source: research/2008-rubik/colorcube/trackball.c @ 2677

Last change on this file since 2677 was 2677, checked in by Sam Hocevar, 14 years ago
  • Test stuff for the Rubik's cube colour reduction.
File size: 8.4 KB
Line 
1/*
2 * (c) Copyright 1993, 1994, Silicon Graphics, Inc.
3 * ALL RIGHTS RESERVED
4 * Permission to use, copy, modify, and distribute this software for
5 * any purpose and without fee is hereby granted, provided that the above
6 * copyright notice appear in all copies and that both the copyright notice
7 * and this permission notice appear in supporting documentation, and that
8 * the name of Silicon Graphics, Inc. not be used in advertising
9 * or publicity pertaining to distribution of the software without specific,
10 * written prior permission.
11 *
12 * THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "AS-IS"
13 * AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE,
14 * INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR
15 * FITNESS FOR A PARTICULAR PURPOSE.  IN NO EVENT SHALL SILICON
16 * GRAPHICS, INC.  BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT,
17 * SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY
18 * KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION,
19 * LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF
20 * THIRD PARTIES, WHETHER OR NOT SILICON GRAPHICS, INC.  HAS BEEN
21 * ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON
22 * ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE
23 * POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE.
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
28 * (c)(1)(ii) of the Rights in Technical Data and Computer Software
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31 * Unpublished-- rights reserved under the copyright laws of the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/*
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#include <math.h>
54#include "trackball.h"
55
56/*
57 * This size should really be based on the distance from the center of
58 * rotation to the point on the object underneath the mouse.  That
59 * point would then track the mouse as closely as possible.  This is a
60 * simple example, though, so that is left as an Exercise for the
61 * Programmer.
62 */
63#define TRACKBALLSIZE  (0.4f)
64
65/*
66 * Local function prototypes (not defined in trackball.h)
67 */
68static float tb_project_to_sphere(float, float, float);
69static void normalize_quat(float [4]);
70
71static void
72vzero(float *v)
73{
74    v[0] = 0.0;
75    v[1] = 0.0;
76    v[2] = 0.0;
77}
78
79static void
80vset(float *v, float x, float y, float z)
81{
82    v[0] = x;
83    v[1] = y;
84    v[2] = z;
85}
86
87static void
88vsub(const float *src1, const float *src2, float *dst)
89{
90    dst[0] = src1[0] - src2[0];
91    dst[1] = src1[1] - src2[1];
92    dst[2] = src1[2] - src2[2];
93}
94
95static void
96vcopy(const float *v1, float *v2)
97{
98    register int i;
99    for (i = 0 ; i < 3 ; i++)
100        v2[i] = v1[i];
101}
102
103static void
104vcross(const float *v1, const float *v2, float *cross)
105{
106    float temp[3];
107
108    temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
109    temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
110    temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
111    vcopy(temp, cross);
112}
113
114static float
115vlength(const float *v)
116{
117    return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
118}
119
120static void
121vscale(float *v, float div)
122{
123    v[0] *= div;
124    v[1] *= div;
125    v[2] *= div;
126}
127
128static void
129vnormal(float *v)
130{
131    vscale(v,1.0f/vlength(v));
132}
133
134static float
135vdot(const float *v1, const float *v2)
136{
137    return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
138}
139
140static void
141vadd(const float *src1, const float *src2, float *dst)
142{
143    dst[0] = src1[0] + src2[0];
144    dst[1] = src1[1] + src2[1];
145    dst[2] = src1[2] + src2[2];
146}
147
148/*
149 * Ok, simulate a track-ball.  Project the points onto the virtual
150 * trackball, then figure out the axis of rotation, which is the cross
151 * product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
152 * Note:  This is a deformed trackball-- is a trackball in the center,
153 * but is deformed into a hyperbolic sheet of rotation away from the
154 * center.  This particular function was chosen after trying out
155 * several variations.
156 *
157 * It is assumed that the arguments to this routine are in the range
158 * (-1.0 ... 1.0)
159 */
160void
161trackball(float q[4], float p1x, float p1y, float p2x, float p2y)
162{
163    float a[3]; /* Axis of rotation */
164    float phi;  /* how much to rotate about axis */
165    float p1[3], p2[3], d[3];
166    float t;
167
168    if (p1x == p2x && p1y == p2y) {
169        /* Zero rotation */
170        vzero(q);
171        q[3] = 1.0;
172        return;
173    }
174
175    /*
176     * First, figure out z-coordinates for projection of P1 and P2 to
177     * deformed sphere
178     */
179    vset(p1,p1x,p1y,tb_project_to_sphere(TRACKBALLSIZE,p1x,p1y));
180    vset(p2,p2x,p2y,tb_project_to_sphere(TRACKBALLSIZE,p2x,p2y));
181
182    /*
183     *  Now, we want the cross product of P1 and P2
184     */
185    vcross(p2,p1,a);
186
187    /*
188     *  Figure out how much to rotate around that axis.
189     */
190    vsub(p1,p2,d);
191    t = vlength(d) / (2.0f*TRACKBALLSIZE);
192
193    /*
194     * Avoid problems with out-of-control values...
195     */
196    if (t > 1.0f) t = 1.0f;
197    if (t < -1.0f) t = -1.0f;
198    phi = 2.0f * asin(t);
199
200    axis_to_quat(a,phi,q);
201}
202
203/*
204 *  Given an axis and angle, compute quaternion.
205 */
206void
207axis_to_quat(float a[3], float phi, float q[4])
208{
209    vnormal(a);
210    vcopy(a,q);
211    vscale(q,sin(phi/2.0f));
212    q[3] = cos(phi/2.0f);
213}
214
215/*
216 * Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
217 * if we are away from the center of the sphere.
218 */
219static float
220tb_project_to_sphere(float r, float x, float y)
221{
222    float d, t, z;
223
224    d = sqrt(x*x + y*y);
225    if (d < r * 0.70710678118654752440f) {    /* Inside sphere */
226        z = sqrt(r*r - d*d);
227    } else {           /* On hyperbola */
228        t = r / 1.41421356237309504880f;
229        z = t*t / d;
230    }
231    return z;
232}
233
234/*
235 * Given two rotations, e1 and e2, expressed as quaternion rotations,
236 * figure out the equivalent single rotation and stuff it into dest.
237 *
238 * This routine also normalizes the result every RENORMCOUNT times it is
239 * called, to keep error from creeping in.
240 *
241 * NOTE: This routine is written so that q1 or q2 may be the same
242 * as dest (or each other).
243 */
244
245#define RENORMCOUNT 97
246
247void
248add_quats(float q1[4], float q2[4], float dest[4])
249{
250    static int count=0;
251    float t1[4], t2[4], t3[4];
252    float tf[4];
253
254    vcopy(q1,t1);
255    vscale(t1,q2[3]);
256
257    vcopy(q2,t2);
258    vscale(t2,q1[3]);
259
260    vcross(q2,q1,t3);
261    vadd(t1,t2,tf);
262    vadd(t3,tf,tf);
263    tf[3] = q1[3] * q2[3] - vdot(q1,q2);
264
265    dest[0] = tf[0];
266    dest[1] = tf[1];
267    dest[2] = tf[2];
268    dest[3] = tf[3];
269
270    if (++count > RENORMCOUNT) {
271        count = 0;
272        normalize_quat(dest);
273    }
274}
275
276/*
277 * Quaternions always obey:  a^2 + b^2 + c^2 + d^2 = 1.0
278 * If they don't add up to 1.0, dividing by their magnitued will
279 * renormalize them.
280 *
281 * Note: See the following for more information on quaternions:
282 *
283 * - Shoemake, K., Animating rotation with quaternion curves, Computer
284 *   Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
285 * - Pletinckx, D., Quaternion calculus as a basic tool in computer
286 *   graphics, The Visual Computer 5, 2-13, 1989.
287 */
288static void
289normalize_quat(float q[4])
290{
291    int i;
292    float mag;
293
294    mag = (q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
295    for (i = 0; i < 4; i++) q[i] /= mag;
296}
297
298/*
299 * Build a rotation matrix, given a quaternion rotation.
300 *
301 */
302void
303build_rotmatrix(float m[4][4], float q[4])
304{
305    m[0][0] = 1.0f - 2.0f * (q[1] * q[1] + q[2] * q[2]);
306    m[0][1] = 2.0f * (q[0] * q[1] - q[2] * q[3]);
307    m[0][2] = 2.0f * (q[2] * q[0] + q[1] * q[3]);
308    m[0][3] = 0.0f;
309
310    m[1][0] = 2.0f * (q[0] * q[1] + q[2] * q[3]);
311    m[1][1]= 1.0f - 2.0f * (q[2] * q[2] + q[0] * q[0]);
312    m[1][2] = 2.0f * (q[1] * q[2] - q[0] * q[3]);
313    m[1][3] = 0.0f;
314
315    m[2][0] = 2.0f * (q[2] * q[0] - q[1] * q[3]);
316    m[2][1] = 2.0f * (q[1] * q[2] + q[0] * q[3]);
317    m[2][2] = 1.0f - 2.0f * (q[1] * q[1] + q[0] * q[0]);
318    m[2][3] = 0.0f;
319
320    m[3][0] = 0.0f;
321    m[3][1] = 0.0f;
322    m[3][2] = 0.0f;
323    m[3][3] = 1.0f;
324}
325
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