)
 115 {
 116     return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
 117 }
 118
 119 void
 120 vscale(float *v, float div)
 121 {
 122     v[0] *= div;
 123     v[1] *= div;
 124     v[2] *= div;
 125 }
 126
 127 void
 128 vnormal(float *v)
 129 {
 130     vscale(v,1.0/vlength(v));
 131 }
 132
 133 float
 134 vdot(const float *v1, const float *v2)
 135 {
 136     return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
 137 }
 138
 139 void
 140 vadd(const float *src1, const float *src2, float *dst)
 141 {
 142     dst[0] = src1[0] + src2[0];
 143     dst[1] = src1[1] + src2[1];
 144     dst[2] = src1[2] + src2[2];
 145 }
 146
 147 /*
 148  * Ok, simulate a track-ball.  Project the points onto the virtual
 149  * trackball, then figure out the axis of rotation, which is the cross
 150  * product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
 151  * Note:  This is a deformed trackball-- is a trackball in the center,
 152  * but is deformed into a hyperbolic sheet of rotation away from the
 153  * center.  This particular function was chosen after trying out
 154  * several variations.
 155  *
 156  * It is assumed that the arguments to this routine are in the range
 157  * (-1.0 ... 1.0)
 158  */
 159 void
 160 trackball(float q[4], float p1x, float p1y, float p2x, float p2y)
 161 {
 162     float a[3]; /* Axis of rotation */
 163     float phi;  /* how much to rotate about axis */
 164     float p1[3], p2[3], d[3];
 165     float t;
 166
 167     if (p1x == p2x && p1y == p2y) {
 168         /* Zero rotation */
 169         vzero(q);
 170         q[3] = 1.0;
 171         return;
 172     }
 173
 174     /*
 175      * First, figure out z-coordinates for projection of P1 and P2 to
 176      * deformed sphere
 177      */
 178     vset(p1,p1x,p1y,tb_project_to_sphere(TRACKBALLSIZE,p1x,p1y));
 179     vset(p2,p2x,p2y,tb_project_to_sphere(TRACKBALLSIZE,p2x,p2y));
 180
 181     /*
 182      *  Now, we want the cross product of P1 and P2
 183      */
 184     vcross(p2,p1,a);
 185
 186     /*
 187      *  Figure out how much to rotate around that axis.
 188      */
 189     vsub(p1,p2,d);
 190     t = vlength(d) / (2.0*TRACKBALLSIZE);
 191
 192     /*
 193      * Avoid problems with out-of-control values...
 194      */
 195     if (t > 1.0) t = 1.0;
 196     if (t < -1.0) t = -1.0;
 197     phi = 2.0 * asin(t);
 198
 199     axis_to_quat(a,phi,q);
 200 }
 201
 202 /*
 203  *  Given an axis and angle, compute quaternion.
 204  */
 205 void
 206 axis_to_quat(float a[3], float phi, float q[4])
 207 {
 208     vnormal(a);
 209     vcopy(a,q);
 210     vscale(q,sin(phi/2.0));
 211     q[3] = cos(phi/2.0);
 212 }
 213
 214 /*
 215  * Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
 216  * if we are away from the center of the sphere.
 217  */
 218 static float
 219 tb_project_to_sphere(float r, float x, float y)
 220 {
 221     float d, t, z;
 222
 223     d = sqrt(x*x + y*y);
 224     if (d < r * 0.70710678118654752440) {    /* Inside sphere */
 225         z = sqrt(r*r - d*d);
 226     } else {           /* On hyperbola */
 227         t = r / 1.41421356237309504880;
 228         z = t*t / d;
 229     }
 230     return z;
 231 }
 232
 233 /*
 234  * Given two rotations, e1 and e2, expressed as quaternion rotations,
 235  * figure out the equivalent single rotation and stuff it into dest.
 236  *
 237  * This routine also normalizes the result every RENORMCOUNT times it is
 238  * called, to keep error from creeping in.
 239  *
 240  * NOTE: This routine is written so that q1 or q2 may be the same
 241  * as dest (or each other).
 242  */
 243
 244 #define RENORMCOUNT 97
 245
 246 void
 247 add_quats(float q1[4], float q2[4], float dest[4])
 248 {
 249     static int count=0;
 250     float t1[4], t2[4], t3[4];
 251     float tf[4];
 252
 253     vcopy(q1,t1);
 254     vscale(t1,q2[3]);
 255
 256     vcopy(q2,t2);
 257     vscale(t2,q1[3]);
 258
 259     vcross(q2,q1,t3);
 260     vadd(t1,t2,tf);
 261     vadd(t3,tf,tf);
 262     tf[3] = q1[3] * q2[3] - vdot(q1,q2);
 263
 264     dest[0] = tf[0];
 265     dest[1] = tf[1];
 266     dest[2] = tf[2];
 267     dest[3] = tf[3];
 268
 269     if (++count > RENORMCOUNT) {
 270         count = 0;
 271         normalize_quat(dest);
 272     }
 273 }
 274
 275 /*
 276  * Quaternions always obey:  a^2 + b^2 + c^2 + d^2 = 1.0
 277  * If they don't add up to 1.0, dividing by their magnitued will
 278  * renormalize them.
 279  *
 280  * Note: See the following for more information on quaternions:
 281  *
 282  * - Shoemake, K., Animating rotation with quaternion curves, Computer
 283  *   Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
 284  * - Pletinckx, D., Quaternion calculus as a basic tool in computer
 285  *   graphics, The Visual Computer 5, 2-13, 1989.
 286  */
 287 static void
 288 normalize_quat(float q[4])
 289 {
 290     int i;
 291     float mag;
 292
 293     mag = (q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
 294     for (i = 0; i < 4; i++) q[i] /= mag;
 295 }
 296
 297 /*
 298  * Build a rotation matrix, given a quaternion rotation.
 299  *
 300  */
 301 void
 302 build_rotmatrix(float m[4][4], float q[4])
 303 {
 304     m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
 305     m[0][1] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
 306     m[0][2] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
 307     m[0][3] = 0.0;
 308
 309     m[1][0] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
 310     m[1][1]= 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
 311     m[1][2] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
 312     m[1][3] = 0.0;
 313
 314     m[2][0] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
 315     m[2][1] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
 316     m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);
 317     m[2][3] = 0.0;
 318
 319     m[3][0] = 0.0;
 320     m[3][1] = 0.0;
 321     m[3][2] = 0.0;
 322     m[3][3] = 1.0;
 323 }
 324