[37] | 1 | /* |
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| 2 | * vect: |
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| 3 | * Functions to support operations on vectors and matrices. |
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| 4 | * |
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| 5 | * Original code from: |
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| 6 | * David M. Ciemiewicz, Mark Grossman, Henry Moreton, and Paul Haeberli |
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| 7 | * |
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| 8 | * Much mucking with by: |
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| 9 | * Gavin Bell |
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| 10 | */ |
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| 11 | #include <stdio.h> |
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| 12 | #include "vect.h" |
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| 13 | |
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| 14 | float * |
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| 15 | vnew() |
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| 16 | { |
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| 17 | register float *v; |
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| 18 | |
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| 19 | v = (float *) malloc(sizeof(float)*3); |
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| 20 | return v; |
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| 21 | } |
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| 22 | |
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| 23 | float * |
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| 24 | vclone(const float *v) |
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| 25 | { |
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| 26 | register float *c; |
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| 27 | |
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| 28 | c = vnew(); |
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| 29 | vcopy(v, c); |
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| 30 | return c; |
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| 31 | } |
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| 32 | |
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| 33 | void |
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| 34 | vcopy(const float *v1, float *v2) |
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| 35 | { |
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| 36 | register int i; |
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| 37 | for (i = 0 ; i < 3 ; i++) |
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| 38 | v2[i] = v1[i]; |
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| 39 | } |
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| 40 | |
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| 41 | void |
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| 42 | vprint(const float *v) |
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| 43 | { |
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| 44 | printf("x: %f y: %f z: %f\n",v[0],v[1],v[2]); |
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| 45 | } |
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| 46 | |
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| 47 | void |
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| 48 | vset(float *v, float x, float y, float z) |
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| 49 | { |
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| 50 | v[0] = x; |
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| 51 | v[1] = y; |
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| 52 | v[2] = z; |
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| 53 | } |
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| 54 | |
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| 55 | void |
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| 56 | vzero(float *v) |
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| 57 | { |
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| 58 | v[0] = 0.0; |
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| 59 | v[1] = 0.0; |
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| 60 | v[2] = 0.0; |
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| 61 | } |
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| 62 | |
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| 63 | void |
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| 64 | vnormal(float *v) |
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| 65 | { |
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| 66 | vscale(v,1.0/vlength(v)); |
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| 67 | } |
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| 68 | |
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| 69 | float |
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| 70 | vlength(const float *v) |
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| 71 | { |
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| 72 | return sqrtf(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]); |
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| 73 | } |
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| 74 | |
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| 75 | void |
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| 76 | vscale(float *v, float div) |
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| 77 | { |
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| 78 | v[0] *= div; |
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| 79 | v[1] *= div; |
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| 80 | v[2] *= div; |
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| 81 | } |
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| 82 | |
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| 83 | void |
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| 84 | vmult(const float *src1, const float *src2, float *dst) |
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| 85 | { |
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| 86 | dst[0] = src1[0] * src2[0]; |
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| 87 | dst[1] = src1[1] * src2[1]; |
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| 88 | dst[2] = src1[2] * src2[2]; |
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| 89 | } |
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| 90 | |
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| 91 | void |
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| 92 | vadd(const float *src1, const float *src2, float *dst) |
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| 93 | { |
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| 94 | dst[0] = src1[0] + src2[0]; |
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| 95 | dst[1] = src1[1] + src2[1]; |
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| 96 | dst[2] = src1[2] + src2[2]; |
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| 97 | } |
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| 98 | |
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| 99 | void |
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| 100 | vsub(const float *src1, const float *src2, float *dst) |
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| 101 | { |
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| 102 | dst[0] = src1[0] - src2[0]; |
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| 103 | dst[1] = src1[1] - src2[1]; |
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| 104 | dst[2] = src1[2] - src2[2]; |
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| 105 | } |
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| 106 | |
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| 107 | void |
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| 108 | vhalf(const float *v1, const float *v2, float *half) |
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| 109 | { |
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| 110 | float len; |
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| 111 | |
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| 112 | vadd(v2,v1,half); |
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| 113 | len = vlength(half); |
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| 114 | if(len>0.0001) |
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| 115 | vscale(half,1.0/len); |
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| 116 | else |
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| 117 | vcopy(v1, half); |
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| 118 | } |
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| 119 | |
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| 120 | float |
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| 121 | vdot(const float *v1, const float *v2) |
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| 122 | { |
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| 123 | return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2]; |
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| 124 | } |
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| 125 | |
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| 126 | void |
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| 127 | vcross(const float *v1, const float *v2, float *cross) |
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| 128 | { |
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| 129 | float temp[3]; |
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| 130 | |
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| 131 | temp[0] = (v1[1] * v2[2]) - (v1[2] * v2[1]); |
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| 132 | temp[1] = (v1[2] * v2[0]) - (v1[0] * v2[2]); |
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| 133 | temp[2] = (v1[0] * v2[1]) - (v1[1] * v2[0]); |
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| 134 | vcopy(temp, cross); |
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| 135 | } |
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| 136 | |
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| 137 | void |
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| 138 | vdirection(const float *v1, float *dir) |
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| 139 | { |
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| 140 | vcopy(v1, dir); |
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| 141 | vnormal(dir); |
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| 142 | } |
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| 143 | |
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| 144 | void |
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| 145 | vreflect(const float *in, const float *mirror, float *out) |
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| 146 | { |
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| 147 | float temp[3]; |
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| 148 | |
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| 149 | vcopy(mirror, temp); |
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| 150 | vscale(temp,vdot(mirror,in)); |
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| 151 | vsub(temp,in,out); |
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| 152 | vadd(temp,out,out); |
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| 153 | } |
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| 154 | |
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| 155 | void |
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| 156 | vmultmatrix(const Matrix m1, const Matrix m2, Matrix prod) |
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| 157 | { |
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| 158 | register int row, col; |
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| 159 | Matrix temp; |
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| 160 | |
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| 161 | for(row=0 ; row<4 ; row++) |
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| 162 | for(col=0 ; col<4 ; col++) |
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| 163 | temp[row][col] = m1[row][0] * m2[0][col] |
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| 164 | + m1[row][1] * m2[1][col] |
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| 165 | + m1[row][2] * m2[2][col] |
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| 166 | + m1[row][3] * m2[3][col]; |
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| 167 | for(row=0 ; row<4 ; row++) |
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| 168 | for(col=0 ; col<4 ; col++) |
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| 169 | prod[row][col] = temp[row][col]; |
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| 170 | } |
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| 171 | |
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| 172 | void |
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| 173 | vtransform(const float *v, const Matrix mat, float *vt) |
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| 174 | { |
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| 175 | float t[3]; |
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| 176 | |
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| 177 | t[0] = v[0]*mat[0][0] + v[1]*mat[1][0] + v[2]*mat[2][0] + mat[3][0]; |
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| 178 | t[1] = v[0]*mat[0][1] + v[1]*mat[1][1] + v[2]*mat[2][1] + mat[3][1]; |
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| 179 | t[2] = v[0]*mat[0][2] + v[1]*mat[1][2] + v[2]*mat[2][2] + mat[3][2]; |
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| 180 | vcopy(t, vt); |
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| 181 | } |
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| 182 | void |
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| 183 | vtransform4(const float *v, const Matrix mat, float *vt) |
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| 184 | { |
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| 185 | float t[3]; |
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| 186 | |
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| 187 | t[0] = v[0]*mat[0][0] + v[1]*mat[1][0] + v[2]*mat[2][0] + mat[3][0]; |
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| 188 | t[1] = v[0]*mat[0][1] + v[1]*mat[1][1] + v[2]*mat[2][1] + mat[3][1]; |
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| 189 | t[2] = v[0]*mat[0][2] + v[1]*mat[1][2] + v[2]*mat[2][2] + mat[3][2]; |
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| 190 | vcopy(t, vt); |
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| 191 | t[3] = v[0]*mat[0][3] + v[1]*mat[1][3] + v[2]*mat[2][3] + mat[3][3]; |
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| 192 | vt[3] = t[3]; |
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| 193 | } |
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| 194 | |
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| 195 | Matrix idmatrix = |
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| 196 | { |
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| 197 | { 1.0, 0.0, 0.0, 0.0,}, |
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| 198 | { 0.0, 1.0, 0.0, 0.0,}, |
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| 199 | { 0.0, 0.0, 1.0, 0.0,}, |
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| 200 | { 0.0, 0.0, 0.0, 1.0,}, |
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| 201 | }; |
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| 202 | |
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| 203 | void |
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| 204 | mcopy(const Matrix m1, Matrix m2) |
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| 205 | { |
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| 206 | int i, j; |
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| 207 | for (i = 0; i < 4; i++) |
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| 208 | for (j = 0; j < 4; j++) |
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| 209 | m2[i][j] = m1[i][j]; |
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| 210 | } |
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| 211 | |
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| 212 | void |
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| 213 | minvert(const Matrix mat, Matrix result) |
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| 214 | { |
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| 215 | int i, j, k; |
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| 216 | double temp; |
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| 217 | double m[8][4]; |
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| 218 | /* Declare identity matrix */ |
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| 219 | |
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| 220 | mcopy(idmatrix, result); |
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| 221 | for (i = 0; i < 4; i++) { |
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| 222 | for (j = 0; j < 4; j++) { |
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| 223 | m[i][j] = mat[i][j]; |
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| 224 | m[i+4][j] = result[i][j]; |
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| 225 | } |
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| 226 | } |
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| 227 | |
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| 228 | /* Work across by columns */ |
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| 229 | |
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| 230 | for (i = 0; i < 4; i++) { |
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| 231 | for (j = i; (m[i][j] == 0.0) && (j < 4); j++) |
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| 232 | ; |
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| 233 | if (j == 4) { |
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| 234 | fprintf (stderr, "error: cannot do inverse matrix\n"); |
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| 235 | exit (2); |
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| 236 | } |
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| 237 | else if (i != j) { |
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| 238 | for (k = 0; k < 8; k++) { |
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| 239 | temp = m[k][i]; |
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| 240 | m[k][i] = m[k][j]; |
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| 241 | m[k][j] = temp; |
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| 242 | } |
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| 243 | } |
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| 244 | |
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| 245 | /* Divide original row */ |
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| 246 | |
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| 247 | for (j = 7; j >= i; j--) |
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| 248 | m[j][i] /= m[i][i]; |
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| 249 | |
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| 250 | /* Subtract other rows */ |
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| 251 | |
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| 252 | for (j = 0; j < 4; j++) |
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| 253 | if (i != j) |
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| 254 | for (k = 7; k >= i; k--) |
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| 255 | m[k][j] -= m[k][i] * m[i][j]; |
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| 256 | } |
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| 257 | |
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| 258 | for (i = 0; i < 4; i++) |
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| 259 | for (j = 0; j < 4; j++) |
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| 260 | result[i][j] = m[i+4][j]; |
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| 261 | } |
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| 262 | |
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| 263 | /* |
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| 264 | * Get combined Model/View/Projection matrix, in any mmode |
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| 265 | */ |
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| 266 | void |
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| 267 | vgetmatrix(Matrix m) |
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| 268 | { |
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| 269 | long mm; |
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| 270 | |
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| 271 | mm = getmmode(); |
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| 272 | |
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| 273 | if (mm == MSINGLE) |
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| 274 | { |
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| 275 | getmatrix(m); |
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| 276 | } |
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| 277 | else |
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| 278 | { |
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| 279 | Matrix mp, mv; |
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| 280 | |
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| 281 | mmode(MPROJECTION); |
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| 282 | getmatrix(mp); |
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| 283 | mmode(MVIEWING); |
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| 284 | getmatrix(mv); |
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| 285 | |
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| 286 | pushmatrix(); /* Multiply them together */ |
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| 287 | loadmatrix(mp); |
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| 288 | multmatrix(mv); |
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| 289 | getmatrix(m); |
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| 290 | popmatrix(); |
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| 291 | |
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| 292 | mmode(mm); /* Back into the mode we started in */ |
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| 293 | } |
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| 294 | } |
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| 295 | |
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| 296 | /* |
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| 297 | * Gaussian Elimination with Scaled Column Pivoting |
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| 298 | * |
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| 299 | * copied out of the book by Wade Olsen |
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| 300 | * Silicon Graphics |
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| 301 | * Feb. 12, 1990 |
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| 302 | */ |
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| 303 | |
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| 304 | void |
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| 305 | linsolve( |
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| 306 | const float *eqs[], /* System of eq's to solve */ |
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| 307 | int n, /* of size inmat[n][n+1] */ |
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| 308 | float *x /* Result float *or of size x[n] */ |
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| 309 | ) |
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| 310 | { |
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| 311 | int i, j, p; |
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| 312 | |
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| 313 | float **a; |
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| 314 | |
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| 315 | /* Allocate space to work in */ |
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| 316 | /* (avoid modifying the equations passed) */ |
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| 317 | a = (float **)malloc(sizeof(float *)*n); |
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| 318 | for (i = 0; i < n; i++) |
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| 319 | { |
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| 320 | a[i] = (float *)malloc(sizeof(float)*(n+1)); |
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| 321 | bcopy(eqs[i], a[i], sizeof(float)*(n+1)); |
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| 322 | } |
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| 323 | |
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| 324 | |
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| 325 | if (n == 1) |
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| 326 | { /* The simple single variable case */ |
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| 327 | x[0] = a[0][1] / a[0][0]; |
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| 328 | return; |
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| 329 | } |
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| 330 | /* Gausian elimination process */ |
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| 331 | for (i = 0; i < n -1; i++) |
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| 332 | { |
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| 333 | |
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| 334 | /* find non-zero pivot row */ |
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| 335 | p = i; |
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| 336 | while (a[p][i] == 0.0) |
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| 337 | { |
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| 338 | p++; |
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| 339 | if (p == n) |
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| 340 | { |
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| 341 | printf("linsolv: No unique solution exists.\n"); |
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| 342 | exit(1); |
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| 343 | } |
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| 344 | } |
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| 345 | /* row swap */ |
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| 346 | if (p != i) |
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| 347 | { |
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| 348 | float *swap; |
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| 349 | |
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| 350 | swap = a[i]; |
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| 351 | a[i] = a[p]; |
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| 352 | a[p] = swap; |
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| 353 | } |
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| 354 | /* row subtractions */ |
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| 355 | for (j = i + 1; j < n; j++) |
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| 356 | { |
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| 357 | float mult = a[j][i] / a[i][i]; |
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| 358 | |
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| 359 | int k; |
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| 360 | for (k = i + 1; k < n + 1; k++) |
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| 361 | a[j][k] -= mult * a[i][k]; |
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| 362 | } |
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| 363 | } |
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| 364 | |
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| 365 | if (a[n-1][n-1] == 0.0) |
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| 366 | { |
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| 367 | printf("linsolv: No unique solution exists.\n"); |
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| 368 | exit(1); |
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| 369 | } |
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| 370 | |
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| 371 | /* backwards substitution */ |
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| 372 | x[n-1] = a[n-1][n] / a[n-1][n-1]; |
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| 373 | for (i = n -2; i > -1; i--) |
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| 374 | { |
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| 375 | float sum = a[i][n]; |
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| 376 | |
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| 377 | for (j = i + 1; j < n; j++) |
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| 378 | sum -= a[i][j] * x[j]; |
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| 379 | |
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| 380 | x[i] = sum / a[i][i]; |
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| 381 | } |
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| 382 | |
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| 383 | /* Free working space */ |
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| 384 | for (i = 0; i < n; i++) |
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| 385 | { |
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| 386 | free(a[i]); |
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| 387 | } |
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| 388 | free(a); |
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| 389 | } |
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