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1 /*
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2 libvmath - a vector math library
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3 Copyright (C) 2004-2011 John Tsiombikas <nuclear@member.fsf.org>
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4
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5 This program is free software: you can redistribute it and/or modify
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6 it under the terms of the GNU Lesser General Public License as published
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7 by the Free Software Foundation, either version 3 of the License, or
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8 (at your option) any later version.
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9
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10 This program is distributed in the hope that it will be useful,
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11 but WITHOUT ANY WARRANTY; without even the implied warranty of
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12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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13 GNU Lesser General Public License for more details.
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14
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15 You should have received a copy of the GNU Lesser General Public License
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16 along with this program. If not, see <http://www.gnu.org/licenses/>.
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17 */
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18
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19
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20 #include <stdio.h>
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21 #include <math.h>
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22 #include "quat.h"
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23
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24 void quat_print(FILE *fp, quat_t q)
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25 {
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26 fprintf(fp, "([ %.4f %.4f %.4f ] %.4f)", q.x, q.y, q.z, q.w);
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27 }
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28
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29 quat_t quat_rotate(quat_t q, scalar_t angle, scalar_t x, scalar_t y, scalar_t z)
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30 {
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31 quat_t rq;
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32 scalar_t half_angle = angle * 0.5;
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33 scalar_t sin_half = sin(half_angle);
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34
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35 rq.w = cos(half_angle);
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36 rq.x = x * sin_half;
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37 rq.y = y * sin_half;
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38 rq.z = z * sin_half;
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39
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40 return quat_mul(q, rq);
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41 }
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42
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43 quat_t quat_rotate_quat(quat_t q, quat_t rotq)
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44 {
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45 return quat_mul(quat_mul(rotq, q), quat_conjugate(rotq));
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46 }
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47
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48 quat_t quat_slerp(quat_t q1, quat_t q2, scalar_t t)
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49 {
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50 quat_t res;
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51 scalar_t a, b, angle, sin_angle, dot;
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52
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53 dot = q1.w * q2.w + q1.x * q2.x + q1.y * q2.y + q1.z * q2.z;
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54 if(dot < 0.0) {
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55 /* make sure we interpolate across the shortest arc */
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56 q1.x = -q1.x;
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57 q1.y = -q1.y;
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58 q1.z = -q1.z;
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59 q1.w = -q1.w;
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60 dot = -dot;
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61 }
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62
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63 /* clamp dot to [-1, 1] in order to avoid domain errors in acos due to
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64 * floating point imprecisions
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65 */
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66 if(dot < -1.0) dot = -1.0;
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67 if(dot > 1.0) dot = 1.0;
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68
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69 angle = acos(dot);
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70 sin_angle = sin(angle);
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71
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72 if(fabs(sin_angle) < SMALL_NUMBER) {
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73 /* for very small angles or completely opposite orientations
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74 * use linear interpolation to avoid div/zero (in the first case it makes sense,
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75 * the second case is pretty much undefined anyway I guess ...
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76 */
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77 a = 1.0f - t;
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78 b = t;
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79 } else {
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80 a = sin((1.0f - t) * angle) / sin_angle;
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81 b = sin(t * angle) / sin_angle;
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82 }
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83
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84 res.x = q1.x * a + q2.x * b;
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85 res.y = q1.y * a + q2.y * b;
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86 res.z = q1.z * a + q2.z * b;
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87 res.w = q1.w * a + q2.w * b;
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88 return res;
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89 }
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