[774] | 1 | #include <gfx/std.h>
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| 2 | #include <gfx/math/Mat4.h>
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| 3 |
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[1025] | 4 | using namespace simplif;
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[774] | 5 |
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| 6 | Mat4 Mat4::identity(Vec4(1,0,0,0),Vec4(0,1,0,0),Vec4(0,0,1,0),Vec4(0,0,0,1));
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| 7 | 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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| 8 | 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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| 9 |
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| 10 | Mat4 Mat4::trans(real x, real y, real z)
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| 11 | {
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| 12 | return Mat4(Vec4(1,0,0,x),
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| 13 | Vec4(0,1,0,y),
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| 14 | Vec4(0,0,1,z),
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| 15 | Vec4(0,0,0,1));
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| 16 | }
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| 17 |
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| 18 | Mat4 Mat4::scale(real x, real y, real z)
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| 19 | {
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| 20 | return Mat4(Vec4(x,0,0,0),
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| 21 | Vec4(0,y,0,0),
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| 22 | Vec4(0,0,z,0),
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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::xrot(real a)
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| 27 | {
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| 28 | real c = cos(a);
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| 29 | real s = sin(a);
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| 30 |
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| 31 | return Mat4(Vec4(1, 0, 0, 0),
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| 32 | Vec4(0, c,-s, 0),
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| 33 | Vec4(0, s, c, 0),
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| 34 | Vec4(0, 0, 0, 1));
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| 35 | }
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| 36 |
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| 37 | Mat4 Mat4::yrot(real a)
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| 38 | {
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| 39 | real c = cos(a);
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| 40 | real s = sin(a);
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| 41 |
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| 42 | return Mat4(Vec4(c, 0, s, 0),
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| 43 | Vec4(0, 1, 0, 0),
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| 44 | Vec4(-s,0, c, 0),
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| 45 | Vec4(0, 0, 0, 1));
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| 46 | }
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| 47 |
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| 48 | Mat4 Mat4::zrot(real a)
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| 49 | {
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| 50 | real c = cos(a);
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| 51 | real s = sin(a);
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| 52 |
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| 53 | return Mat4(Vec4(c,-s, 0, 0),
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| 54 | Vec4(s, c, 0, 0),
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| 55 | Vec4(0, 0, 1, 0),
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| 56 | Vec4(0, 0, 0, 1));
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| 57 | }
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| 58 |
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| 59 | Mat4 Mat4::operator*(const Mat4& m) const
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| 60 | {
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| 61 | Mat4 A;
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| 62 | int i,j;
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| 63 |
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| 64 | for(i=0;i<4;i++)
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| 65 | for(j=0;j<4;j++)
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| 66 | A(i,j) = row[i]*m.col(j);
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| 67 |
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| 68 | return A;
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| 69 | }
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| 70 |
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| 71 | real Mat4::det() const
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| 72 | {
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| 73 | return row[0] * cross(row[1], row[2], row[3]);
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| 74 | }
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| 75 |
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| 76 | Mat4 Mat4::transpose() const
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| 77 | {
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| 78 | return Mat4(col(0), col(1), col(2), col(3));
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| 79 | }
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| 80 |
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| 81 | Mat4 Mat4::adjoint() const
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| 82 | {
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| 83 | Mat4 A;
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| 84 |
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| 85 | A.row[0] = cross( row[1], row[2], row[3]);
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| 86 | A.row[1] = cross(-row[0], row[2], row[3]);
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| 87 | A.row[2] = cross( row[0], row[1], row[3]);
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| 88 | A.row[3] = cross(-row[0], row[1], row[2]);
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| 89 |
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| 90 | return A;
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| 91 | }
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| 92 |
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| 93 | real Mat4::cramerInverse(Mat4& inv) const
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| 94 | {
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| 95 | Mat4 A = adjoint();
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| 96 | real d = A.row[0] * row[0];
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| 97 |
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| 98 | if( d==0.0 )
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| 99 | return 0.0;
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| 100 |
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| 101 | inv = A.transpose() / d;
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| 102 | return d;
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| 103 | }
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| 104 |
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| 105 |
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| 106 |
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| 107 | // Matrix inversion code for 4x4 matrices.
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| 108 | // Originally ripped off and degeneralized from Paul's matrix library
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| 109 | // for the view synthesis (Chen) software.
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| 110 | //
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| 111 | // Returns determinant of a, and b=a inverse.
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| 112 | // If matrix is singular, returns 0 and leaves trash in b.
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| 113 | //
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| 114 | // Uses Gaussian elimination with partial pivoting.
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| 115 |
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| 116 | #define SWAP(a, b, t) {t = a; a = b; b = t;}
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| 117 | real Mat4::inverse(Mat4& B) const
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| 118 | {
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| 119 | Mat4 A(*this);
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| 120 |
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| 121 | int i, j, k;
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| 122 | real max, t, det, pivot;
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| 123 |
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| 124 | /*---------- forward elimination ----------*/
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| 125 |
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| 126 | for (i=0; i<4; i++) /* put identity matrix in B */
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| 127 | for (j=0; j<4; j++)
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| 128 | B(i, j) = (real)(i==j);
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| 129 |
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| 130 | det = 1.0;
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| 131 | for (i=0; i<4; i++) { /* eliminate in column i, below diag */
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| 132 | max = -1.;
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| 133 | for (k=i; k<4; k++) /* find pivot for column i */
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| 134 | if (fabs(A(k, i)) > max) {
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| 135 | max = fabs(A(k, i));
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| 136 | j = k;
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| 137 | }
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| 138 | if (max<=0.) return 0.; /* if no nonzero pivot, PUNT */
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| 139 | if (j!=i) { /* swap rows i and j */
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| 140 | for (k=i; k<4; k++)
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| 141 | SWAP(A(i, k), A(j, k), t);
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| 142 | for (k=0; k<4; k++)
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| 143 | SWAP(B(i, k), B(j, k), t);
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| 144 | det = -det;
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| 145 | }
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| 146 | pivot = A(i, i);
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| 147 | det *= pivot;
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| 148 | for (k=i+1; k<4; k++) /* only do elems to right of pivot */
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| 149 | A(i, k) /= pivot;
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| 150 | for (k=0; k<4; k++)
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| 151 | B(i, k) /= pivot;
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| 152 | /* we know that A(i, i) will be set to 1, so don't bother to do it */
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| 153 |
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| 154 | for (j=i+1; j<4; j++) { /* eliminate in rows below i */
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| 155 | t = A(j, i); /* we're gonna zero this guy */
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| 156 | for (k=i+1; k<4; k++) /* subtract scaled row i from row j */
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| 157 | A(j, k) -= A(i, k)*t; /* (ignore k<=i, we know they're 0) */
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| 158 | for (k=0; k<4; k++)
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| 159 | B(j, k) -= B(i, k)*t;
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| 160 | }
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| 161 | }
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| 162 |
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| 163 | /*---------- backward elimination ----------*/
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| 164 |
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| 165 | for (i=4-1; i>0; i--) { /* eliminate in column i, above diag */
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| 166 | for (j=0; j<i; j++) { /* eliminate in rows above i */
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| 167 | t = A(j, i); /* we're gonna zero this guy */
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| 168 | for (k=0; k<4; k++) /* subtract scaled row i from row j */
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| 169 | B(j, k) -= B(i, k)*t;
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| 170 | }
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| 171 | }
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| 172 |
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| 173 | return det;
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| 174 | }
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