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31 * Unpublished-- rights reserved under the copyright laws of the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 #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
vzero(float * v)71 vzero(float *v)
72 {
73 v[0] = 0.0;
74 v[1] = 0.0;
75 v[2] = 0.0;
76 }
77
78 void
vset(float * v,float x,float y,float z)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
vsub(const float * src1,const float * src2,float * dst)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
vcopy(const float * v1,float * v2)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
vcross(const float * v1,const float * v2,float * cross)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
vlength(const float * v)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
vscale(float * v,float div)120 vscale(float *v, float div)
121 {
122 v[0] *= div;
123 v[1] *= div;
124 v[2] *= div;
125 }
126
127 void
vnormal(float * v)128 vnormal(float *v)
129 {
130 vscale(v,1.0/vlength(v));
131 }
132
133 float
vdot(const float * v1,const float * v2)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
vadd(const float * src1,const float * src2,float * dst)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
trackball(float q[4],float p1x,float p1y,float p2x,float p2y)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
axis_to_quat(float a[3],float phi,float q[4])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
tb_project_to_sphere(float r,float x,float y)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
add_quats(float q1[4],float q2[4],float dest[4])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
normalize_quat(float q[4])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
build_rotmatrix(float m[4][4],float q[4])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
325