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31 * Unpublished-- rights reserved under the copyright laws of the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
vzero(float * v)70 void vzero(float *v)
71 {
72 v[0] = 0.0;
73 v[1] = 0.0;
74 v[2] = 0.0;
75 }
76
vset(float * v,float x,float y,float z)77 void vset(float *v, float x, float y, float z)
78 {
79 v[0] = x;
80 v[1] = y;
81 v[2] = z;
82 }
83
vsub(const float * src1,const float * src2,float * dst)84 void vsub(const float *src1, const float *src2, float *dst)
85 {
86 dst[0] = src1[0] - src2[0];
87 dst[1] = src1[1] - src2[1];
88 dst[2] = src1[2] - src2[2];
89 }
90
vcopy(const float * v1,float * v2)91 void vcopy(const float *v1, float *v2)
92 {
93 register int i;
94 for (i = 0; i < 3; i++)
95 v2[i] = v1[i];
96 }
97
vcross(const float * v1,const float * v2,float * cross)98 void vcross(const float *v1, const float *v2, float *cross)
99 {
100 float temp[3];
101
102 temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
103 temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
104 temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
105 vcopy(temp, cross);
106 }
107
vlength(const float * v)108 float vlength(const float *v)
109 {
110 return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
111 }
112
vscale(float * v,float div)113 void vscale(float *v, float div)
114 {
115 v[0] *= div;
116 v[1] *= div;
117 v[2] *= div;
118 }
119
vnormal(float * v)120 void vnormal(float *v)
121 {
122 vscale(v, 1.0 / vlength(v));
123 }
124
vdot(const float * v1,const float * v2)125 float vdot(const float *v1, const float *v2)
126 {
127 return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
128 }
129
vadd(const float * src1,const float * src2,float * dst)130 void vadd(const float *src1, const float *src2, float *dst)
131 {
132 dst[0] = src1[0] + src2[0];
133 dst[1] = src1[1] + src2[1];
134 dst[2] = src1[2] + src2[2];
135 }
136
137 /*
138 * Ok, simulate a track-ball. Project the points onto the virtual
139 * trackball, then figure out the axis of rotation, which is the cross
140 * product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
141 * Note: This is a deformed trackball-- is a trackball in the center,
142 * but is deformed into a hyperbolic sheet of rotation away from the
143 * center. This particular function was chosen after trying out
144 * several variations.
145 *
146 * It is assumed that the arguments to this routine are in the range
147 * (-1.0 ... 1.0)
148 */
trackball(float q[4],float p1x,float p1y,float p2x,float p2y)149 void trackball(float q[4], float p1x, float p1y, float p2x, float p2y)
150 {
151 float a[3]; /* Axis of rotation */
152 float phi; /* how much to rotate about axis */
153 float p1[3], p2[3], d[3];
154 float t;
155
156 if (p1x == p2x && p1y == p2y) {
157 /* Zero rotation */
158 vzero(q);
159 q[3] = 1.0;
160 return;
161 }
162
163 /*
164 * First, figure out z-coordinates for projection of P1 and P2 to
165 * deformed sphere
166 */
167 vset(p1, p1x, p1y, tb_project_to_sphere(TRACKBALLSIZE, p1x, p1y));
168 vset(p2, p2x, p2y, tb_project_to_sphere(TRACKBALLSIZE, p2x, p2y));
169
170 /*
171 * Now, we want the cross product of P1 and P2
172 */
173 vcross(p2, p1, a);
174
175 /*
176 * Figure out how much to rotate around that axis.
177 */
178 vsub(p1, p2, d);
179 t = vlength(d) / (2.0 * TRACKBALLSIZE);
180
181 /*
182 * Avoid problems with out-of-control values...
183 */
184 if (t > 1.0)
185 t = 1.0;
186 if (t < -1.0)
187 t = -1.0;
188 phi = 2.0 * asin(t);
189
190 axis_to_quat(a, phi, q);
191 }
192
193 /*
194 * Given an axis and angle, compute quaternion.
195 */
axis_to_quat(float a[3],float phi,float q[4])196 void axis_to_quat(float a[3], float phi, float q[4])
197 {
198 vnormal(a);
199 vcopy(a, q);
200 vscale(q, sin(phi / 2.0));
201 q[3] = cos(phi / 2.0);
202 }
203
204 /*
205 * Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
206 * if we are away from the center of the sphere.
207 */
tb_project_to_sphere(float r,float x,float y)208 static float tb_project_to_sphere(float r, float x, float y)
209 {
210 float d, t, z;
211
212 d = sqrt(x * x + y * y);
213 if (d < r * 0.70710678118654752440) { /* Inside sphere */
214 z = sqrt(r * r - d * d);
215 } else { /* On hyperbola */
216 t = r / 1.41421356237309504880;
217 z = t * t / d;
218 }
219 return z;
220 }
221
222 /*
223 * Given two rotations, e1 and e2, expressed as quaternion rotations,
224 * figure out the equivalent single rotation and stuff it into dest.
225 *
226 * This routine also normalizes the result every RENORMCOUNT times it is
227 * called, to keep error from creeping in.
228 *
229 * NOTE: This routine is written so that q1 or q2 may be the same
230 * as dest (or each other).
231 */
232
233 #define RENORMCOUNT 97
234
add_quats(float q1[4],float q2[4],float dest[4])235 void add_quats(float q1[4], float q2[4], float dest[4])
236 {
237 static int count = 0;
238 float t1[4], t2[4], t3[4];
239 float tf[4];
240
241 vcopy(q1, t1);
242 vscale(t1, q2[3]);
243
244 vcopy(q2, t2);
245 vscale(t2, q1[3]);
246
247 vcross(q2, q1, t3);
248 vadd(t1, t2, tf);
249 vadd(t3, tf, tf);
250 tf[3] = q1[3] * q2[3] - vdot(q1, q2);
251
252 dest[0] = tf[0];
253 dest[1] = tf[1];
254 dest[2] = tf[2];
255 dest[3] = tf[3];
256
257 if (++count > RENORMCOUNT) {
258 count = 0;
259 normalize_quat(dest);
260 }
261 }
262
263 /*
264 * Quaternions always obey: a^2 + b^2 + c^2 + d^2 = 1.0
265 * If they don't add up to 1.0, dividing by their magnitued will
266 * renormalize them.
267 *
268 * Note: See the following for more information on quaternions:
269 *
270 * - Shoemake, K., Animating rotation with quaternion curves, Computer
271 * Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
272 * - Pletinckx, D., Quaternion calculus as a basic tool in computer
273 * graphics, The Visual Computer 5, 2-13, 1989.
274 */
normalize_quat(float q[4])275 static void normalize_quat(float q[4])
276 {
277 int i;
278 float mag;
279
280 mag = (q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]);
281 for (i = 0; i < 4; i++)
282 q[i] /= mag;
283 }
284
285 /*
286 * Build a rotation matrix, given a quaternion rotation.
287 *
288 */
build_rotmatrix(float m[4][4],float q[4])289 void build_rotmatrix(float m[4][4], float q[4])
290 {
291 m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
292 m[0][1] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
293 m[0][2] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
294 m[0][3] = 0.0;
295
296 m[1][0] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
297 m[1][1] = 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
298 m[1][2] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
299 m[1][3] = 0.0;
300
301 m[2][0] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
302 m[2][1] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
303 m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);
304 m[2][3] = 0.0;
305
306 m[3][0] = 0.0;
307 m[3][1] = 0.0;
308 m[3][2] = 0.0;
309 m[3][3] = 1.0;
310 }
311