[162] | 1 | #include "Matrix4x4.h"
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| 2 | #include "Vector3.h"
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| 3 |
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| 4 | // standard headers
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| 5 | #include <iomanip>
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| 6 | using namespace std;
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| 7 |
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| 8 |
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[209] | 9 | Matrix4x4::Matrix4x4(const Vector3 &a, const Vector3 &b, const Vector3 &c)
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| 10 | {
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| 11 | // first index is column [x], the second is row [y]
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| 12 | x[0][0] = a.x;
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[245] | 13 | x[1][0] = b.x;
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| 14 | x[2][0] = c.x;
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[209] | 15 | x[3][0] = 0.0f;
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[162] | 16 |
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[245] | 17 | x[0][1] = a.y;
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[209] | 18 | x[1][1] = b.y;
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[245] | 19 | x[2][1] = c.y;
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[209] | 20 | x[3][1] = 0.0f;
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| 21 |
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[245] | 22 | x[0][2] = a.z;
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| 23 | x[1][2] = b.z;
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[209] | 24 | x[2][2] = c.z;
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| 25 | x[3][2] = 0.0f;
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| 26 |
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| 27 | x[0][3] = 0.0f;
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| 28 | x[1][3] = 0.0f;
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| 29 | x[2][3] = 0.0f;
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| 30 | x[3][3] = 1.0f;
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[245] | 31 |
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[209] | 32 | }
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| 33 |
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| 34 | void
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| 35 | Matrix4x4::SetColumns(const Vector3 &a, const Vector3 &b, const Vector3 &c)
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| 36 | {
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| 37 | // first index is column [x], the second is row [y]
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| 38 | x[0][0] = a.x;
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[245] | 39 | x[1][0] = a.y;
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| 40 | x[2][0] = a.z;
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[209] | 41 | x[3][0] = 0.0f;
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| 42 |
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[245] | 43 | x[0][1] = b.x;
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[209] | 44 | x[1][1] = b.y;
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[245] | 45 | x[2][1] = b.z;
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[209] | 46 | x[3][1] = 0.0f;
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| 47 |
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[245] | 48 | x[0][2] = c.x;
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| 49 | x[1][2] = c.y;
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[209] | 50 | x[2][2] = c.z;
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| 51 | x[3][2] = 0.0f;
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| 52 |
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| 53 | x[0][3] = 0.0f;
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| 54 | x[1][3] = 0.0f;
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| 55 | x[2][3] = 0.0f;
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| 56 | x[3][3] = 1.0f;
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| 57 | }
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| 58 |
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[162] | 59 | // full constructor
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| 60 | Matrix4x4::Matrix4x4(float x11, float x12, float x13, float x14,
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| 61 | float x21, float x22, float x23, float x24,
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| 62 | float x31, float x32, float x33, float x34,
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| 63 | float x41, float x42, float x43, float x44)
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| 64 | {
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[209] | 65 | // first index is column [x], the second is row [y]
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[162] | 66 | x[0][0] = x11;
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| 67 | x[1][0] = x12;
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| 68 | x[2][0] = x13;
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| 69 | x[3][0] = x14;
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| 70 |
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| 71 | x[0][1] = x21;
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| 72 | x[1][1] = x22;
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| 73 | x[2][1] = x23;
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| 74 | x[3][1] = x24;
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| 75 |
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| 76 | x[0][2] = x31;
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| 77 | x[1][2] = x32;
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| 78 | x[2][2] = x33;
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| 79 | x[3][2] = x34;
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| 80 |
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| 81 | x[0][3] = x41;
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| 82 | x[1][3] = x42;
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| 83 | x[2][3] = x43;
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| 84 | x[3][3] = x44;
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| 85 | }
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| 86 |
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| 87 | // inverse matrix computation gauss_jacobiho method .. from N.R. in C
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| 88 | // if matrix is regular = computatation successfull = returns 0
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| 89 | // in case of singular matrix returns 1
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| 90 | int
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| 91 | Matrix4x4::Invert()
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| 92 | {
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| 93 | int indxc[4],indxr[4],ipiv[4];
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| 94 | int i,icol,irow,j,k,l,ll,n;
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| 95 | float big,dum,pivinv,temp;
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| 96 | // satisfy the compiler
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| 97 | icol = irow = 0;
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| 98 |
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| 99 | // the size of the matrix
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| 100 | n = 4;
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| 101 |
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| 102 | for ( j = 0 ; j < n ; j++) /* zero pivots */
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| 103 | ipiv[j] = 0;
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| 104 |
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| 105 | for ( i = 0; i < n; i++)
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| 106 | {
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| 107 | big = 0.0;
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| 108 | for (j = 0 ; j < n ; j++)
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| 109 | if (ipiv[j] != 1)
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| 110 | for ( k = 0 ; k<n ; k++)
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| 111 | {
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| 112 | if (ipiv[k] == 0)
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| 113 | {
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| 114 | if (fabs(x[k][j]) >= big)
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| 115 | {
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| 116 | big = fabs(x[k][j]);
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| 117 | irow = j;
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| 118 | icol = k;
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| 119 | }
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| 120 | }
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| 121 | else
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| 122 | if (ipiv[k] > 1)
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| 123 | return 1; /* singular matrix */
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| 124 | }
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| 125 | ++(ipiv[icol]);
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| 126 | if (irow != icol)
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| 127 | {
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| 128 | for ( l = 0 ; l<n ; l++)
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| 129 | {
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| 130 | temp = x[l][icol];
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| 131 | x[l][icol] = x[l][irow];
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| 132 | x[l][irow] = temp;
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| 133 | }
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| 134 | }
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| 135 | indxr[i] = irow;
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| 136 | indxc[i] = icol;
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| 137 | if (x[icol][icol] == 0.0)
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| 138 | return 1; /* singular matrix */
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| 139 |
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| 140 | pivinv = 1.0 / x[icol][icol];
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| 141 | x[icol][icol] = 1.0 ;
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| 142 | for ( l = 0 ; l<n ; l++)
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| 143 | x[l][icol] = x[l][icol] * pivinv ;
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| 144 |
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| 145 | for (ll = 0 ; ll < n ; ll++)
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| 146 | if (ll != icol)
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| 147 | {
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| 148 | dum = x[icol][ll];
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| 149 | x[icol][ll] = 0.0;
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| 150 | for ( l = 0 ; l<n ; l++)
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| 151 | x[l][ll] = x[l][ll] - x[l][icol] * dum ;
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| 152 | }
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| 153 | }
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| 154 | for ( l = n; l--; )
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| 155 | {
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| 156 | if (indxr[l] != indxc[l])
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| 157 | for ( k = 0; k<n ; k++)
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| 158 | {
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| 159 | temp = x[indxr[l]][k];
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| 160 | x[indxr[l]][k] = x[indxc[l]][k];
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| 161 | x[indxc[l]][k] = temp;
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| 162 | }
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| 163 | }
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| 164 |
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| 165 | return 0 ; // matrix is regular .. inversion has been succesfull
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| 166 | }
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| 167 |
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| 168 | // Invert the given matrix using the above inversion routine.
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| 169 | Matrix4x4
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| 170 | Invert(const Matrix4x4& M)
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| 171 | {
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| 172 | Matrix4x4 InvertMe = M;
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| 173 | InvertMe.Invert();
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| 174 | return InvertMe;
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| 175 | }
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| 176 |
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| 177 |
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| 178 | // Transpose the matrix.
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| 179 | void
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| 180 | Matrix4x4::Transpose()
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| 181 | {
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| 182 | for (int i = 0; i < 4; i++)
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| 183 | for (int j = i; j < 4; j++)
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| 184 | if (i != j) {
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| 185 | float temp = x[i][j];
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| 186 | x[i][j] = x[j][i];
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| 187 | x[j][i] = temp;
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| 188 | }
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| 189 | }
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| 190 |
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| 191 | // Transpose the given matrix using the transpose routine above.
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| 192 | Matrix4x4
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| 193 | Transpose(const Matrix4x4& M)
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| 194 | {
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| 195 | Matrix4x4 TransposeMe = M;
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| 196 | TransposeMe.Transpose();
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| 197 | return TransposeMe;
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| 198 | }
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| 199 |
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| 200 | // Construct an identity matrix.
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| 201 | Matrix4x4
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| 202 | IdentityMatrix()
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| 203 | {
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| 204 | Matrix4x4 M;
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| 205 |
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| 206 | for (int i = 0; i < 4; i++)
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| 207 | for (int j = 0; j < 4; j++)
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| 208 | M.x[i][j] = (i == j) ? 1.0 : 0.0;
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| 209 | return M;
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| 210 | }
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| 211 |
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| 212 | // Construct a zero matrix.
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| 213 | Matrix4x4
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| 214 | ZeroMatrix()
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| 215 | {
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| 216 | Matrix4x4 M;
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| 217 | for (int i = 0; i < 4; i++)
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| 218 | for (int j = 0; j < 4; j++)
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| 219 | M.x[i][j] = 0;
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| 220 | return M;
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| 221 | }
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| 222 |
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| 223 | // Construct a translation matrix given the location to translate to.
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| 224 | Matrix4x4
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| 225 | TranslationMatrix(const Vector3& Location)
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| 226 | {
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| 227 | Matrix4x4 M = IdentityMatrix();
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| 228 | M.x[3][0] = Location.x;
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| 229 | M.x[3][1] = Location.y;
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| 230 | M.x[3][2] = Location.z;
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| 231 | return M;
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| 232 | }
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| 233 |
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| 234 | // Construct a rotation matrix. Rotates Angle radians about the
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| 235 | // X axis.
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| 236 | Matrix4x4
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| 237 | RotationXMatrix(float Angle)
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| 238 | {
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| 239 | Matrix4x4 M = IdentityMatrix();
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| 240 | float Cosine = cos(Angle);
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| 241 | float Sine = sin(Angle);
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| 242 | M.x[1][1] = Cosine;
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| 243 | M.x[2][1] = -Sine;
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| 244 | M.x[1][2] = Sine;
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| 245 | M.x[2][2] = Cosine;
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| 246 | return M;
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| 247 | }
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| 248 |
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| 249 | // Construct a rotation matrix. Rotates Angle radians about the
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| 250 | // Y axis.
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| 251 | Matrix4x4
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| 252 | RotationYMatrix(float Angle)
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| 253 | {
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| 254 | Matrix4x4 M = IdentityMatrix();
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| 255 | float Cosine = cos(Angle);
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| 256 | float Sine = sin(Angle);
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| 257 | M.x[0][0] = Cosine;
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| 258 | M.x[2][0] = -Sine;
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| 259 | M.x[0][2] = Sine;
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| 260 | M.x[2][2] = Cosine;
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| 261 | return M;
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| 262 | }
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| 263 |
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| 264 | // Construct a rotation matrix. Rotates Angle radians about the
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| 265 | // Z axis.
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| 266 | Matrix4x4
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| 267 | RotationZMatrix(float Angle)
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| 268 | {
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| 269 | Matrix4x4 M = IdentityMatrix();
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| 270 | float Cosine = cos(Angle);
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| 271 | float Sine = sin(Angle);
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| 272 | M.x[0][0] = Cosine;
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| 273 | M.x[1][0] = -Sine;
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| 274 | M.x[0][1] = Sine;
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| 275 | M.x[1][1] = Cosine;
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| 276 | return M;
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| 277 | }
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| 278 |
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| 279 | // Construct a yaw-pitch-roll rotation matrix. Rotate Yaw
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| 280 | // radians about the XY axis, rotate Pitch radians in the
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| 281 | // plane defined by the Yaw rotation, and rotate Roll radians
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| 282 | // about the axis defined by the previous two angles.
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| 283 | Matrix4x4
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| 284 | RotationYPRMatrix(float Yaw, float Pitch, float Roll)
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| 285 | {
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| 286 | Matrix4x4 M;
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| 287 | float ch = cos(Yaw);
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| 288 | float sh = sin(Yaw);
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| 289 | float cp = cos(Pitch);
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| 290 | float sp = sin(Pitch);
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| 291 | float cr = cos(Roll);
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| 292 | float sr = sin(Roll);
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| 293 |
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| 294 | M.x[0][0] = ch * cr + sh * sp * sr;
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| 295 | M.x[1][0] = -ch * sr + sh * sp * cr;
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| 296 | M.x[2][0] = sh * cp;
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| 297 | M.x[0][1] = sr * cp;
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| 298 | M.x[1][1] = cr * cp;
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| 299 | M.x[2][1] = -sp;
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| 300 | M.x[0][2] = -sh * cr - ch * sp * sr;
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| 301 | M.x[1][2] = sr * sh + ch * sp * cr;
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| 302 | M.x[2][2] = ch * cp;
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| 303 | for (int i = 0; i < 4; i++)
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| 304 | M.x[3][i] = M.x[i][3] = 0;
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| 305 | M.x[3][3] = 1;
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| 306 |
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| 307 | return M;
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| 308 | }
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| 309 |
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| 310 | // Construct a rotation of a given angle about a given axis.
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| 311 | // Derived from Eric Haines's SPD (Standard Procedural
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| 312 | // Database).
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| 313 | Matrix4x4
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| 314 | RotationAxisMatrix(const Vector3& axis, float angle)
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| 315 | {
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| 316 | Matrix4x4 M;
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| 317 | double cosine = cos(angle);
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| 318 | double sine = sin(angle);
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| 319 | double one_minus_cosine = 1 - cosine;
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| 320 |
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| 321 | M.x[0][0] = axis.x * axis.x + (1.0 - axis.x * axis.x) * cosine;
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| 322 | M.x[0][1] = axis.x * axis.y * one_minus_cosine + axis.z * sine;
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| 323 | M.x[0][2] = axis.x * axis.z * one_minus_cosine - axis.y * sine;
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| 324 | M.x[0][3] = 0;
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| 325 |
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| 326 | M.x[1][0] = axis.x * axis.y * one_minus_cosine - axis.z * sine;
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| 327 | M.x[1][1] = axis.y * axis.y + (1.0 - axis.y * axis.y) * cosine;
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| 328 | M.x[1][2] = axis.y * axis.z * one_minus_cosine + axis.x * sine;
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| 329 | M.x[1][3] = 0;
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| 330 |
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| 331 | M.x[2][0] = axis.x * axis.z * one_minus_cosine + axis.y * sine;
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| 332 | M.x[2][1] = axis.y * axis.z * one_minus_cosine - axis.x * sine;
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| 333 | M.x[2][2] = axis.z * axis.z + (1.0 - axis.z * axis.z) * cosine;
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| 334 | M.x[2][3] = 0;
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| 335 |
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| 336 | M.x[3][0] = 0;
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| 337 | M.x[3][1] = 0;
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| 338 | M.x[3][2] = 0;
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| 339 | M.x[3][3] = 1;
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| 340 |
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| 341 | return M;
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| 342 | }
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| 343 |
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| 344 |
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| 345 | // Constructs the rotation matrix that rotates 'vec1' to 'vec2'
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| 346 | Matrix4x4
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| 347 | RotationVectorsMatrix(const Vector3 &vecStart,
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| 348 | const Vector3 &vecTo)
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| 349 | {
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| 350 | Vector3 vec = CrossProd(vecStart, vecTo);
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[176] | 351 |
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[162] | 352 | if (Magnitude(vec) > Limits::Small) {
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| 353 | // vector exist, compute angle
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| 354 | float angle = acos(DotProd(vecStart, vecTo));
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| 355 | // normalize for sure
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| 356 | vec.Normalize();
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| 357 | return RotationAxisMatrix(vec, angle);
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| 358 | }
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| 359 |
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| 360 | // opposite or colinear vectors
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| 361 | Matrix4x4 ret = IdentityMatrix();
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| 362 | if (DotProd(vecStart, vecTo) < 0.0)
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| 363 | ret *= -1.0; // opposite vectors
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| 364 |
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| 365 | return ret;
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| 366 | }
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| 367 |
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| 368 |
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| 369 | // Construct a scale matrix given the X, Y, and Z parameters
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| 370 | // to scale by. To scale uniformly, let X==Y==Z.
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| 371 | Matrix4x4
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| 372 | ScaleMatrix(float X, float Y, float Z)
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| 373 | {
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| 374 | Matrix4x4 M = IdentityMatrix();
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| 375 |
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| 376 | M.x[0][0] = X;
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| 377 | M.x[1][1] = Y;
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| 378 | M.x[2][2] = Z;
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| 379 |
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| 380 | return M;
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| 381 | }
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| 382 |
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| 383 | // Construct a rotation matrix that makes the x, y, z axes
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| 384 | // correspond to the vectors given.
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| 385 | Matrix4x4
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| 386 | GenRotation(const Vector3 &x, const Vector3 &y, const Vector3 &z)
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| 387 | {
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| 388 | Matrix4x4 M = IdentityMatrix();
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| 389 |
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| 390 | #if 1
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| 391 | // x y
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| 392 | M.x[0][0] = x.x;
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| 393 | M.x[1][0] = x.y;
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| 394 | M.x[2][0] = x.z;
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| 395 |
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| 396 | M.x[0][1] = y.x;
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| 397 | M.x[1][1] = y.y;
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| 398 | M.x[2][1] = y.z;
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| 399 |
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| 400 | M.x[0][2] = z.x;
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| 401 | M.x[1][2] = z.y;
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| 402 | M.x[2][2] = z.z;
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| 403 | #else
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| 404 | // x y -- old version
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| 405 | M.x[0][0] = x.x;
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| 406 | M.x[0][1] = x.y;
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| 407 | M.x[0][2] = x.z;
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| 408 |
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| 409 | M.x[1][0] = y.x;
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| 410 | M.x[1][1] = y.y;
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| 411 | M.x[1][2] = y.z;
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| 412 |
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| 413 | M.x[2][0] = z.x;
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| 414 | M.x[2][1] = z.y;
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| 415 | M.x[2][2] = z.z;
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| 416 | #endif
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| 417 |
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| 418 | return M;
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| 419 | }
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| 420 |
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| 421 | // Construct a quadric matrix. After Foley et al. pp. 528-529.
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| 422 | Matrix4x4
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| 423 | QuadricMatrix(float a, float b, float c, float d, float e,
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| 424 | float f, float g, float h, float j, float k)
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| 425 | {
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| 426 | Matrix4x4 M;
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| 427 |
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| 428 | M.x[0][0] = a; M.x[0][1] = d; M.x[0][2] = f; M.x[0][3] = g;
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| 429 | M.x[1][0] = d; M.x[1][1] = b; M.x[1][2] = e; M.x[1][3] = h;
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| 430 | M.x[2][0] = f; M.x[2][1] = e; M.x[2][2] = c; M.x[2][3] = j;
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| 431 | M.x[3][0] = g; M.x[3][1] = h; M.x[3][2] = j; M.x[3][3] = k;
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| 432 |
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| 433 | return M;
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| 434 | }
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| 435 |
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| 436 | // Construct various "mirror" matrices, which flip coordinate
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| 437 | // signs in the various axes specified.
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| 438 | Matrix4x4
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| 439 | MirrorX()
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| 440 | {
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| 441 | Matrix4x4 M = IdentityMatrix();
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| 442 | M.x[0][0] = -1;
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| 443 | return M;
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| 444 | }
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| 445 |
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| 446 | Matrix4x4
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| 447 | MirrorY()
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| 448 | {
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| 449 | Matrix4x4 M = IdentityMatrix();
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| 450 | M.x[1][1] = -1;
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| 451 | return M;
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| 452 | }
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| 453 |
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| 454 | Matrix4x4
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| 455 | MirrorZ()
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| 456 | {
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| 457 | Matrix4x4 M = IdentityMatrix();
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| 458 | M.x[2][2] = -1;
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| 459 | return M;
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| 460 | }
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| 461 |
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| 462 | Matrix4x4
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| 463 | RotationOnly(const Matrix4x4& x)
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| 464 | {
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| 465 | Matrix4x4 M = x;
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| 466 | M.x[3][0] = M.x[3][1] = M.x[3][2] = 0;
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| 467 | return M;
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| 468 | }
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| 469 |
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| 470 | // Add corresponding elements of the two matrices.
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| 471 | Matrix4x4&
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| 472 | Matrix4x4::operator+= (const Matrix4x4& A)
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| 473 | {
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| 474 | for (int i = 0; i < 4; i++)
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| 475 | for (int j = 0; j < 4; j++)
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| 476 | x[i][j] += A.x[i][j];
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| 477 | return *this;
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| 478 | }
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| 479 |
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| 480 | // Subtract corresponding elements of the matrices.
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| 481 | Matrix4x4&
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| 482 | Matrix4x4::operator-= (const Matrix4x4& A)
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| 483 | {
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| 484 | for (int i = 0; i < 4; i++)
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| 485 | for (int j = 0; j < 4; j++)
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| 486 | x[i][j] -= A.x[i][j];
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| 487 | return *this;
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| 488 | }
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| 489 |
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| 490 | // Scale each element of the matrix by A.
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| 491 | Matrix4x4&
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| 492 | Matrix4x4::operator*= (float A)
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| 493 | {
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| 494 | for (int i = 0; i < 4; i++)
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| 495 | for (int j = 0; j < 4; j++)
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| 496 | x[i][j] *= A;
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| 497 | return *this;
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| 498 | }
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| 499 |
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| 500 | // Multiply two matrices.
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| 501 | Matrix4x4&
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| 502 | Matrix4x4::operator*= (const Matrix4x4& A)
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| 503 | {
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| 504 | Matrix4x4 ret = *this;
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| 505 |
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| 506 | for (int i = 0; i < 4; i++)
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| 507 | for (int j = 0; j < 4; j++) {
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| 508 | float subt = 0;
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| 509 | for (int k = 0; k < 4; k++)
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| 510 | subt += ret.x[i][k] * A.x[k][j];
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| 511 | x[i][j] = subt;
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| 512 | }
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| 513 | return *this;
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| 514 | }
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| 515 |
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| 516 | // Add corresponding elements of the matrices.
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| 517 | Matrix4x4
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| 518 | operator+ (const Matrix4x4& A, const Matrix4x4& B)
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| 519 | {
|
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| 520 | Matrix4x4 ret;
|
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| 521 |
|
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| 522 | for (int i = 0; i < 4; i++)
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| 523 | for (int j = 0; j < 4; j++)
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| 524 | ret.x[i][j] = A.x[i][j] + B.x[i][j];
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| 525 | return ret;
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| 526 | }
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| 527 |
|
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| 528 | // Subtract corresponding elements of the matrices.
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| 529 | Matrix4x4
|
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| 530 | operator- (const Matrix4x4& A, const Matrix4x4& B)
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| 531 | {
|
---|
| 532 | Matrix4x4 ret;
|
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| 533 |
|
---|
| 534 | for (int i = 0; i < 4; i++)
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| 535 | for (int j = 0; j < 4; j++)
|
---|
| 536 | ret.x[i][j] = A.x[i][j] - B.x[i][j];
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| 537 | return ret;
|
---|
| 538 | }
|
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| 539 |
|
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| 540 | // Multiply matrices.
|
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| 541 | Matrix4x4
|
---|
| 542 | operator* (const Matrix4x4& A, const Matrix4x4& B)
|
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| 543 | {
|
---|
| 544 | Matrix4x4 ret;
|
---|
| 545 |
|
---|
| 546 | for (int i = 0; i < 4; i++)
|
---|
| 547 | for (int j = 0; j < 4; j++) {
|
---|
| 548 | float subt = 0;
|
---|
| 549 | for (int k = 0; k < 4; k++)
|
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| 550 | subt += A.x[i][k] * B.x[k][j];
|
---|
| 551 | ret.x[i][j] = subt;
|
---|
| 552 | }
|
---|
| 553 | return ret;
|
---|
| 554 | }
|
---|
| 555 |
|
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| 556 | // Transform a vector by a matrix.
|
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| 557 | Vector3
|
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| 558 | operator* (const Matrix4x4& M, const Vector3& v)
|
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| 559 | {
|
---|
| 560 | Vector3 ret;
|
---|
| 561 | float denom;
|
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| 562 |
|
---|
| 563 | ret.x = v.x * M.x[0][0] + v.y * M.x[1][0] + v.z * M.x[2][0] + M.x[3][0];
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| 564 | ret.y = v.x * M.x[0][1] + v.y * M.x[1][1] + v.z * M.x[2][1] + M.x[3][1];
|
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| 565 | ret.z = v.x * M.x[0][2] + v.y * M.x[1][2] + v.z * M.x[2][2] + M.x[3][2];
|
---|
| 566 | denom = M.x[0][3] + M.x[1][3] + M.x[2][3] + M.x[3][3];
|
---|
| 567 | if (denom != 1.0)
|
---|
| 568 | ret /= denom;
|
---|
| 569 | return ret;
|
---|
| 570 | }
|
---|
| 571 |
|
---|
| 572 | // Apply the rotation portion of a matrix to a vector.
|
---|
| 573 | Vector3
|
---|
| 574 | RotateOnly(const Matrix4x4& M, const Vector3& v)
|
---|
| 575 | {
|
---|
| 576 | Vector3 ret;
|
---|
| 577 | float denom;
|
---|
| 578 |
|
---|
| 579 | ret.x = v.x * M.x[0][0] + v.y * M.x[1][0] + v.z * M.x[2][0];
|
---|
| 580 | ret.y = v.x * M.x[0][1] + v.y * M.x[1][1] + v.z * M.x[2][1];
|
---|
| 581 | ret.z = v.x * M.x[0][2] + v.y * M.x[1][2] + v.z * M.x[2][2];
|
---|
| 582 | denom = M.x[0][3] + M.x[1][3] + M.x[2][3] + M.x[3][3];
|
---|
| 583 | if (denom != 1.0)
|
---|
| 584 | ret /= denom;
|
---|
| 585 | return ret;
|
---|
| 586 | }
|
---|
| 587 |
|
---|
| 588 | // Scale each element of the matrix by B.
|
---|
| 589 | Matrix4x4
|
---|
| 590 | operator* (const Matrix4x4& A, float B)
|
---|
| 591 | {
|
---|
| 592 | Matrix4x4 ret;
|
---|
| 593 |
|
---|
| 594 | for (int i = 0; i < 4; i++)
|
---|
| 595 | for (int j = 0; j < 4; j++)
|
---|
| 596 | ret.x[i][j] = A.x[i][j] * B;
|
---|
| 597 | return ret;
|
---|
| 598 | }
|
---|
| 599 |
|
---|
| 600 | // Overloaded << for C++-style output.
|
---|
| 601 | ostream&
|
---|
| 602 | operator<< (ostream& s, const Matrix4x4& M)
|
---|
| 603 | {
|
---|
| 604 | for (int i = 0; i < 4; i++) { // y
|
---|
| 605 | for (int j = 0; j < 4; j++) { // x
|
---|
| 606 | // x y
|
---|
| 607 | s << setprecision(4) << setw(10) << M.x[j][i];
|
---|
| 608 | }
|
---|
| 609 | s << '\n';
|
---|
| 610 | }
|
---|
| 611 | return s;
|
---|
| 612 | }
|
---|
| 613 |
|
---|
| 614 | // Rotate a direction vector...
|
---|
| 615 | Vector3
|
---|
| 616 | PlaneRotate(const Matrix4x4& tform, const Vector3& p)
|
---|
| 617 | {
|
---|
| 618 | // I sure hope that matrix is invertible...
|
---|
| 619 | Matrix4x4 use = Transpose(Invert(tform));
|
---|
| 620 |
|
---|
| 621 | return RotateOnly(use, p);
|
---|
| 622 | }
|
---|
| 623 |
|
---|
| 624 | // Transform a normal
|
---|
| 625 | Vector3
|
---|
| 626 | TransformNormal(const Matrix4x4& tform, const Vector3& n)
|
---|
| 627 | {
|
---|
| 628 | Matrix4x4 use = NormalTransformMatrix(tform);
|
---|
| 629 |
|
---|
| 630 | return RotateOnly(use, n);
|
---|
| 631 | }
|
---|
| 632 |
|
---|
| 633 | Matrix4x4
|
---|
| 634 | NormalTransformMatrix(const Matrix4x4 &tform)
|
---|
| 635 | {
|
---|
| 636 | Matrix4x4 m = tform;
|
---|
| 637 | // for normal translation vector must be zero!
|
---|
| 638 | m.x[3][0] = m.x[3][1] = m.x[3][2] = 0.0;
|
---|
| 639 | // I sure hope that matrix is invertible...
|
---|
| 640 | return Transpose(Invert(m));
|
---|
| 641 | }
|
---|
| 642 |
|
---|
| 643 | Vector3
|
---|
| 644 | GetTranslation(const Matrix4x4 &M)
|
---|
| 645 | {
|
---|
| 646 | return Vector3(M.x[3][0], M.x[3][1], M.x[3][2]);
|
---|
| 647 | }
|
---|