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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/common.h> |
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24 #include <ode/odemath.h> |
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25 |
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26 |
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27 // this may be called for vectors `a' with extremely small magnitude, for |
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28 // example the result of a cross product on two nearly perpendicular vectors. |
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29 // we must be robust to these small vectors. to prevent numerical error, |
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30 // first find the component a[i] with the largest magnitude and then scale |
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31 // all the components by 1/a[i]. then we can compute the length of `a' and |
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32 // scale the components by 1/l. this has been verified to work with vectors |
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33 // containing the smallest representable numbers. |
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34 |
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35 EXPORT_C void dNormalize3 (dVector3 a) |
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36 { |
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37 dReal a0,a1,a2,aa0,aa1,aa2,l; |
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38 a0 = a[0]; |
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39 a1 = a[1]; |
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40 a2 = a[2]; |
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41 aa0 = dFabs(a0); |
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42 aa1 = dFabs(a1); |
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43 aa2 = dFabs(a2); |
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44 if (aa1 > aa0) { |
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45 if (aa2 > aa1) { |
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46 goto aa2_largest; |
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47 } |
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48 else { // aa1 is largest |
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49 a0 = dDIV(a0,aa1); |
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50 a2 = dDIV(a2,aa1); |
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51 l = dRecipSqrt (dMUL(a0,a0) + dMUL(a2,a2) + REAL(1.0)); |
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52 a[0] = dMUL(a0,l); |
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53 a[1] = dCopySign(l,a1); |
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54 a[2] = dMUL(a2,l); |
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55 } |
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56 } |
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57 else { |
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58 if (aa2 > aa0) { |
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59 aa2_largest: // aa2 is largest |
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60 a0 = dDIV(a0,aa2); |
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61 a1 = dDIV(a1,aa2); |
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62 l = dRecipSqrt (dMUL(a0,a0) + dMUL(a1,a1) + REAL(1.0)); |
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63 a[0] = dMUL(a0,l); |
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64 a[1] = dMUL(a1,l); |
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65 a[2] = dCopySign(l,a2); |
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66 } |
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67 else { // aa0 is largest |
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68 if (aa0 <= 0) { |
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69 a[0] = REAL(1.0); // if all a's are zero, this is where we'll end up. |
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70 a[1] = 0; // return a default unit length vector. |
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71 a[2] = 0; |
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72 return; |
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73 } |
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74 a1 = dDIV(a1,aa0); |
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75 a2 = dDIV(a2,aa0); |
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76 l = dRecipSqrt (dMUL(a1,a1) + dMUL(a2,a2) + REAL(1.0)); |
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77 a[0] = dCopySign(l,a0); |
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78 a[1] = dMUL(a1,l); |
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79 a[2] = dMUL(a2,l); |
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80 } |
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81 } |
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82 } |
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83 |
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84 |
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85 /* OLD VERSION */ |
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86 /* |
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87 void dNormalize3 (dVector3 a) |
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88 { |
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89 |
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90 dReal l = dDOT(a,a); |
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91 if (l > 0) { |
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92 l = dRecipSqrt(l); |
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93 a[0] *= l; |
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94 a[1] *= l; |
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95 a[2] *= l; |
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96 } |
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97 else { |
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98 a[0] = 1; |
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99 a[1] = 0; |
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100 a[2] = 0; |
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101 } |
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102 } |
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103 */ |
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104 |
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105 |
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106 EXPORT_C void dNormalize4 (dVector4 a) |
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107 { |
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108 |
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109 dReal l = dDOT(a,a)+dMUL(a[3],a[3]); |
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110 if (l > 0) { |
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111 l = dRecipSqrt(l); |
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112 a[0] = dMUL(a[0],l); |
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113 a[1] = dMUL(a[1],l); |
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114 a[2] = dMUL(a[2],l); |
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115 a[3] = dMUL(a[3],l); |
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116 } |
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117 else { |
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118 a[0] = REAL(1.0); |
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119 a[1] = 0; |
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120 a[2] = 0; |
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121 a[3] = 0; |
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122 } |
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123 } |
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124 |
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125 |
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126 EXPORT_C void dPlaneSpace (const dVector3 n, dVector3 p, dVector3 q) |
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127 { |
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128 if (dFabs(n[2]) > dSQRT1_2) { |
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129 // choose p in y-z plane |
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130 dReal a = dMUL(n[1],n[1]) + dMUL(n[2],n[2]); |
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131 dReal k = dRecipSqrt (a); |
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132 p[0] = 0; |
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133 p[1] = -dMUL(n[2],k); |
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134 p[2] = dMUL(n[1],k); |
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135 // set q = n x p |
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136 q[0] = dMUL(a,k); |
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137 q[1] = -dMUL(n[0],p[2]); |
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138 q[2] = dMUL(n[0],p[1]); |
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139 } |
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140 else { |
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141 // choose p in x-y plane |
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142 dReal a = dMUL(n[0],n[0]) + dMUL(n[1],n[1]); |
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143 dReal k = dRecipSqrt (a); |
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144 p[0] = -dMUL(n[1],k); |
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145 p[1] = dMUL(n[0],k); |
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146 p[2] = 0; |
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147 // set q = n x p |
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148 q[0] = -dMUL(n[2],p[1]); |
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149 q[1] = dMUL(n[2],p[0]); |
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150 q[2] = dMUL(a,k); |
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151 } |
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152 } |
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153 |
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154 EXPORT_C dReal dArcTan2(const dReal y, const dReal x) |
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155 { |
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156 dReal coeff_1 = dPI/4; |
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157 dReal coeff_2 = 3*coeff_1; |
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158 dReal abs_y = dFabs(y) + dEpsilon; // kludge to prevent 0/0 condition |
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159 dReal angle; |
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160 if (x>=0) |
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161 { |
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162 dReal r = dDIV((x - abs_y),(x + abs_y)); |
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163 //angle = coeff_1 - dMUL(coeff_1,r); |
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164 angle = dMUL(REAL(0.1963),dMUL(r,dMUL(r,r))) - dMUL(REAL(0.9817),r) + coeff_1; |
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165 } |
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166 else |
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167 { |
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168 dReal r = dDIV((x + abs_y),(abs_y - x)); |
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169 //angle = coeff_2 - dMUL(coeff_1,r); |
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170 angle = dMUL(REAL(0.1963),dMUL(r,dMUL(r,r))) - dMUL(REAL(0.9817),r) + coeff_2; |
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171 } |
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172 if (y < 0) |
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173 return(-angle); // negate if in quad III or IV |
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174 else |
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175 return(angle); |
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176 } |
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177 |
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178 EXPORT_C dReal dArcSin(dReal arg) |
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179 { |
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180 dReal temp; |
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181 int sign; |
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182 |
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183 sign = 0; |
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184 if(arg < 0) |
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185 { |
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186 arg = -arg; |
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187 sign++; |
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188 } |
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189 if(arg > REAL(1.0)) { |
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190 arg = REAL(1.0); |
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191 //return dInfinity; |
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192 } |
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193 temp = dSqrt(REAL(1.0) - dMUL(arg,arg)); |
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194 if(arg > REAL(0.7)) |
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195 temp = dPI/2 - dArcTan2(temp,arg); |
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196 else |
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197 temp = dArcTan2(arg,temp); |
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198 if(sign > 0) |
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199 temp = -temp; |
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200 return temp; |
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201 } |
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202 |