1 | /************************************************************************* |
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2 | * * |
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3 | * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. * |
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4 | * All rights reserved. Email: russ@q12.org Web: www.q12.org * |
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5 | * * |
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6 | * This library is free software; you can redistribute it and/or * |
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7 | * modify it under the terms of EITHER: * |
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8 | * (1) The GNU Lesser General Public License as published by the Free * |
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9 | * Software Foundation; either version 2.1 of the License, or (at * |
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10 | * your option) any later version. The text of the GNU Lesser * |
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11 | * General Public License is included with this library in the * |
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12 | * file LICENSE.TXT. * |
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13 | * (2) The BSD-style license that is included with this library in * |
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14 | * the file LICENSE-BSD.TXT. * |
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15 | * * |
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16 | * This library is distributed in the hope that it will be useful, * |
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17 | * but WITHOUT ANY WARRANTY; without even the implied warranty of * |
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18 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files * |
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19 | * LICENSE.TXT and LICENSE-BSD.TXT for more details. * |
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20 | * * |
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21 | *************************************************************************/ |
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22 | |
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23 | #include <ode/common.h> |
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24 | #include <ode/odemath.h> |
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25 | |
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26 | // get some math functions under windows |
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27 | #ifdef WIN32 |
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28 | #include <float.h> |
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29 | #ifndef CYGWIN // added by andy for cygwin |
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30 | #undef copysign |
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31 | #define copysign(a,b) ((dReal)_copysign(a,b)) |
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32 | #endif // added by andy for cygwin |
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33 | #endif |
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34 | |
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35 | #undef dNormalize3 |
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36 | #undef dNormalize4 |
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37 | |
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38 | |
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39 | // this may be called for vectors `a' with extremely small magnitude, for |
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40 | // example the result of a cross product on two nearly perpendicular vectors. |
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41 | // we must be robust to these small vectors. to prevent numerical error, |
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42 | // first find the component a[i] with the largest magnitude and then scale |
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43 | // all the components by 1/a[i]. then we can compute the length of `a' and |
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44 | // scale the components by 1/l. this has been verified to work with vectors |
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45 | // containing the smallest representable numbers. |
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46 | |
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47 | int dSafeNormalize3 (dVector3 a) |
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48 | { |
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49 | dReal a0,a1,a2,aa0,aa1,aa2,l; |
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50 | dAASSERT (a); |
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51 | a0 = a[0]; |
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52 | a1 = a[1]; |
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53 | a2 = a[2]; |
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54 | aa0 = dFabs(a0); |
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55 | aa1 = dFabs(a1); |
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56 | aa2 = dFabs(a2); |
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57 | if (aa1 > aa0) { |
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58 | if (aa2 > aa1) { |
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59 | goto aa2_largest; |
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60 | } |
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61 | else { // aa1 is largest |
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62 | a0 /= aa1; |
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63 | a2 /= aa1; |
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64 | l = dRecipSqrt (a0*a0 + a2*a2 + 1); |
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65 | a[0] = a0*l; |
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66 | a[1] = dCopySign(l,a1); |
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67 | a[2] = a2*l; |
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68 | } |
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69 | } |
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70 | else { |
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71 | if (aa2 > aa0) { |
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72 | aa2_largest: // aa2 is largest |
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73 | a0 /= aa2; |
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74 | a1 /= aa2; |
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75 | l = dRecipSqrt (a0*a0 + a1*a1 + 1); |
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76 | a[0] = a0*l; |
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77 | a[1] = a1*l; |
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78 | a[2] = dCopySign(l,a2); |
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79 | } |
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80 | else { // aa0 is largest |
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81 | if (aa0 <= 0) { |
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82 | a[0] = 1; // if all a's are zero, this is where we'll end up. |
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83 | a[1] = 0; // return a default unit length vector. |
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84 | a[2] = 0; |
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85 | return 0; |
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86 | } |
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87 | a1 /= aa0; |
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88 | a2 /= aa0; |
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89 | l = dRecipSqrt (a1*a1 + a2*a2 + 1); |
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90 | a[0] = dCopySign(l,a0); |
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91 | a[1] = a1*l; |
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92 | a[2] = a2*l; |
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93 | } |
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94 | } |
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95 | return 1; |
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96 | } |
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97 | |
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98 | /* OLD VERSION */ |
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99 | /* |
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100 | void dNormalize3 (dVector3 a) |
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101 | { |
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102 | dIASSERT (a); |
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103 | dReal l = dDOT(a,a); |
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104 | if (l > 0) { |
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105 | l = dRecipSqrt(l); |
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106 | a[0] *= l; |
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107 | a[1] *= l; |
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108 | a[2] *= l; |
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109 | } |
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110 | else { |
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111 | a[0] = 1; |
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112 | a[1] = 0; |
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113 | a[2] = 0; |
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114 | } |
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115 | } |
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116 | */ |
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117 | |
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118 | void dNormalize3(dVector3 a) |
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119 | { |
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120 | _dNormalize3(a); |
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121 | } |
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122 | |
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123 | |
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124 | int dSafeNormalize4 (dVector4 a) |
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125 | { |
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126 | dAASSERT (a); |
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127 | dReal l = dDOT(a,a)+a[3]*a[3]; |
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128 | if (l > 0) { |
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129 | l = dRecipSqrt(l); |
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130 | a[0] *= l; |
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131 | a[1] *= l; |
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132 | a[2] *= l; |
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133 | a[3] *= l; |
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134 | return 1; |
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135 | } |
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136 | else { |
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137 | a[0] = 1; |
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138 | a[1] = 0; |
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139 | a[2] = 0; |
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140 | a[3] = 0; |
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141 | return 0; |
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142 | } |
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143 | } |
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144 | |
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145 | void dNormalize4(dVector4 a) |
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146 | { |
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147 | _dNormalize4(a); |
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148 | } |
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149 | |
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150 | |
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151 | void dPlaneSpace (const dVector3 n, dVector3 p, dVector3 q) |
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152 | { |
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153 | dAASSERT (n && p && q); |
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154 | if (dFabs(n[2]) > M_SQRT1_2) { |
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155 | // choose p in y-z plane |
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156 | dReal a = n[1]*n[1] + n[2]*n[2]; |
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157 | dReal k = dRecipSqrt (a); |
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158 | p[0] = 0; |
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159 | p[1] = -n[2]*k; |
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160 | p[2] = n[1]*k; |
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161 | // set q = n x p |
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162 | q[0] = a*k; |
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163 | q[1] = -n[0]*p[2]; |
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164 | q[2] = n[0]*p[1]; |
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165 | } |
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166 | else { |
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167 | // choose p in x-y plane |
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168 | dReal a = n[0]*n[0] + n[1]*n[1]; |
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169 | dReal k = dRecipSqrt (a); |
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170 | p[0] = -n[1]*k; |
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171 | p[1] = n[0]*k; |
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172 | p[2] = 0; |
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173 | // set q = n x p |
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174 | q[0] = -n[2]*p[1]; |
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175 | q[1] = n[2]*p[0]; |
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176 | q[2] = a*k; |
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177 | } |
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178 | } |
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