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| 31 | + * Unpublished-- rights reserved under the copyright laws of the |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