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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/config.h> |
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24 #include <ode/mass.h> |
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25 #include <ode/odemath.h> |
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26 #include <ode/matrix.h> |
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27 |
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28 // Local dependencies |
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29 #include "collision_kernel.h" |
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30 |
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31 #define SQR(x) (dMUL((x),(x))) //!< Returns x square |
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32 #define CUBE(x) (dMUL((x),dMUL((x),(x)))) //!< Returns x cube |
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33 |
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34 #define _I(i,j) I[(i)*4+(j)] |
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35 |
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36 |
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37 // return 1 if ok, 0 if bad |
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38 |
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39 EXPORT_C int dMassCheck (const dMass *m) |
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40 { |
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41 int i; |
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42 |
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43 if (m->mass <= 0) { |
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44 return 0; |
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45 } |
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46 if (!dIsPositiveDefinite (m->I,3)) { |
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47 return 0; |
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48 } |
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49 |
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50 // verify that the center of mass position is consistent with the mass |
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51 // and inertia matrix. this is done by checking that the inertia around |
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52 // the center of mass is also positive definite. from the comment in |
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53 // dMassTranslate(), if the body is translated so that its center of mass |
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54 // is at the point of reference, then the new inertia is: |
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55 // I + mass*crossmat(c)^2 |
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56 // note that requiring this to be positive definite is exactly equivalent |
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57 // to requiring that the spatial inertia matrix |
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58 // [ mass*eye(3,3) M*crossmat(c)^T ] |
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59 // [ M*crossmat(c) I ] |
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60 // is positive definite, given that I is PD and mass>0. see the theorem |
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61 // about partitioned PD matrices for proof. |
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62 |
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63 dMatrix3 I2,chat; |
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64 dSetZero (chat,12); |
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65 dCROSSMAT (chat,m->c,4,+,-); |
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66 dMULTIPLY0_333 (I2,chat,chat); |
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67 for (i=0; i<3; i++) I2[i] = m->I[i] + dMUL(m->mass,I2[i]); |
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68 for (i=4; i<7; i++) I2[i] = m->I[i] + dMUL(m->mass,I2[i]); |
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69 for (i=8; i<11; i++) I2[i] = m->I[i] + dMUL(m->mass,I2[i]); |
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70 if (!dIsPositiveDefinite (I2,3)) { |
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71 return 0; |
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72 } |
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73 return 1; |
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74 } |
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75 |
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76 |
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77 EXPORT_C void dMassSetZero (dMass *m) |
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78 { |
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79 m->mass = REAL(0.0); |
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80 dSetZero (m->c,sizeof(m->c) / sizeof(dReal)); |
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81 dSetZero (m->I,sizeof(m->I) / sizeof(dReal)); |
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82 } |
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83 |
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84 |
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85 EXPORT_C void dMassSetParameters (dMass *m, dReal themass, |
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86 dReal cgx, dReal cgy, dReal cgz, |
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87 dReal I11, dReal I22, dReal I33, |
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88 dReal I12, dReal I13, dReal I23) |
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89 { |
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90 dMassSetZero (m); |
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91 m->mass = themass; |
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92 m->c[0] = cgx; |
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93 m->c[1] = cgy; |
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94 m->c[2] = cgz; |
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95 m->_I(0,0) = I11; |
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96 m->_I(1,1) = I22; |
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97 m->_I(2,2) = I33; |
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98 m->_I(0,1) = I12; |
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99 m->_I(0,2) = I13; |
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100 m->_I(1,2) = I23; |
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101 m->_I(1,0) = I12; |
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102 m->_I(2,0) = I13; |
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103 m->_I(2,1) = I23; |
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104 dMassCheck (m); |
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105 } |
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106 |
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107 |
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108 EXPORT_C void dMassSetSphere (dMass *m, dReal density, dReal radius) |
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109 { |
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110 dMassSetSphereTotal (m, dMUL(dDIV(REAL(4.0),REAL(3.0)), dMUL(dPI,dMUL(CUBE(radius),density))), radius); |
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111 } |
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112 |
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113 |
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114 EXPORT_C void dMassSetSphereTotal (dMass *m, dReal total_mass, dReal radius) |
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115 { |
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116 dMassSetZero (m); |
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117 m->mass = total_mass; |
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118 dReal II = dMUL(REAL(0.4),dMUL(total_mass,SQR(radius))); |
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119 m->_I(0,0) = II; |
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120 m->_I(1,1) = II; |
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121 m->_I(2,2) = II; |
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122 |
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123 # ifndef dNODEBUG |
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124 dMassCheck (m); |
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125 # endif |
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126 } |
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127 |
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128 |
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129 EXPORT_C void dMassSetCapsule (dMass *m, dReal density, int direction, |
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130 dReal radius, dReal length) |
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131 { |
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132 dReal M1,M2,Ia,Ib; |
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133 dMassSetZero (m); |
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134 M1 = dMUL(dPI,dMUL(SQR(radius),dMUL(length,density))); // cylinder mass |
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135 M2 = dMUL(dDIV(REAL(4.0),REAL(3.0)),dMUL(dPI,dMUL(CUBE(radius),density))); // total cap mass |
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136 m->mass = M1+M2; |
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137 Ia = dMUL(M1,(dMUL(REAL(0.25),SQR(radius)) + dMUL(dDIV(REAL(1.0),REAL(12.0)),SQR(length)))) + |
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138 dMUL(M2,(dMUL(REAL(0.4),SQR(radius)) + dMUL(REAL(0.375),dMUL(radius,length)) + dMUL(REAL(0.25),SQR(length)))); |
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139 Ib = dMUL((dMUL(M1,REAL(0.5)) + dMUL(M2,REAL(0.4))),SQR(radius)); |
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140 m->_I(0,0) = Ia; |
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141 m->_I(1,1) = Ia; |
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142 m->_I(2,2) = Ia; |
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143 m->_I(direction-1,direction-1) = Ib; |
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144 |
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145 # ifndef dNODEBUG |
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146 dMassCheck (m); |
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147 # endif |
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148 } |
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149 |
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150 |
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151 EXPORT_C void dMassSetCapsuleTotal (dMass *m, dReal total_mass, int direction, |
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152 dReal a, dReal b) |
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153 { |
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154 dMassSetCapsule (m, REAL(1.0), direction, a, b); |
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155 dMassAdjust (m, total_mass); |
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156 } |
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157 |
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158 |
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159 EXPORT_C void dMassSetCylinder (dMass *m, dReal density, int direction, |
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160 dReal radius, dReal length) |
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161 { |
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162 dMassSetCylinderTotal (m, dMUL(dPI,dMUL(SQR(radius),dMUL(length,density))), |
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163 direction, radius, length); |
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164 } |
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165 |
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166 EXPORT_C void dMassSetCylinderTotal (dMass *m, dReal total_mass, int direction, |
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167 dReal radius, dReal length) |
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168 { |
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169 dReal r2,I; |
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170 dMassSetZero (m); |
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171 r2 = SQR(radius); |
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172 m->mass = total_mass; |
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173 I = dMUL(total_mass,(dMUL(REAL(0.25),r2) + dMUL(dDIV(REAL(1.0),REAL(12.0)),SQR(length)))); |
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174 m->_I(0,0) = I; |
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175 m->_I(1,1) = I; |
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176 m->_I(2,2) = I; |
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177 m->_I(direction-1,direction-1) = dMUL(total_mass,dMUL(REAL(0.5),r2)); |
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178 |
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179 # ifndef dNODEBUG |
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180 dMassCheck (m); |
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181 # endif |
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182 } |
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183 |
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184 |
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185 EXPORT_C void dMassSetBox (dMass *m, dReal density, |
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186 dReal lx, dReal ly, dReal lz) |
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187 { |
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188 dMassSetBoxTotal (m, dMUL(lx,dMUL(ly,dMUL(lz,density))), lx, ly, lz); |
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189 } |
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190 |
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191 |
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192 EXPORT_C void dMassSetBoxTotal (dMass *m, dReal total_mass, |
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193 dReal lx, dReal ly, dReal lz) |
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194 { |
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195 dMassSetZero (m); |
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196 m->mass = total_mass; |
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197 m->_I(0,0) = dMUL(dDIV(total_mass,REAL(12.0)),(SQR(ly) + SQR(lz))); |
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198 m->_I(1,1) = dMUL(dDIV(total_mass,REAL(12.0)),(SQR(lx) + SQR(lz))); |
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199 m->_I(2,2) = dMUL(dDIV(total_mass,REAL(12.0)),(SQR(lx) + SQR(ly))); |
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200 |
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201 # ifndef dNODEBUG |
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202 dMassCheck (m); |
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203 # endif |
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204 } |
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205 |
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206 EXPORT_C void dMassAdjust (dMass *m, dReal newmass) |
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207 { |
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208 dReal scale = dDIV(newmass,m->mass); |
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209 m->mass = newmass; |
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210 for (int i=0; i<3; i++) for (int j=0; j<3; j++) m->_I(i,j) = dMUL(m->_I(i,j),scale); |
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211 |
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212 # ifndef dNODEBUG |
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213 dMassCheck (m); |
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214 # endif |
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215 } |
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216 |
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217 |
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218 EXPORT_C void dMassTranslate (dMass *m, dReal x, dReal y, dReal z) |
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219 { |
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220 // if the body is translated by `a' relative to its point of reference, |
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221 // the new inertia about the point of reference is: |
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222 // |
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223 // I + mass*(crossmat(c)^2 - crossmat(c+a)^2) |
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224 // |
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225 // where c is the existing center of mass and I is the old inertia. |
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226 |
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227 int i,j; |
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228 dMatrix3 ahat,chat,t1,t2; |
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229 dReal a[3]; |
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230 |
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231 // adjust inertia matrix |
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232 dSetZero (chat,12); |
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233 dCROSSMAT (chat,m->c,4,+,-); |
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234 a[0] = x + m->c[0]; |
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235 a[1] = y + m->c[1]; |
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236 a[2] = z + m->c[2]; |
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237 dSetZero (ahat,12); |
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238 dCROSSMAT (ahat,a,4,+,-); |
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239 dMULTIPLY0_333 (t1,ahat,ahat); |
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240 dMULTIPLY0_333 (t2,chat,chat); |
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241 for (i=0; i<3; i++) for (j=0; j<3; j++) |
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242 m->_I(i,j) += dMUL(m->mass,(t2[i*4+j]-t1[i*4+j])); |
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243 |
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244 // ensure perfect symmetry |
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245 m->_I(1,0) = m->_I(0,1); |
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246 m->_I(2,0) = m->_I(0,2); |
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247 m->_I(2,1) = m->_I(1,2); |
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248 |
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249 // adjust center of mass |
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250 m->c[0] += x; |
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251 m->c[1] += y; |
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252 m->c[2] += z; |
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253 |
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254 # ifndef dNODEBUG |
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255 dMassCheck (m); |
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256 # endif |
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257 } |
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258 |
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259 |
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260 EXPORT_C void dMassRotate (dMass *m, const dMatrix3 R) |
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261 { |
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262 // if the body is rotated by `R' relative to its point of reference, |
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263 // the new inertia about the point of reference is: |
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264 // |
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265 // R * I * R' |
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266 // |
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267 // where I is the old inertia. |
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268 |
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269 dMatrix3 t1; |
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270 dReal t2[3]; |
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271 |
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272 // rotate inertia matrix |
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273 dMULTIPLY2_333 (t1,m->I,R); |
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274 dMULTIPLY0_333 (m->I,R,t1); |
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275 |
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276 // ensure perfect symmetry |
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277 m->_I(1,0) = m->_I(0,1); |
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278 m->_I(2,0) = m->_I(0,2); |
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279 m->_I(2,1) = m->_I(1,2); |
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280 |
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281 // rotate center of mass |
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282 dMULTIPLY0_331 (t2,R,m->c); |
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283 m->c[0] = t2[0]; |
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284 m->c[1] = t2[1]; |
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285 m->c[2] = t2[2]; |
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286 |
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287 # ifndef dNODEBUG |
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288 dMassCheck (m); |
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289 # endif |
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290 } |
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291 |
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292 |
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293 EXPORT_C void dMassAdd (dMass *a, const dMass *b) |
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294 { |
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295 int i; |
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296 dReal denom = dRecip (a->mass + b->mass); |
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297 for (i=0; i<3; i++) a->c[i] = dMUL((dMUL(a->c[i],a->mass) + dMUL(b->c[i],b->mass)),denom); |
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298 a->mass += b->mass; |
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299 for (i=0; i<12; i++) a->I[i] += b->I[i]; |
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300 } |