demos/gl/TrackBall.d

   1 /*
   2  * Adapted to D by Antonio Monteiro
   3  */
   4 /*
   5  * (c) Copyright 1993, 1994, Silicon Graphics, Inc.
   6  * ALL RIGHTS RESERVED
   7  * Permission to use, copy, modify, and distribute this software for
   8  * any purpose and without fee is hereby granted, provided that the above
   9  * copyright notice appear in all copies and that both the copyright notice
  10  * and this permission notice appear in supporting documentation, and that
  11  * the name of Silicon Graphics, Inc. not be used in advertising
  12  * or publicity pertaining to distribution of the software without specific,
  13  * written prior permission.
  14  *
  15  * THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "AS-IS"
  16  * AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE,
  17  * INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR
  18  * FITNESS FOR A PARTICULAR PURPOSE.  IN NO EVENT SHALL SILICON
  19  * GRAPHICS, INC.  BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT,
  20  * SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY
  21  * KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION,
  22  * LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF
  23  * THIRD PARTIES, WHETHER OR NOT SILICON GRAPHICS, INC.  HAS BEEN
  24  * ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON
  25  * ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE
  26  * POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE.
  27  *
  28  * US Government Users Restricted Rights
  29  * Use, duplication, or disclosure by the Government is subject to
  30  * restrictions set forth in FAR 52.227.19(c)(2) or subparagraph
  31  * (c)(1)(ii) of the Rights in Technical Data and Computer Software
  32  * clause at DFARS 252.227-7013 and/or in similar or successor
  33  * clauses in the FAR or the DOD or NASA FAR Supplement.
  34  * Unpublished-- rights reserved under the copyright laws of the
  35  * United States.  Contractor/manufacturer is Silicon Graphics,
  36  * Inc., 2011 N.  Shoreline Blvd., Mountain View, CA 94039-7311.
  37  *
  38  * OpenGL(TM) is a trademark of Silicon Graphics, Inc.
  39  */
  40 /*
  41  * trackball.h
  42  * A virtual trackball implementation
  43  * Written by Gavin Bell for Silicon Graphics, November 1988.
  44  */
  45
  46 /*
  47  * This size should really be based on the distance from the center of
  48  * rotation to the point on the object underneath the mouse.  That
  49  * point would then track the mouse as closely as possible.  This is a
  50  * simple example, though, so that is left as an Exercise for the
  51  * Programmer.
  52  */
  53
  54 module gl.TrackBall;
  55
  56 private import std.math;
  57
  58 public:
  59 const float TRACKBALLSIZE = 0.8;
  60 const int RENORMCOUNT = 97;
  61
  62 /**
  63  * Pass the x and y coordinates of the last and current positions of
  64  * the mouse, scaled so they are from (-1.0 ... 1.0).
  65  *
  66  * The resulting rotation is returned as a quaternion rotation in the
  67  * first paramater.
  68  */
  69 void
  70 trackball(float q[4], float p1x, float p1y, float p2x, float p2y)
  71 {
  72 /*
  73  * Ok, simulate a track-ball.  Project the points onto the virtual
  74  * trackball, then figure out the axis of rotation, which is the cross
  75  * product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
  76  * Note:  This is a deformed trackball-- is a trackball in the center,
  77  * but is deformed into a hyperbolic sheet of rotation away from the
  78  * center.  This particular function was chosen after trying out
  79  * several variations.
  80  *
  81  * It is assumed that the arguments to this routine are in the range
  82  * (-1.0 ... 1.0)
  83  */
  84     float[3] a; /* Axis of rotation */
  85     float phi;  /* how much to rotate about axis */
  86     float[3] p1;
  87         float[3] p2;
  88         float[3] d;
  89     float t;
  90
  91     if (p1x == p2x && p1y == p2y) {
  92         /* Zero rotation */
  93         vzero(q.ptr);
  94         q[3] = 1.0;
  95         return;
  96     }
  97
  98     /*
  99      * First, figure out z-coordinates for projection of P1 and P2 to
 100      * deformed sphere
 101      */
 102     vset(p1,p1x,p1y,tb_project_to_sphere(TRACKBALLSIZE,p1x,p1y));
 103     vset(p2,p2x,p2y,tb_project_to_sphere(TRACKBALLSIZE,p2x,p2y));
 104
 105     /*
 106      *  Now, we want the cross product of P1 and P2
 107      */
 108     vcross(p2.ptr,p1.ptr,a.ptr);
 109
 110     /*
 111      *  Figure out how much to rotate around that axis.
 112      */
 113     vsub(p1,p2,d);
 114     t = vlength(d) / (2.0*TRACKBALLSIZE);
 115
 116     /*
 117      * Avoid problems with out-of-control values...
 118      */
 119     if (t > 1.0) t = 1.0;
 120     if (t < -1.0) t = -1.0;
 121     phi = 2.0 * std.math.asin(t);
 122
 123     axis_to_quat(a,phi,q);
 124 }
 125
 126
 127 /*
 128  * Given two quaternions, add them together to get a third quaternion.
 129  * Adding quaternions to get a compound rotation is analagous to adding
 130  * translations to get a compound translation.  When incrementally
 131  * adding rotations, the first argument here should be the new
 132  * rotation, the second and third the total rotation (which will be
 133  * over-written with the resulting new total rotation).
 134  */
 135 void
 136 add_quats(float[4] q1, float[4] q2, float[4] dest)
 137 {
 138 /*
 139  * Given two rotations, e1 and e2, expressed as quaternion rotations,
 140  * figure out the equivalent single rotation and stuff it into dest.
 141  *
 142  * This routine also normalizes the result every RENORMCOUNT times it is
 143  * called, to keep error from creeping in.
 144  *
 145  * NOTE: This routine is written so that q1 or q2 may be the same
 146  * as dest (or each other).
 147  */
 148     static int count=0;
 149     float[4] t1;
 150     float[4] t2;
 151     float[4] t3;
 152     float tf[4];
 153
 154     vcopy(q1.ptr,t1.ptr);
 155     vscale(t1.ptr,q2[3]);
 156
 157     vcopy(q2.ptr,t2.ptr);
 158     vscale(t2.ptr,q1[3]);
 159
 160     vcross(q2.ptr,q1.ptr,t3.ptr);
 161     vadd(t1.ptr,t2.ptr,tf.ptr);
 162     vadd(t3.ptr,tf.ptr,tf.ptr);
 163     tf[3] = q1[3] * q2[3] - vdot(q1.ptr,q2.ptr);
 164
 165     dest[0] = tf[0];
 166     dest[1] = tf[1];
 167     dest[2] = tf[2];
 168     dest[3] = tf[3];
 169
 170     if (++count > RENORMCOUNT) {
 171         count = 0;
 172         normalize_quat(dest);
 173     }
 174 }
 175
 176
 177 /*
 178  * A useful function, builds a rotation matrix in Matrix based on
 179  * given quaternion.
 180  */
 181 void
 182 build_rotmatrix(float[4][4] m, float[4] q)
 183 {
 184     m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
 185     m[0][1] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
 186     m[0][2] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
 187     m[0][3] = 0.0;
 188
 189     m[1][0] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
 190     m[1][1]= 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
 191     m[1][2] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
 192     m[1][3] = 0.0;
 193
 194     m[2][0] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
 195     m[2][1] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
 196     m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);
 197     m[2][3] = 0.0;
 198
 199     m[3][0] = 0.0;
 200     m[3][1] = 0.0;
 201     m[3][2] = 0.0;
 202     m[3][3] = 1.0;
 203 }
 204
 205
 206 /*
 207  * This function computes a quaternion based on an axis (defined by
 208  * the given vector) and an angle about which to rotate.  The angle is
 209  * expressed in radians.  The result is put into the third argument.
 210  */
 211 void
 212 axis_to_quat(float[3] a, float phi, float[4] q)
 213 {
 214     vnormal(a);
 215     vcopy(a.ptr,q.ptr);
 216     vscale(q.ptr,sin(phi/2.0));
 217     q[3] = cos(phi/2.0);
 218 }
 219
 220 /*
 221  * Quaternions always obey:  a^2 + b^2 + c^2 + d^2 = 1.0
 222  * If they don't add up to 1.0, dividing by their magnitued will
 223  * renormalize them.
 224  *
 225  * Note: See the following for more information on quaternions:
 226  *
 227  * - Shoemake, K., Animating rotation with quaternion curves, Computer
 228  *   Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
 229  * - Pletinckx, D., Quaternion calculus as a basic tool in computer
 230  *   graphics, The Visual Computer 5, 2-13, 1989.
 231  */
 232 static void
 233 normalize_quat(float[4] q)
 234 {
 235     int i;
 236     float mag;
 237
 238     mag = (q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
 239     for (i = 0; i < 4; i++) q[i] /= mag;
 240 }
 241
 242 /*
 243  * Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
 244  * if we are away from the center of the sphere.
 245  */
 246 static float
 247 tb_project_to_sphere(float r, float x, float y)
 248 {
 249     float d, t, z;
 250
 251     d = sqrt(x*x + y*y);
 252     if (d < r * 0.70710678118654752440) {    /* Inside sphere */
 253         z = sqrt(r*r - d*d);
 254     } else {           /* On hyperbola */
 255         t = r / 1.41421356237309504880;
 256         z = t*t / d;
 257     }
 258     return z;
 259 }
 260
 261 void
 262 vzero(float* v)
 263 {
 264     v[0] = 0.0;
 265     v[1] = 0.0;
 266     v[2] = 0.0;
 267 }
 268
 269 void
 270 vset(float[3] v, float x, float y, float z)
 271 {
 272     v[0] = x;
 273     v[1] = y;
 274     v[2] = z;
 275 }
 276
 277 void
 278 vsub(float[3] src1, float[3] src2, float[3] dst)
 279 {
 280     dst[0] = src1[0] - src2[0];
 281     dst[1] = src1[1] - src2[1];
 282     dst[2] = src1[2] - src2[2];
 283 }
 284
 285 void
 286 vcopy(float* v1, float* v2)
 287 {
 288     int i;
 289     for (i = 0 ; i < 3 ; i++)
 290         v2[i] = v1[i];
 291 }
 292
 293 void
 294 vcross(float* v1, float* v2, float* cross)
 295 {
 296     float[3] temp;
 297
 298     temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
 299     temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
 300     temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
 301     vcopy(temp.ptr, cross);
 302 }
 303
 304 float
 305 vlength(float[3] v)
 306 {
 307     return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
 308 }
 309
 310 void
 311 vscale(float* v, float div)
 312 {
 313     v[0] *= div;
 314     v[1] *= div;
 315     v[2] *= div;
 316 }
 317
 318 void
 319 vnormal(float[3] v)
 320 {
 321     vscale(v.ptr,1.0/vlength(v));
 322 }
 323
 324 float
 325 vdot(float* v1, float* v2)
 326 {
 327     return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
 328 }
 329
 330 void
 331 vadd(float* src1, float* src2, float* dst)
 332 {
 333     dst[0] = src1[0] + src2[0];
 334     dst[1] = src1[1] + src2[1];
 335     dst[2] = src1[2] + src2[2];
 336 }
 337