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
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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,
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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31  * Unpublished-- rights reserved under the copyright laws of the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 #ifdef __clang__
53 #pragma clang diagnostic ignored "-Weverything"
54 #endif
55 
56 #include <cmath>
57 #include "trackball.h"
58 
59 #ifdef _MSC_VER
60 #pragma warning(disable : 4244)
61 #pragma warning(disable : 4305)
62 #endif
63 
64 #ifdef __clang__
65 #pragma clang diagnostic ignored "-Weverything"
66 #endif
67 
68 /*
69  * This size should really be based on the distance from the center of
70  * rotation to the point on the object underneath the mouse.  That
71  * point would then track the mouse as closely as possible.  This is a
72  * simple example, though, so that is left as an Exercise for the
73  * Programmer.
74  */
75 #define TRACKBALLSIZE (0.8)
76 
77 /*
78  * Local function prototypes (not defined in trackball.h)
79  */
80 static float tb_project_to_sphere(float, float, float);
81 static void normalize_quat(float[4]);
82 
vzero(float * v)83 static void vzero(float *v) {
84   v[0] = 0.0;
85   v[1] = 0.0;
86   v[2] = 0.0;
87 }
88 
vset(float * v,float x,float y,float z)89 static void vset(float *v, float x, float y, float z) {
90   v[0] = x;
91   v[1] = y;
92   v[2] = z;
93 }
94 
vsub(const float * src1,const float * src2,float * dst)95 static void vsub(const float *src1, const float *src2, float *dst) {
96   dst[0] = src1[0] - src2[0];
97   dst[1] = src1[1] - src2[1];
98   dst[2] = src1[2] - src2[2];
99 }
100 
vcopy(const float * v1,float * v2)101 static void vcopy(const float *v1, float *v2) {
102   int i;
103   for (i = 0; i < 3; i++)
104     v2[i] = v1[i];
105 }
106 
vcross(const float * v1,const float * v2,float * cross)107 static void vcross(const float *v1, const float *v2, float *cross) {
108   float temp[3];
109 
110   temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]);
111   temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]);
112   temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]);
113   vcopy(temp, cross);
114 }
115 
vlength(const float * v)116 static float vlength(const float *v) {
117   return std::sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
118 }
119 
vscale(float * v,float div)120 static void vscale(float *v, float div) {
121   v[0] *= div;
122   v[1] *= div;
123   v[2] *= div;
124 }
125 
vnormal(float * v)126 static void vnormal(float *v) { vscale(v, 1.0f / vlength(v)); }
127 
vdot(const float * v1,const float * v2)128 static float vdot(const float *v1, const float *v2) {
129   return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
130 }
131 
vadd(const float * src1,const float * src2,float * dst)132 static void vadd(const float *src1, const float *src2, float *dst) {
133   dst[0] = src1[0] + src2[0];
134   dst[1] = src1[1] + src2[1];
135   dst[2] = src1[2] + src2[2];
136 }
137 
138 /*
139  * Ok, simulate a track-ball.  Project the points onto the virtual
140  * trackball, then figure out the axis of rotation, which is the cross
141  * product of P1 P2 and O P1 (O is the center of the ball, 0,0,0)
142  * Note:  This is a deformed trackball-- is a trackball in the center,
143  * but is deformed into a hyperbolic sheet of rotation away from the
144  * center.  This particular function was chosen after trying out
145  * several variations.
146  *
147  * It is assumed that the arguments to this routine are in the range
148  * (-1.0 ... 1.0)
149  */
trackball(float q[4],float p1x,float p1y,float p2x,float p2y)150 void trackball(float q[4], float p1x, float p1y, float p2x, float p2y) {
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 > 1.0f)
185     t = 1.0f;
186   if (t < -1.0f)
187     t = -1.0f;
188   phi = 2.0f * asinf(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   vnormal(a);
198   vcopy(a, q);
199   vscale(q, sin(phi / 2.0));
200   q[3] = cos(phi / 2.0);
201 }
202 
203 /*
204  * Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
205  * if we are away from the center of the sphere.
206  */
tb_project_to_sphere(float r,float x,float y)207 static float tb_project_to_sphere(float r, float x, float y) {
208   float d, t, z;
209 
210   d = sqrt(x * x + y * y);
211   if (d < r * 0.70710678118654752440) { /* Inside sphere */
212     z = sqrt(r * r - d * d);
213   } else { /* On hyperbola */
214     t = r / 1.41421356237309504880;
215     z = t * t / d;
216   }
217   return z;
218 }
219 
220 /*
221  * Given two rotations, e1 and e2, expressed as quaternion rotations,
222  * figure out the equivalent single rotation and stuff it into dest.
223  *
224  * This routine also normalizes the result every RENORMCOUNT times it is
225  * called, to keep error from creeping in.
226  *
227  * NOTE: This routine is written so that q1 or q2 may be the same
228  * as dest (or each other).
229  */
230 
231 #define RENORMCOUNT 97
232 
add_quats(float q1[4],float q2[4],float dest[4])233 void add_quats(float q1[4], float q2[4], float dest[4]) {
234   static int count = 0;
235   float t1[4], t2[4], t3[4];
236   float tf[4];
237 
238   vcopy(q1, t1);
239   vscale(t1, q2[3]);
240 
241   vcopy(q2, t2);
242   vscale(t2, q1[3]);
243 
244   vcross(q2, q1, t3);
245   vadd(t1, t2, tf);
246   vadd(t3, tf, tf);
247   tf[3] = q1[3] * q2[3] - vdot(q1, q2);
248 
249   dest[0] = tf[0];
250   dest[1] = tf[1];
251   dest[2] = tf[2];
252   dest[3] = tf[3];
253 
254   if (++count > RENORMCOUNT) {
255     count = 0;
256     normalize_quat(dest);
257   }
258 }
259 
260 /*
261  * Quaternions always obey:  a^2 + b^2 + c^2 + d^2 = 1.0
262  * If they don't add up to 1.0, dividing by their magnitued will
263  * renormalize them.
264  *
265  * Note: See the following for more information on quaternions:
266  *
267  * - Shoemake, K., Animating rotation with quaternion curves, Computer
268  *   Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985.
269  * - Pletinckx, D., Quaternion calculus as a basic tool in computer
270  *   graphics, The Visual Computer 5, 2-13, 1989.
271  */
normalize_quat(float q[4])272 static void normalize_quat(float q[4]) {
273   int i;
274   float mag;
275 
276   mag = (q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]);
277   for (i = 0; i < 4; i++)
278     q[i] /= mag;
279 }
280 
281 /*
282  * Build a rotation matrix, given a quaternion rotation.
283  *
284  */
build_rotmatrix(float m[4][4],const float q[4])285 void build_rotmatrix(float m[4][4], const float q[4]) {
286   m[0][0] = 1.0 - 2.0 * (q[1] * q[1] + q[2] * q[2]);
287   m[0][1] = 2.0 * (q[0] * q[1] - q[2] * q[3]);
288   m[0][2] = 2.0 * (q[2] * q[0] + q[1] * q[3]);
289   m[0][3] = 0.0;
290 
291   m[1][0] = 2.0 * (q[0] * q[1] + q[2] * q[3]);
292   m[1][1] = 1.0 - 2.0 * (q[2] * q[2] + q[0] * q[0]);
293   m[1][2] = 2.0 * (q[1] * q[2] - q[0] * q[3]);
294   m[1][3] = 0.0;
295 
296   m[2][0] = 2.0 * (q[2] * q[0] - q[1] * q[3]);
297   m[2][1] = 2.0 * (q[1] * q[2] + q[0] * q[3]);
298   m[2][2] = 1.0 - 2.0 * (q[1] * q[1] + q[0] * q[0]);
299   m[2][3] = 0.0;
300 
301   m[3][0] = 0.0;
302   m[3][1] = 0.0;
303   m[3][2] = 0.0;
304   m[3][3] = 1.0;
305 }
306