1 | /************************************************************************
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2 |
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3 | 4x4 Matrix class
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4 |
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5 | Copyright (C) 1998 Michael Garland. See "COPYING.txt" for details.
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6 |
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7 | $Id: MxMat4.cxx,v 1.1 2002/09/24 16:53:54 wimmer Exp $
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8 |
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9 | ************************************************************************/
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10 |
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11 | #include "stdmix.h"
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12 | #include "MxMat4.h"
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13 |
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14 | Mat4 Mat4::I(Vec4(1,0,0,0),Vec4(0,1,0,0),Vec4(0,0,1,0),Vec4(0,0,0,1));
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15 | Mat4 Mat4::zero(Vec4(0,0,0,0),Vec4(0,0,0,0),Vec4(0,0,0,0),Vec4(0,0,0,0));
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16 | Mat4 Mat4::unit(Vec4(1,1,1,1),Vec4(1,1,1,1),Vec4(1,1,1,1),Vec4(1,1,1,1));
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17 |
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18 | Mat4 Mat4::trans(double x, double y, double z)
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19 | {
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20 | return Mat4(Vec4(1,0,0,x),
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21 | Vec4(0,1,0,y),
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22 | Vec4(0,0,1,z),
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23 | Vec4(0,0,0,1));
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24 | }
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25 |
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26 | Mat4 Mat4::scale(double x, double y, double z)
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27 | {
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28 | return Mat4(Vec4(x,0,0,0),
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29 | Vec4(0,y,0,0),
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30 | Vec4(0,0,z,0),
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31 | Vec4(0,0,0,1));
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32 | }
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33 |
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34 | Mat4 Mat4::xrot(double a)
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35 | {
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36 | double c = cos(a);
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37 | double s = sin(a);
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38 |
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39 | return Mat4(Vec4(1, 0, 0, 0),
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40 | Vec4(0, c,-s, 0),
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41 | Vec4(0, s, c, 0),
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42 | Vec4(0, 0, 0, 1));
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43 | }
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44 |
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45 | Mat4 Mat4::yrot(double a)
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46 | {
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47 | double c = cos(a);
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48 | double s = sin(a);
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49 |
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50 | return Mat4(Vec4(c, 0, s, 0),
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51 | Vec4(0, 1, 0, 0),
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52 | Vec4(-s,0, c, 0),
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53 | Vec4(0, 0, 0, 1));
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54 | }
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55 |
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56 | Mat4 Mat4::zrot(double a)
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57 | {
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58 | double c = cos(a);
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59 | double s = sin(a);
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60 |
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61 | return Mat4(Vec4(c,-s, 0, 0),
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62 | Vec4(s, c, 0, 0),
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63 | Vec4(0, 0, 1, 0),
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64 | Vec4(0, 0, 0, 1));
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65 | }
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66 |
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67 | Mat4 Mat4::operator*(const Mat4& m) const
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68 | {
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69 | Mat4 A;
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70 | int i,j;
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71 |
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72 | for(i=0;i<4;i++)
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73 | for(j=0;j<4;j++)
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74 | A(i,j) = row[i]*m.col(j);
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75 |
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76 | return A;
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77 | }
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78 |
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79 | double Mat4::det() const
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80 | {
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81 | return row[0] * cross(row[1], row[2], row[3]);
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82 | }
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83 |
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84 | Mat4 Mat4::transpose() const
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85 | {
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86 | return Mat4(col(0), col(1), col(2), col(3));
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87 | }
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88 |
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89 | Mat4 Mat4::adjoint() const
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90 | {
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91 | Mat4 A;
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92 |
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93 | A.row[0] = cross( row[1], row[2], row[3]);
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94 | A.row[1] = cross(-row[0], row[2], row[3]);
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95 | A.row[2] = cross( row[0], row[1], row[3]);
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96 | A.row[3] = cross(-row[0], row[1], row[2]);
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97 |
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98 | return A;
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99 | }
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100 |
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101 | double Mat4::cramerInvert(Mat4& inv) const
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102 | {
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103 | Mat4 A = adjoint();
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104 | double d = A.row[0] * row[0];
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105 |
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106 | if( d==0.0 )
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107 | return 0.0;
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108 |
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109 | inv = A.transpose() / d;
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110 | return d;
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111 | }
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112 |
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113 |
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114 |
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115 | // Matrix inversion code for 4x4 matrices.
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116 | // Originally ripped off and degeneralized from Paul's matrix library
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117 | // for the view synthesis (Chen) software.
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118 | //
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119 | // Returns determinant of a, and b=a inverse.
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120 | // If matrix is singular, returns 0 and leaves trash in b.
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121 | //
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122 | // Uses Gaussian elimination with partial pivoting.
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123 |
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124 | #define SWAP(a, b, t) {t = a; a = b; b = t;}
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125 | double Mat4::invert(Mat4& B) const
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126 | {
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127 | Mat4 A(*this);
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128 |
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129 | int i, j, k;
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130 | double max, t, det, pivot;
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131 |
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132 | /*---------- forward elimination ----------*/
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133 |
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134 | for (i=0; i<4; i++) /* put identity matrix in B */
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135 | for (j=0; j<4; j++)
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136 | B(i, j) = (double)(i==j);
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137 |
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138 | det = 1.0;
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139 | for (i=0; i<4; i++) { /* eliminate in column i, below diag */
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140 | max = -1.;
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141 | for (k=i; k<4; k++) /* find pivot for column i */
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142 | if (fabs(A(k, i)) > max) {
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143 | max = fabs(A(k, i));
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144 | j = k;
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145 | }
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146 | if (max<=0.) return 0.; /* if no nonzero pivot, PUNT */
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147 | if (j!=i) { /* swap rows i and j */
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148 | for (k=i; k<4; k++)
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149 | SWAP(A(i, k), A(j, k), t);
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150 | for (k=0; k<4; k++)
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151 | SWAP(B(i, k), B(j, k), t);
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152 | det = -det;
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153 | }
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154 | pivot = A(i, i);
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155 | det *= pivot;
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156 | for (k=i+1; k<4; k++) /* only do elems to right of pivot */
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157 | A(i, k) /= pivot;
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158 | for (k=0; k<4; k++)
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159 | B(i, k) /= pivot;
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160 | /* we know that A(i, i) will be set to 1, so don't bother to do it */
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161 |
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162 | for (j=i+1; j<4; j++) { /* eliminate in rows below i */
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163 | t = A(j, i); /* we're gonna zero this guy */
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164 | for (k=i+1; k<4; k++) /* subtract scaled row i from row j */
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165 | A(j, k) -= A(i, k)*t; /* (ignore k<=i, we know they're 0) */
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166 | for (k=0; k<4; k++)
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167 | B(j, k) -= B(i, k)*t;
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168 | }
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169 | }
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170 |
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171 | /*---------- backward elimination ----------*/
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172 |
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173 | for (i=4-1; i>0; i--) { /* eliminate in column i, above diag */
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174 | for (j=0; j<i; j++) { /* eliminate in rows above i */
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175 | t = A(j, i); /* we're gonna zero this guy */
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176 | for (k=0; k<4; k++) /* subtract scaled row i from row j */
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177 | B(j, k) -= B(i, k)*t;
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178 | }
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179 | }
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180 |
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181 | return det;
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182 | }
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