1 | /* |
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2 | * (c) Copyright 1993, 1994, Silicon Graphics, Inc. |
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3 | * ALL RIGHTS RESERVED |
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4 | * Permission to use, copy, modify, and distribute this software for |
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5 | * any purpose and without fee is hereby granted, provided that the above |
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6 | * copyright notice appear in all copies and that both the copyright notice |
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7 | * and this permission notice appear in supporting documentation, and that |
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8 | * the name of Silicon Graphics, Inc. not be used in advertising |
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9 | * or publicity pertaining to distribution of the software without specific, |
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10 | * written prior permission. |
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11 | * |
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12 | * THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "AS-IS" |
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13 | * AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE, |
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14 | * INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR |
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15 | * FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL SILICON |
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16 | * GRAPHICS, INC. BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT, |
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17 | * SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY |
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18 | * KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION, |
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19 | * LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF |
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20 | * THIRD PARTIES, WHETHER OR NOT SILICON GRAPHICS, INC. HAS BEEN |
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21 | * ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON |
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22 | * ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE |
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23 | * POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE. |
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24 | * |
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25 | * US Government Users Restricted Rights |
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26 | * Use, duplication, or disclosure by the Government is subject to |
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27 | * restrictions set forth in FAR 52.227.19(c)(2) or subparagraph |
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28 | * (c)(1)(ii) of the Rights in Technical Data and Computer Software |
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29 | * clause at DFARS 252.227-7013 and/or in similar or successor |
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30 | * clauses in the FAR or the DOD or NASA FAR Supplement. |
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31 | * Unpublished-- rights reserved under the copyright laws of the |
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32 | * United States. Contractor/manufacturer is Silicon Graphics, |
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33 | * Inc., 2011 N. Shoreline Blvd., Mountain View, CA 94039-7311. |
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34 | * |
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35 | * OpenGL(TM) is a trademark of Silicon Graphics, Inc. |
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36 | */ |
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37 | |
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38 | /* |
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39 | * Trackball code: |
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40 | * |
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41 | * Implementation of a virtual trackball. |
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42 | * Implemented by Gavin Bell, lots of ideas from Thant Tessman and |
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43 | * the August '88 issue of Siggraph's "Computer Graphics," pp. 121-129. |
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44 | * |
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45 | * Vector manip code: |
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46 | * |
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47 | * Original code from: |
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48 | * David M. Ciemiewicz, Mark Grossman, Henry Moreton, and Paul Haeberli |
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49 | * |
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50 | * Much mucking with by: |
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51 | * Gavin Bell |
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52 | */ |
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53 | #include <math.h> |
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54 | #include "trackball.h" |
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55 | |
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56 | /* |
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57 | * This size should really be based on the distance from the center of |
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58 | * rotation to the point on the object underneath the mouse. That |
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59 | * point would then track the mouse as closely as possible. This is a |
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60 | * simple example, though, so that is left as an Exercise for the |
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61 | * Programmer. |
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62 | */ |
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63 | #define TRACKBALLSIZE (0.4f) |
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64 | |
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65 | /* |
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66 | * Local function prototypes (not defined in trackball.h) |
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67 | */ |
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68 | static float tb_project_to_sphere(float, float, float); |
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69 | static void normalize_quat(float [4]); |
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70 | |
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71 | static void |
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72 | vzero(float *v) |
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73 | { |
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74 | v[0] = 0.0; |
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75 | v[1] = 0.0; |
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76 | v[2] = 0.0; |
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77 | } |
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78 | |
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79 | static void |
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80 | vset(float *v, float x, float y, float z) |
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81 | { |
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82 | v[0] = x; |
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83 | v[1] = y; |
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84 | v[2] = z; |
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85 | } |
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86 | |
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87 | static void |
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88 | vsub(const float *src1, const float *src2, float *dst) |
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89 | { |
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90 | dst[0] = src1[0] - src2[0]; |
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91 | dst[1] = src1[1] - src2[1]; |
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92 | dst[2] = src1[2] - src2[2]; |
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93 | } |
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94 | |
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95 | static void |
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96 | vcopy(const float *v1, float *v2) |
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97 | { |
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98 | register int i; |
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99 | for (i = 0 ; i < 3 ; i++) |
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100 | v2[i] = v1[i]; |
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101 | } |
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102 | |
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103 | static void |
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104 | vcross(const float *v1, const float *v2, float *cross) |
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105 | { |
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106 | float temp[3]; |
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107 | |
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108 | temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]); |
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109 | temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]); |
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110 | temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]); |
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111 | vcopy(temp, cross); |
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112 | } |
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113 | |
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114 | static float |
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115 | vlength(const float *v) |
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116 | { |
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117 | return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]); |
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118 | } |
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119 | |
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120 | static void |
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121 | vscale(float *v, float div) |
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122 | { |
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123 | v[0] *= div; |
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124 | v[1] *= div; |
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125 | v[2] *= div; |
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126 | } |
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127 | |
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128 | static void |
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129 | vnormal(float *v) |
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130 | { |
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131 | vscale(v,1.0f/vlength(v)); |
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132 | } |
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133 | |
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134 | static float |
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135 | vdot(const float *v1, const float *v2) |
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136 | { |
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137 | return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2]; |
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138 | } |
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139 | |
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140 | static void |
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141 | vadd(const float *src1, const float *src2, float *dst) |
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142 | { |
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143 | dst[0] = src1[0] + src2[0]; |
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144 | dst[1] = src1[1] + src2[1]; |
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145 | dst[2] = src1[2] + src2[2]; |
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146 | } |
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147 | |
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148 | /* |
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149 | * Ok, simulate a track-ball. Project the points onto the virtual |
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150 | * trackball, then figure out the axis of rotation, which is the cross |
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151 | * product of P1 P2 and O P1 (O is the center of the ball, 0,0,0) |
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152 | * Note: This is a deformed trackball-- is a trackball in the center, |
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153 | * but is deformed into a hyperbolic sheet of rotation away from the |
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154 | * center. This particular function was chosen after trying out |
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155 | * several variations. |
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156 | * |
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157 | * It is assumed that the arguments to this routine are in the range |
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158 | * (-1.0 ... 1.0) |
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159 | */ |
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160 | void |
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161 | trackball(float q[4], float p1x, float p1y, float p2x, float p2y) |
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162 | { |
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163 | float a[3]; /* Axis of rotation */ |
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164 | float phi; /* how much to rotate about axis */ |
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165 | float p1[3], p2[3], d[3]; |
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166 | float t; |
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167 | |
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168 | if (p1x == p2x && p1y == p2y) { |
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169 | /* Zero rotation */ |
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170 | vzero(q); |
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171 | q[3] = 1.0; |
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172 | return; |
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173 | } |
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174 | |
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175 | /* |
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176 | * First, figure out z-coordinates for projection of P1 and P2 to |
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177 | * deformed sphere |
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178 | */ |
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179 | vset(p1,p1x,p1y,tb_project_to_sphere(TRACKBALLSIZE,p1x,p1y)); |
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180 | vset(p2,p2x,p2y,tb_project_to_sphere(TRACKBALLSIZE,p2x,p2y)); |
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181 | |
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182 | /* |
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183 | * Now, we want the cross product of P1 and P2 |
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184 | */ |
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185 | vcross(p2,p1,a); |
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186 | |
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187 | /* |
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188 | * Figure out how much to rotate around that axis. |
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189 | */ |
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190 | vsub(p1,p2,d); |
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191 | t = vlength(d) / (2.0f*TRACKBALLSIZE); |
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192 | |
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193 | /* |
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194 | * Avoid problems with out-of-control values... |
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195 | */ |
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196 | if (t > 1.0f) t = 1.0f; |
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197 | if (t < -1.0f) t = -1.0f; |
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198 | phi = 2.0f * asin(t); |
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199 | |
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200 | axis_to_quat(a,phi,q); |
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201 | } |
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202 | |
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203 | /* |
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204 | * Given an axis and angle, compute quaternion. |
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205 | */ |
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206 | void |
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207 | axis_to_quat(float a[3], float phi, float q[4]) |
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208 | { |
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209 | vnormal(a); |
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210 | vcopy(a,q); |
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211 | vscale(q,sin(phi/2.0f)); |
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212 | q[3] = cos(phi/2.0f); |
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213 | } |
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214 | |
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215 | /* |
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216 | * Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet |
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217 | * if we are away from the center of the sphere. |
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218 | */ |
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219 | static float |
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220 | tb_project_to_sphere(float r, float x, float y) |
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221 | { |
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222 | float d, t, z; |
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223 | |
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224 | d = sqrt(x*x + y*y); |
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225 | if (d < r * 0.70710678118654752440f) { /* Inside sphere */ |
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226 | z = sqrt(r*r - d*d); |
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227 | } else { /* On hyperbola */ |
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228 | t = r / 1.41421356237309504880f; |
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229 | z = t*t / d; |
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230 | } |
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231 | return z; |
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232 | } |
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233 | |
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234 | /* |
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235 | * Given two rotations, e1 and e2, expressed as quaternion rotations, |
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236 | * figure out the equivalent single rotation and stuff it into dest. |
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237 | * |
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238 | * This routine also normalizes the result every RENORMCOUNT times it is |
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239 | * called, to keep error from creeping in. |
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240 | * |
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241 | * NOTE: This routine is written so that q1 or q2 may be the same |
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242 | * as dest (or each other). |
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243 | */ |
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244 | |
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245 | #define RENORMCOUNT 97 |
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246 | |
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247 | void |
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248 | add_quats(float q1[4], float q2[4], float dest[4]) |
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249 | { |
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250 | static int count=0; |
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251 | float t1[4], t2[4], t3[4]; |
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252 | float tf[4]; |
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253 | |
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254 | vcopy(q1,t1); |
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255 | vscale(t1,q2[3]); |
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256 | |
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257 | vcopy(q2,t2); |
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258 | vscale(t2,q1[3]); |
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259 | |
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260 | vcross(q2,q1,t3); |
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261 | vadd(t1,t2,tf); |
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262 | vadd(t3,tf,tf); |
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263 | tf[3] = q1[3] * q2[3] - vdot(q1,q2); |
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264 | |
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265 | dest[0] = tf[0]; |
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266 | dest[1] = tf[1]; |
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267 | dest[2] = tf[2]; |
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268 | dest[3] = tf[3]; |
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269 | |
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270 | if (++count > RENORMCOUNT) { |
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271 | count = 0; |
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272 | normalize_quat(dest); |
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273 | } |
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274 | } |
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275 | |
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276 | /* |
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277 | * Quaternions always obey: a^2 + b^2 + c^2 + d^2 = 1.0 |
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278 | * If they don't add up to 1.0, dividing by their magnitued will |
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279 | * renormalize them. |
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280 | * |
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281 | * Note: See the following for more information on quaternions: |
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282 | * |
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283 | * - Shoemake, K., Animating rotation with quaternion curves, Computer |
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284 | * Graphics 19, No 3 (Proc. SIGGRAPH'85), 245-254, 1985. |
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285 | * - Pletinckx, D., Quaternion calculus as a basic tool in computer |
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286 | * graphics, The Visual Computer 5, 2-13, 1989. |
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287 | */ |
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288 | static void |
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289 | normalize_quat(float q[4]) |
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290 | { |
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291 | int i; |
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292 | float mag; |
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293 | |
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294 | mag = (q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]); |
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295 | for (i = 0; i < 4; i++) q[i] /= mag; |
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296 | } |
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297 | |
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298 | /* |
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299 | * Build a rotation matrix, given a quaternion rotation. |
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300 | * |
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301 | */ |
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302 | void |
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303 | build_rotmatrix(float m[4][4], float q[4]) |
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304 | { |
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305 | m[0][0] = 1.0f - 2.0f * (q[1] * q[1] + q[2] * q[2]); |
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306 | m[0][1] = 2.0f * (q[0] * q[1] - q[2] * q[3]); |
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307 | m[0][2] = 2.0f * (q[2] * q[0] + q[1] * q[3]); |
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308 | m[0][3] = 0.0f; |
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309 | |
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310 | m[1][0] = 2.0f * (q[0] * q[1] + q[2] * q[3]); |
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311 | m[1][1]= 1.0f - 2.0f * (q[2] * q[2] + q[0] * q[0]); |
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312 | m[1][2] = 2.0f * (q[1] * q[2] - q[0] * q[3]); |
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313 | m[1][3] = 0.0f; |
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314 | |
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315 | m[2][0] = 2.0f * (q[2] * q[0] - q[1] * q[3]); |
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316 | m[2][1] = 2.0f * (q[1] * q[2] + q[0] * q[3]); |
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317 | m[2][2] = 1.0f - 2.0f * (q[1] * q[1] + q[0] * q[0]); |
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318 | m[2][3] = 0.0f; |
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319 | |
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320 | m[3][0] = 0.0f; |
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321 | m[3][1] = 0.0f; |
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322 | m[3][2] = 0.0f; |
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323 | m[3][3] = 1.0f; |
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324 | } |
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325 | |
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