opengl/trackball.cpp

   1 #include <stdio.h>
   2 /*
   3  * (c) Copyright 1993, 1994, Silicon Graphics, Inc.
   4  * ALL RIGHTS RESERVED
   5  * Permission to use, copy, modify, and distribute this software for
   6  * any purpose and without fee is hereby granted, provided that the above
   7  * copyright notice appear in all copies and that both the copyright notice
   8  * and this permission notice appear in supporting documentation, and that
   9  * the name of Silicon Graphics, Inc. not be used in advertising
  10  * or publicity pertaining to distribution of the software without specific,
  11  * written prior permission.
  12  *
  13  * THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "AS-IS"
  14  * AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE,
  15  * INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR
  16  * FITNESS FOR A PARTICULAR PURPOSE.  IN NO EVENT SHALL SILICON
  17  * GRAPHICS, INC.  BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT,
  18  * SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY
  19  * KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION,
  20  * LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF
  21  * THIRD PARTIES, WHETHER OR NOT SILICON GRAPHICS, INC.  HAS BEEN
  22  * ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON
  23  * ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE
  24  * POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE.
  25  *
  26  * US Government Users Restricted Rights
  27  * Use, duplication, or disclosure by the Government is subject to
  28  * restrictions set forth in FAR 52.227.19(c)(2) or subparagraph
  29  * (c)(1)(ii) of the Rights in Technical Data and Computer Software
  30  * clause at DFARS 252.227-7013 and/or in similar or successor
  31  * clauses in the FAR or the DOD or NASA FAR Supplement.
  32  * Unpublished-- rights reserved under the copyright laws of the
  33  * United States.  Contractor/manufacturer is Silicon Graphics,
  34  * Inc., 2011 N.  Shoreline Blvd., Mountain View, CA 94039-7311.
  35  *
  36  * OpenGL(TM) is a trademark of Silicon Graphics, Inc.
  37  */
  38 /*
  39  * Trackball code:
  40  *
  41  * Implementation of a virtual trackball.
  42  * Implemented by Gavin Bell, lots of ideas from Thant Tessman and
  43  *   the August '88 issue of Siggraph's "Computer Graphics," pp. 121-129.
  44  *
  45  * Vector manip code:
  46  *
  47  * Original code from:
  48  * David M. Ciemiewicz, Mark Grossman, Henry Moreton, and Paul Haeberli
  49  *
  50  * Much mucking with by:
  51  * Gavin Bell
  52  */
  53 #if defined(_WIN32)
  54 #pragma warning (disable:4244)          /* disable bogus conversion warnings */
  55 #endif
  56 #include <math.h>
  57 #include "trackball.h"
  58
  59 /*
  60  * This size should really be based on the distance from the center of
  61  * rotation to the point on the object underneath the mouse.  That
  62  * point would then track the mouse as closely as possible.  This is a
  63  * simple example, though, so that is left as an Exercise for the
  64  * Programmer.
  65  */
  66 #define TRACKBALLSIZE  (0.8f)
  67
  68 /*
  69  * Local function prototypes (not defined in trackball.h)
  70  */
  71 static float tb_project_to_sphere(float, float, float);
  72 static void normalize_quat(float [4]);
  73
  74 static void
  75 vzero(float v[3])
  76 {
  77     v[0] = 0.0;
  78     v[1] = 0.0;
  79     v[2] = 0.0;
  80 }
  81
  82 static void
  83 vset(float v[3], float x, float y, float z)
  84 {
  85     v[0] = x;
  86     v[1] = y;
  87     v[2] = z;
  88 }
  89
  90 static void
  91 vsub(const float src1[3], const float src2[3], float dst[3])
  92 {
  93     dst[0] = src1[0] - src2[0];
  94     dst[1] = src1[1] - src2[1];
  95     dst[2] = src1[2] - src2[2];
  96 }
  97
  98 static void
  99 vcopy(const float v1[3], float v2[3])
 100 {
 101     register int i;
 102     for (i = 0 ; i < 3 ; i++)
 103         v2[i] = v1[i];
 104 }
 105
 106 static void
 107 vcross(const float v1[3], const float v2[3], float cross[3])
 108 {
 109     float temp[3];
 110
 111     temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
 112     temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
 113     temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
 114     vcopy(temp, cross);
 115 }
 116
 117 static float
 118 vlength(const float v[3])
 119 {
 120     return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
 121 }
 122
 123 static void
 124 vscale(float v[3], float div)
 125 {
 126     v[0] *= div;
 127     v[1] *= div;
 128     v[2] *= div;
 129 }
 130
 131 static void
 132 vnormal(float v[3])
 133 {
 134     vscale(v,1.0/vlength(v));
 135 }
 136
 137 static float
 138 vdot(const float v1[3], const float v2[3])
 139 {
 140     return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
 141 }
 142
 143 static void
 144 vadd(const float src1[3], const float src2[3], float dst[3])
 145 {
 146     dst[0] = src1[0] + src2[0];
 147     dst[1] = src1[1] + src2[1];
 148     dst[2] = src1[2] + src2[2];
 149 }
 150
 151 /*
 152  * Ok, simulate a track-ball.  Project the points onto the virtual
 153  * trackball, then figure out the axis of rotation, which is the cross
 154  * product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
 155  * Note:  This is a deformed trackball-- is a trackball in the center,
 156  * but is deformed into a hyperbolic sheet of rotation away from the
 157  * center.  This particular function was chosen after trying out
 158  * several variations.
 159  *
 160  * It is assumed that the arguments to this routine are in the range
 161  * (-1.0 ... 1.0)
 162  */
 163 void
 164 trackball(float q[4], float p1x, float p1y, float p2x, float p2y)
 165 {
 166     float a[3]; /* Axis of rotation */
 167     float phi;  /* how much to rotate about axis */
 168     float p1[3], p2[3], d[3];
 169     float t;
 170
 171     if (p1x == p2x && p1y == p2y) {
 172         /* Zero rotation */
 173         vzero(q);
 174         q[3] = 1.0;
 175         return;
 176     }
 177
 178     /*
 179      * First, figure out z-coordinates for projection of P1 and P2 to
 180      * deformed sphere
 181      */
 182     vset(p1,p1x,p1y,tb_project_to_sphere(TRACKBALLSIZE,p1x,p1y));
 183     vset(p2,p2x,p2y,tb_project_to_sphere(TRACKBALLSIZE,p2x,p2y));
 184
 185     /*
 186      *  Now, we want the cross product of P1 and P2
 187      */
 188     vcross(p2,p1,a);
 189
 190     /*
 191      *  Figure out how much to rotate around that axis.
 192      */
 193     vsub(p1,p2,d);
 194     t = vlength(d) / (2.0*TRACKBALLSIZE);
 195
 196     /*
 197      * Avoid problems with out-of-control values...
 198      */
 199     if (t > 1.0) t = 1.0;
 200     if (t < -1.0) t = -1.0;
 201     phi = 2.0 * asin(t);
 202
 203     axis_to_quat(a,phi,q);
 204 }
 205
 206 /*
 207  *  Given an axis and angle, compute quaternion.
 208  */
 209 void
 210 axis_to_quat(const float a[3], float phi, float q[4])
 211 {
 212     vcopy(a,q);
 213     vnormal(q);
 214     vscale(q, sin(phi/2.0));
 215     q[3] = cos(phi/2.0);
 216 }
 217
 218 /*
 219  * Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
 220  * if we are away from the center of the sphere.
 221  */
 222 static float
 223 tb_project_to_sphere(float r, float x, float y)
 224 {
 225     float d, t, z;
 226
 227     d = sqrt(x*x + y*y);
 228     if (d < r * 0.70710678118654752440) {    /* Inside sphere */
 229         z = sqrt(r*r - d*d);
 230     } else {           /* On hyperbola */
 231         t = r / 1.41421356237309504880;
 232         z = t*t / d;
 233     }
 234     return z;
 235 }
 236
 237 /*
 238  * Given two rotations, e1 and e2, expressed as quaternion rotations,
 239  * figure out the equivalent single rotation and stuff it into dest.
 240  *
 241  * This routine also normalizes the result every RENORMCOUNT times it is
 242  * called, to keep error from creeping in.
 243  *
 244  * NOTE: This routine is written so that q1 or q2 may be the same
 245  * as dest (or each other).
 246  */
 247
 248 #define RENORMCOUNT 97
 249
 250 void
 251 add_quats(const float q1[4], const float q2[4], float dest[4])
 252 {
 253     static int count=0;
 254     float t1[4], t2[4], t3[4];
 255     float tf[4];
 256
 257 #if 0
 258 printf("q1 = %f %f %f %f\n", q1[0], q1[1], q1[2], q1[3]);
 259 printf("q2 = %f %f %f %f\n", q2[0], q2[1], q2[2], q2[3]);
 260 #endif
 261
 262     vcopy(q1,t1);
 263     vscale(t1,q2[3]);
 264
 265     vcopy(q2,t2);
 266     vscale(t2,q1[3]);
 267
 268     vcross(q2,q1,t3);
 269     vadd(t1,t2,tf);
 270     vadd(t3,tf,tf);
 271     tf[3] = q1[3] * q2[3] - vdot(q1,q2);
 272
 273 #if 0
 274 printf("tf = %f %f %f %f\n", tf[0], tf[1], tf[2], tf[3]);
 275 #endif
 276
 277     dest[0] = tf[0];
 278     dest[1] = tf[1];
 279     dest[2] = tf[2];
 280     dest[3] = tf[3];
 281
 282     if (++count > RENORMCOUNT) {
 283         count = 0;
 284         normalize_quat(dest);
 285     }
 286 }
 287
 288 /*
 289  * Quaternions always obey:  a^2 + b^2 + c^2 + d^2 = 1.0
 290  * If they don't add up to 1.0, dividing by their magnitued will
 291  * renormalize them.
 292  *
 293  * Note: See the following for more information on quaternions:
 294  *
 295  * - Shoemake, K., Animating rotation with quaternion curves, Computer
 296  *   Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
 297  * - Pletinckx, D., Quaternion calculus as a basic tool in computer
 298  *   graphics, The Visual Computer 5, 2-13, 1989.
 299  */
 300 static void
 301 normalize_quat(float q[4])
 302 {
 303     int i;
 304     float mag;
 305
 306     mag = sqrt(q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
 307     for (i = 0; i < 4; i++)
 308         q[i] /= mag;
 309 }
 310
 311 /*
 312  * Build a rotation matrix, given a quaternion rotation.
 313  *
 314  */
 315 void
 316 build_rotmatrix(float m[4][4], const float q[4])
 317 {
 318     m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
 319     m[0][1] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
 320     m[0][2] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
 321     m[0][3] = 0.0;
 322
 323     m[1][0] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
 324     m[1][1]= 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
 325     m[1][2] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
 326     m[1][3] = 0.0;
 327
 328     m[2][0] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
 329     m[2][1] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
 330     m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);
 331     m[2][3] = 0.0;
 332
 333     m[3][0] = 0.0;
 334     m[3][1] = 0.0;
 335     m[3][2] = 0.0;
 336     m[3][3] = 1.0;
 337 }
 338