tutorial: trackball.c

File trackball.c, 8.9 KB (added by leon, 6 years ago)

Virtual trackball source for interactivity

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31 * Unpublished-- rights reserved under the copyright laws of the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 * 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#if defined(_WIN32)
53#pragma warning (disable:4244)          /* disable bogus conversion warnings */
54#endif
55#include <math.h>
56#include "trackball.h"
57
58/*
59 * This size should really be based on the distance from the center of
60 * rotation to the point on the object underneath the mouse.  That
61 * point would then track the mouse as closely as possible.  This is a
62 * simple example, though, so that is left as an Exercise for the
63 * Programmer.
64 */
65#define TRACKBALLSIZE  (0.8f)
66
67/*
68 * Local function prototypes (not defined in trackball.h)
69 */
70static float tb_project_to_sphere(float, float, float);
71static void normalize_quat(float [4]);
72
73void vzero(float *v)
74{
75    v[0] = 0.0;
76    v[1] = 0.0;
77    v[2] = 0.0;
78}
79
80void vset(float *v, float x, float y, float z)
81{
82    v[0] = x;
83    v[1] = y;
84    v[2] = z;
85}
86
87void 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
94void vcopy(const float *v1, float *v2)
95{
96    register int i;
97    for (i = 0 ; i < 3 ; i++)
98        v2[i] = v1[i];
99}
100
101void vcross(const float *v1, const float *v2, float *cross)
102{
103    float temp[3];
104
105    temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
106    temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
107    temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
108    vcopy(temp, cross);
109}
110
111float vlength(const float *v)
112{
113    return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
114}
115
116void vscale(float *v, float div)
117{
118    v[0] *= div;
119    v[1] *= div;
120    v[2] *= div;
121}
122
123void vnormal(float *v)
124{
125    vscale(v,1.0/vlength(v));
126}
127
128float vdot(const float *v1, const float *v2)
129{
130    return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
131}
132
133void vadd(const float *src1, const float *src2, float *dst)
134{
135    dst[0] = src1[0] + src2[0];
136    dst[1] = src1[1] + src2[1];
137    dst[2] = src1[2] + src2[2];
138}
139
140/*
141 * Ok, simulate a track-ball.  Project the points onto the virtual
142 * trackball, then figure out the axis of rotation, which is the cross
143 * product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
144 * Note:  This is a deformed trackball-- is a trackball in the center,
145 * but is deformed into a hyperbolic sheet of rotation away from the
146 * center.  This particular function was chosen after trying out
147 * several variations.
148 *
149 * It is assumed that the arguments to this routine are in the range
150 * (-1.0 ... 1.0)
151 */
152void trackball(float q[4], float p1x, float p1y, float p2x, float p2y)
153{
154    float a[3]; /* Axis of rotation */
155    float phi;  /* how much to rotate about axis */
156    float p1[3], p2[3], d[3];
157    float t;
158
159    if (p1x == p2x && p1y == p2y) {
160        /* Zero rotation */
161        vzero(q);
162        q[3] = 1.0;
163        return;
164    }
165
166    /*
167     * First, figure out z-coordinates for projection of P1 and P2 to
168     * deformed sphere
169     */
170    vset(p1,p1x,p1y,tb_project_to_sphere(TRACKBALLSIZE,p1x,p1y));
171    vset(p2,p2x,p2y,tb_project_to_sphere(TRACKBALLSIZE,p2x,p2y));
172
173    /*
174     *  Now, we want the cross product of P1 and P2
175     */
176    vcross(p2,p1,a);
177
178    /*
179     *  Figure out how much to rotate around that axis.
180     */
181    vsub(p1,p2,d);
182    t = vlength(d) / (2.0*TRACKBALLSIZE);
183
184    /*
185     * Avoid problems with out-of-control values...
186     */
187    if (t > 1.0) t = 1.0;
188    if (t < -1.0) t = -1.0;
189    phi = 2.0 * asin(t);
190
191    axis_to_quat(a,phi,q);
192}
193
194/*
195 *  Given an axis and angle, compute quaternion.
196 */
197void axis_to_quat(float a[3], float phi, float q[4])
198{
199    vnormal(a);
200    vcopy(a,q);
201    vscale(q,sin(phi/2.0));
202    q[3] = cos(phi/2.0);
203}
204
205/*
206 * Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
207 * if we are away from the center of the sphere.
208 */
209static float tb_project_to_sphere(float r, float x, float y)
210{
211    float d, t, z;
212
213    d = sqrt(x*x + y*y);
214    if (d < r * 0.70710678118654752440) {    /* Inside sphere */
215        z = sqrt(r*r - d*d);
216    } else {           /* On hyperbola */
217        t = r / 1.41421356237309504880;
218        z = t*t / d;
219    }
220    return z;
221}
222
223/*
224 * Given two rotations, e1 and e2, expressed as quaternion rotations,
225 * figure out the equivalent single rotation and stuff it into dest.
226 *
227 * This routine also normalizes the result every RENORMCOUNT times it is
228 * called, to keep error from creeping in.
229 *
230 * NOTE: This routine is written so that q1 or q2 may be the same
231 * as dest (or each other).
232 */
233
234#define RENORMCOUNT 97
235
236void add_quats(float q1[4], float q2[4], float dest[4])
237{
238    static int count=0;
239    float t1[4], t2[4], t3[4];
240    float tf[4];
241
242#if 0
243printf("q1 = %f %f %f %f\n", q1[0], q1[1], q1[2], q1[3]);
244printf("q2 = %f %f %f %f\n", q2[0], q2[1], q2[2], q2[3]);
245#endif
246
247    vcopy(q1,t1);
248    vscale(t1,q2[3]);
249
250    vcopy(q2,t2);
251    vscale(t2,q1[3]);
252
253    vcross(q2,q1,t3);
254    vadd(t1,t2,tf);
255    vadd(t3,tf,tf);
256    tf[3] = q1[3] * q2[3] - vdot(q1,q2);
257
258#if 0
259printf("tf = %f %f %f %f\n", tf[0], tf[1], tf[2], tf[3]);
260#endif
261
262    dest[0] = tf[0];
263    dest[1] = tf[1];
264    dest[2] = tf[2];
265    dest[3] = tf[3];
266
267    if (++count > RENORMCOUNT) {
268        count = 0;
269        normalize_quat(dest);
270    }
271}
272
273/*
274 * Quaternions always obey:  a^2 + b^2 + c^2 + d^2 = 1.0
275 * If they don't add up to 1.0, dividing by their magnitued will
276 * renormalize them.
277 *
278 * Note: See the following for more information on quaternions:
279 *
280 * - Shoemake, K., Animating rotation with quaternion curves, Computer
281 *   Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
282 * - Pletinckx, D., Quaternion calculus as a basic tool in computer
283 *   graphics, The Visual Computer 5, 2-13, 1989.
284 */
285static void normalize_quat(float q[4])
286{
287    int i;
288    float mag;
289
290    mag = sqrt(q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);
291    for (i = 0; i < 4; i++) q[i] /= mag;
292}
293
294/*
295 * Build a rotation matrix, given a quaternion rotation.
296 *
297 */
298void build_rotmatrix(float m[4][4], float q[4])
299{
300    m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
301    m[0][1] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
302    m[0][2] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
303    m[0][3] = 0.0;
304
305    m[1][0] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
306    m[1][1]= 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
307    m[1][2] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
308    m[1][3] = 0.0;
309
310    m[2][0] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
311    m[2][1] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
312    m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);
313    m[2][3] = 0.0;
314
315    m[3][0] = 0.0;
316    m[3][1] = 0.0;
317    m[3][2] = 0.0;
318    m[3][3] = 1.0;
319}
320
321/* Fortran wrappers */
322void trackball_(float *q, float *p1x, float *p1y, float *p2x, float *p2y)
323{
324   trackball( q, *p1x, *p1y, *p2x, *p2y);
325}
326 
327void add_quats__(float q1[4], float q2[4], float dest[4])
328{
329        add_quats(q1, q2, dest);
330}
331
332void build_rotmatrix__(float m[4][4], float q[4])
333{
334     /* matrix m is transposed twice. No need to do this here */
335     build_rotmatrix(m, q);
336}
337
338