[2746] | 1 | #include "Matrix4x4.h"
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| 2 | #include "Vector3.h"
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[2913] | 3 | #include "AxisAlignedBox3.h"
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| 4 |
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[3078] | 5 |
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[2746] | 6 | using namespace std;
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| 7 |
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[3078] | 8 |
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[2776] | 9 | namespace CHCDemoEngine
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[2751] | 10 | {
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[2746] | 11 |
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[2751] | 12 | Matrix4x4::Matrix4x4()
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| 13 | {}
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[2746] | 14 |
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[2751] | 15 |
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[2746] | 16 | Matrix4x4::Matrix4x4(const Vector3 &a, const Vector3 &b, const Vector3 &c)
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| 17 | {
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| 18 | // first index is column [x], the second is row [y]
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| 19 | x[0][0] = a.x;
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| 20 | x[1][0] = b.x;
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| 21 | x[2][0] = c.x;
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| 22 | x[3][0] = 0.0f;
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| 23 |
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| 24 | x[0][1] = a.y;
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| 25 | x[1][1] = b.y;
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| 26 | x[2][1] = c.y;
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| 27 | x[3][1] = 0.0f;
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| 28 |
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| 29 | x[0][2] = a.z;
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| 30 | x[1][2] = b.z;
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| 31 | x[2][2] = c.z;
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| 32 | x[3][2] = 0.0f;
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| 33 |
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| 34 | x[0][3] = 0.0f;
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| 35 | x[1][3] = 0.0f;
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| 36 | x[2][3] = 0.0f;
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| 37 | x[3][3] = 1.0f;
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| 38 | }
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| 39 |
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| 40 |
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| 41 | void Matrix4x4::SetColumns(const Vector3 &a, const Vector3 &b, const Vector3 &c)
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| 42 | {
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| 43 | // first index is column [x], the second is row [y]
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| 44 | x[0][0] = a.x;
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| 45 | x[1][0] = a.y;
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| 46 | x[2][0] = a.z;
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| 47 | x[3][0] = 0.0f;
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| 48 |
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| 49 | x[0][1] = b.x;
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| 50 | x[1][1] = b.y;
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| 51 | x[2][1] = b.z;
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| 52 | x[3][1] = 0.0f;
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| 53 |
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| 54 | x[0][2] = c.x;
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| 55 | x[1][2] = c.y;
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| 56 | x[2][2] = c.z;
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| 57 | x[3][2] = 0.0f;
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| 58 |
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| 59 | x[0][3] = 0.0f;
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| 60 | x[1][3] = 0.0f;
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| 61 | x[2][3] = 0.0f;
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| 62 | x[3][3] = 1.0f;
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| 63 | }
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| 64 |
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| 65 | // full constructor
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| 66 | Matrix4x4::Matrix4x4(float x11, float x12, float x13, float x14,
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| 67 | float x21, float x22, float x23, float x24,
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| 68 | float x31, float x32, float x33, float x34,
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| 69 | float x41, float x42, float x43, float x44)
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| 70 | {
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| 71 | // first index is column [x], the second is row [y]
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| 72 | x[0][0] = x11;
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| 73 | x[1][0] = x12;
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| 74 | x[2][0] = x13;
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| 75 | x[3][0] = x14;
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| 76 |
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| 77 | x[0][1] = x21;
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| 78 | x[1][1] = x22;
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| 79 | x[2][1] = x23;
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| 80 | x[3][1] = x24;
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| 81 |
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| 82 | x[0][2] = x31;
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| 83 | x[1][2] = x32;
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| 84 | x[2][2] = x33;
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| 85 | x[3][2] = x34;
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| 86 |
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| 87 | x[0][3] = x41;
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| 88 | x[1][3] = x42;
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| 89 | x[2][3] = x43;
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| 90 | x[3][3] = x44;
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| 91 | }
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| 92 |
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| 93 |
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[2751] | 94 | float Matrix4x4::Det3x3() const
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| 95 | {
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| 96 | return (x[0][0]*x[1][1]*x[2][2] + \
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| 97 | x[1][0]*x[2][1]*x[0][2] + \
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| 98 | x[2][0]*x[0][1]*x[1][2] - \
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| 99 | x[2][0]*x[1][1]*x[0][2] - \
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| 100 | x[0][0]*x[2][1]*x[1][2] - \
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| 101 | x[1][0]*x[0][1]*x[2][2]);
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| 102 | }
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| 103 |
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| 104 |
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| 105 |
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[2746] | 106 | // inverse matrix computation gauss_jacobiho method .. from N.R. in C
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| 107 | // if matrix is regular = computatation successfull = returns 0
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| 108 | // in case of singular matrix returns 1
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| 109 | int Matrix4x4::Invert()
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| 110 | {
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| 111 | int indxc[4],indxr[4],ipiv[4];
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| 112 | int i,icol,irow,j,k,l,ll,n;
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| 113 | float big,dum,pivinv,temp;
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| 114 | // satisfy the compiler
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| 115 | icol = irow = 0;
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| 116 |
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| 117 | // the size of the matrix
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| 118 | n = 4;
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| 119 |
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| 120 | for ( j = 0 ; j < n ; j++) /* zero pivots */
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| 121 | ipiv[j] = 0;
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| 122 |
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| 123 | for ( i = 0; i < n; i++)
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| 124 | {
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| 125 | big = 0.0;
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| 126 | for (j = 0 ; j < n ; j++)
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| 127 | if (ipiv[j] != 1)
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| 128 | for ( k = 0 ; k<n ; k++)
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| 129 | {
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| 130 | if (ipiv[k] == 0)
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| 131 | {
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| 132 | if (fabs(x[k][j]) >= big)
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| 133 | {
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| 134 | big = fabs(x[k][j]);
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| 135 | irow = j;
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| 136 | icol = k;
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| 137 | }
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| 138 | }
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| 139 | else
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| 140 | if (ipiv[k] > 1)
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| 141 | return 1; /* singular matrix */
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| 142 | }
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| 143 | ++(ipiv[icol]);
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| 144 | if (irow != icol)
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| 145 | {
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| 146 | for ( l = 0 ; l<n ; l++)
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| 147 | {
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| 148 | temp = x[l][icol];
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| 149 | x[l][icol] = x[l][irow];
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| 150 | x[l][irow] = temp;
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| 151 | }
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| 152 | }
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| 153 | indxr[i] = irow;
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| 154 | indxc[i] = icol;
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| 155 | if (x[icol][icol] == 0.0)
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| 156 | return 1; /* singular matrix */
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| 157 |
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| 158 | pivinv = 1.0f / x[icol][icol];
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| 159 | x[icol][icol] = 1.0f ;
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| 160 | for ( l = 0 ; l<n ; l++)
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| 161 | x[l][icol] = x[l][icol] * pivinv ;
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| 162 |
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| 163 | for (ll = 0 ; ll < n ; ll++)
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| 164 | if (ll != icol)
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| 165 | {
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| 166 | dum = x[icol][ll];
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| 167 | x[icol][ll] = 0.0;
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| 168 | for ( l = 0 ; l<n ; l++)
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| 169 | x[l][ll] = x[l][ll] - x[l][icol] * dum ;
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| 170 | }
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| 171 | }
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| 172 | for ( l = n; l--; )
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| 173 | {
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| 174 | if (indxr[l] != indxc[l])
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| 175 | for ( k = 0; k<n ; k++)
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| 176 | {
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| 177 | temp = x[indxr[l]][k];
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| 178 | x[indxr[l]][k] = x[indxc[l]][k];
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| 179 | x[indxc[l]][k] = temp;
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| 180 | }
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| 181 | }
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| 182 |
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| 183 | return 0 ; // matrix is regular .. inversion has been succesfull
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| 184 | }
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| 185 |
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[2751] | 186 |
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[2746] | 187 | // Invert the given matrix using the above inversion routine.
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[2751] | 188 | Matrix4x4 Invert(const Matrix4x4& M)
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[2746] | 189 | {
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| 190 | Matrix4x4 InvertMe = M;
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| 191 | InvertMe.Invert();
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| 192 | return InvertMe;
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| 193 | }
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| 194 |
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| 195 |
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| 196 | // Transpose the matrix.
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[2751] | 197 | void Matrix4x4::Transpose()
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[2746] | 198 | {
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| 199 | for (int i = 0; i < 4; i++)
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| 200 | for (int j = i; j < 4; j++)
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| 201 | if (i != j) {
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| 202 | float temp = x[i][j];
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| 203 | x[i][j] = x[j][i];
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| 204 | x[j][i] = temp;
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| 205 | }
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| 206 | }
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| 207 |
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[2751] | 208 |
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[2746] | 209 | // Transpose the given matrix using the transpose routine above.
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[2751] | 210 | Matrix4x4 Transpose(const Matrix4x4& M)
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[2746] | 211 | {
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| 212 | Matrix4x4 TransposeMe = M;
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| 213 | TransposeMe.Transpose();
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| 214 | return TransposeMe;
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| 215 | }
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| 216 |
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[2751] | 217 |
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[2746] | 218 | // Construct an identity matrix.
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[2751] | 219 | Matrix4x4 IdentityMatrix()
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[2746] | 220 | {
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| 221 | Matrix4x4 M;
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| 222 |
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| 223 | for (int i = 0; i < 4; i++)
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| 224 | for (int j = 0; j < 4; j++)
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| 225 | M.x[i][j] = (i == j) ? 1.0f : 0.0f;
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| 226 | return M;
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| 227 | }
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| 228 |
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[2751] | 229 |
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[2746] | 230 | // Construct a zero matrix.
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[2751] | 231 | Matrix4x4 ZeroMatrix()
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[2746] | 232 | {
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| 233 | Matrix4x4 M;
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| 234 | for (int i = 0; i < 4; i++)
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| 235 | for (int j = 0; j < 4; j++)
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| 236 | M.x[i][j] = 0;
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| 237 | return M;
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| 238 | }
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| 239 |
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| 240 | // Construct a translation matrix given the location to translate to.
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| 241 | Matrix4x4
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| 242 | TranslationMatrix(const Vector3& Location)
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| 243 | {
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| 244 | Matrix4x4 M = IdentityMatrix();
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| 245 | M.x[3][0] = Location.x;
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| 246 | M.x[3][1] = Location.y;
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| 247 | M.x[3][2] = Location.z;
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| 248 | return M;
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| 249 | }
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| 250 |
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| 251 | // Construct a rotation matrix. Rotates Angle radians about the
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| 252 | // X axis.
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| 253 | Matrix4x4
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| 254 | RotationXMatrix(float Angle)
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| 255 | {
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| 256 | Matrix4x4 M = IdentityMatrix();
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| 257 | float Cosine = cos(Angle);
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| 258 | float Sine = sin(Angle);
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| 259 | M.x[1][1] = Cosine;
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| 260 | M.x[2][1] = -Sine;
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| 261 | M.x[1][2] = Sine;
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| 262 | M.x[2][2] = Cosine;
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| 263 | return M;
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| 264 | }
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| 265 |
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| 266 | // Construct a rotation matrix. Rotates Angle radians about the
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| 267 | // Y axis.
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| 268 | Matrix4x4 RotationYMatrix(float angle)
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| 269 | {
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| 270 | Matrix4x4 m = IdentityMatrix();
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| 271 |
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| 272 | float cosine = cos(angle);
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| 273 | float sine = sin(angle);
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| 274 |
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| 275 | m.x[0][0] = cosine;
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| 276 | m.x[2][0] = -sine;
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| 277 | m.x[0][2] = sine;
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| 278 | m.x[2][2] = cosine;
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| 279 |
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| 280 | return m;
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| 281 | }
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| 282 |
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| 283 |
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| 284 | // Construct a rotation matrix. Rotates Angle radians about the
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| 285 | // Z axis.
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| 286 | Matrix4x4 RotationZMatrix(float angle)
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| 287 | {
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| 288 | Matrix4x4 m = IdentityMatrix();
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| 289 |
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| 290 | float cosine = cos(angle);
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| 291 | float sine = sin(angle);
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| 292 |
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| 293 | m.x[0][0] = cosine;
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| 294 | m.x[1][0] = -sine;
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| 295 | m.x[0][1] = sine;
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| 296 | m.x[1][1] = cosine;
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| 297 |
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| 298 | return m;
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| 299 | }
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| 300 |
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| 301 |
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| 302 | // Construct a yaw-pitch-roll rotation matrix. Rotate Yaw
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| 303 | // radians about the XY axis, rotate Pitch radians in the
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| 304 | // plane defined by the Yaw rotation, and rotate Roll radians
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| 305 | // about the axis defined by the previous two angles.
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| 306 | Matrix4x4 RotationYPRMatrix(float Yaw, float Pitch, float Roll)
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| 307 | {
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| 308 | Matrix4x4 M;
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| 309 | float ch = cos(Yaw);
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| 310 | float sh = sin(Yaw);
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| 311 | float cp = cos(Pitch);
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| 312 | float sp = sin(Pitch);
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| 313 | float cr = cos(Roll);
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| 314 | float sr = sin(Roll);
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| 315 |
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| 316 | M.x[0][0] = ch * cr + sh * sp * sr;
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| 317 | M.x[1][0] = -ch * sr + sh * sp * cr;
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| 318 | M.x[2][0] = sh * cp;
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| 319 | M.x[0][1] = sr * cp;
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| 320 | M.x[1][1] = cr * cp;
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| 321 | M.x[2][1] = -sp;
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| 322 | M.x[0][2] = -sh * cr - ch * sp * sr;
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| 323 | M.x[1][2] = sr * sh + ch * sp * cr;
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| 324 | M.x[2][2] = ch * cp;
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| 325 | for (int i = 0; i < 4; i++)
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| 326 | M.x[3][i] = M.x[i][3] = 0;
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| 327 | M.x[3][3] = 1;
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| 328 |
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| 329 | return M;
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| 330 | }
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| 331 |
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| 332 | // Construct a rotation of a given angle about a given axis.
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| 333 | // Derived from Eric Haines's SPD (Standard Procedural
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| 334 | // Database).
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| 335 | Matrix4x4 RotationAxisMatrix(const Vector3& axis, float angle)
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| 336 | {
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| 337 | Matrix4x4 M;
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| 338 |
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| 339 | float cosine = cos(angle);
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| 340 | float sine = sin(angle);
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| 341 | float one_minus_cosine = 1 - cosine;
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| 342 |
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| 343 | M.x[0][0] = axis.x * axis.x + (1.0f - axis.x * axis.x) * cosine;
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| 344 | M.x[0][1] = axis.x * axis.y * one_minus_cosine + axis.z * sine;
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| 345 | M.x[0][2] = axis.x * axis.z * one_minus_cosine - axis.y * sine;
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| 346 | M.x[0][3] = 0;
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| 347 |
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| 348 | M.x[1][0] = axis.x * axis.y * one_minus_cosine - axis.z * sine;
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| 349 | M.x[1][1] = axis.y * axis.y + (1.0f - axis.y * axis.y) * cosine;
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| 350 | M.x[1][2] = axis.y * axis.z * one_minus_cosine + axis.x * sine;
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| 351 | M.x[1][3] = 0;
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| 352 |
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| 353 | M.x[2][0] = axis.x * axis.z * one_minus_cosine + axis.y * sine;
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| 354 | M.x[2][1] = axis.y * axis.z * one_minus_cosine - axis.x * sine;
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| 355 | M.x[2][2] = axis.z * axis.z + (1.0f - axis.z * axis.z) * cosine;
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| 356 | M.x[2][3] = 0;
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| 357 |
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| 358 | M.x[3][0] = 0;
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| 359 | M.x[3][1] = 0;
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| 360 | M.x[3][2] = 0;
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| 361 | M.x[3][3] = 1;
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| 362 |
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| 363 | return M;
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| 364 | }
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| 365 |
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| 366 |
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| 367 | // Constructs the rotation matrix that rotates 'vec1' to 'vec2'
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| 368 | Matrix4x4 RotationVectorsMatrix(const Vector3 &vecStart, const Vector3 &vecTo)
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| 369 | {
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| 370 | Vector3 vec = CrossProd(vecStart, vecTo);
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| 371 |
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| 372 | if (Magnitude(vec) > Limits::Small) {
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| 373 | // vector exist, compute angle
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| 374 | float angle = acos(DotProd(vecStart, vecTo));
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| 375 | // normalize for sure
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| 376 | vec.Normalize();
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| 377 | return RotationAxisMatrix(vec, angle);
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| 378 | }
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| 379 |
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| 380 | // opposite or colinear vectors
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| 381 | Matrix4x4 ret = IdentityMatrix();
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| 382 | if (DotProd(vecStart, vecTo) < 0.0f)
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| 383 | ret *= -1.0f; // opposite vectors
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| 384 |
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| 385 | return ret;
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| 386 | }
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| 387 |
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| 388 |
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| 389 | // Construct a scale matrix given the X, Y, and Z parameters
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| 390 | // to scale by. To scale uniformly, let X==Y==Z.
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| 391 | Matrix4x4 ScaleMatrix(float X, float Y, float Z)
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| 392 | {
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| 393 | Matrix4x4 M = IdentityMatrix();
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| 394 |
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| 395 | M.x[0][0] = X;
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| 396 | M.x[1][1] = Y;
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| 397 | M.x[2][2] = Z;
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| 398 |
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| 399 | return M;
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| 400 | }
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| 401 |
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| 402 |
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| 403 | // Construct a rotation matrix that makes the x, y, z axes
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| 404 | // correspond to the vectors given.
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| 405 | Matrix4x4 GenRotation(const Vector3 &x, const Vector3 &y, const Vector3 &z)
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| 406 | {
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| 407 | Matrix4x4 M = IdentityMatrix();
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| 408 |
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| 409 | // x y
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| 410 | M.x[0][0] = x.x;
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| 411 | M.x[1][0] = x.y;
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| 412 | M.x[2][0] = x.z;
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| 413 |
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| 414 | M.x[0][1] = y.x;
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| 415 | M.x[1][1] = y.y;
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| 416 | M.x[2][1] = y.z;
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| 417 |
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| 418 | M.x[0][2] = z.x;
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| 419 | M.x[1][2] = z.y;
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| 420 | M.x[2][2] = z.z;
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| 421 |
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| 422 | return M;
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| 423 | }
|
---|
| 424 |
|
---|
| 425 | // Construct a quadric matrix. After Foley et al. pp. 528-529.
|
---|
| 426 | Matrix4x4
|
---|
| 427 | QuadricMatrix(float a, float b, float c, float d, float e,
|
---|
| 428 | float f, float g, float h, float j, float k)
|
---|
| 429 | {
|
---|
| 430 | Matrix4x4 M;
|
---|
| 431 |
|
---|
| 432 | M.x[0][0] = a; M.x[0][1] = d; M.x[0][2] = f; M.x[0][3] = g;
|
---|
| 433 | M.x[1][0] = d; M.x[1][1] = b; M.x[1][2] = e; M.x[1][3] = h;
|
---|
| 434 | M.x[2][0] = f; M.x[2][1] = e; M.x[2][2] = c; M.x[2][3] = j;
|
---|
| 435 | M.x[3][0] = g; M.x[3][1] = h; M.x[3][2] = j; M.x[3][3] = k;
|
---|
| 436 |
|
---|
| 437 | return M;
|
---|
| 438 | }
|
---|
| 439 |
|
---|
| 440 | // Construct various "mirror" matrices, which flip coordinate
|
---|
| 441 | // signs in the various axes specified.
|
---|
| 442 | Matrix4x4
|
---|
| 443 | MirrorX()
|
---|
| 444 | {
|
---|
| 445 | Matrix4x4 M = IdentityMatrix();
|
---|
| 446 | M.x[0][0] = -1;
|
---|
| 447 | return M;
|
---|
| 448 | }
|
---|
| 449 |
|
---|
| 450 | Matrix4x4
|
---|
| 451 | MirrorY()
|
---|
| 452 | {
|
---|
| 453 | Matrix4x4 M = IdentityMatrix();
|
---|
| 454 | M.x[1][1] = -1;
|
---|
| 455 | return M;
|
---|
| 456 | }
|
---|
| 457 |
|
---|
| 458 | Matrix4x4
|
---|
| 459 | MirrorZ()
|
---|
| 460 | {
|
---|
| 461 | Matrix4x4 M = IdentityMatrix();
|
---|
| 462 | M.x[2][2] = -1;
|
---|
| 463 | return M;
|
---|
| 464 | }
|
---|
| 465 |
|
---|
| 466 | Matrix4x4
|
---|
| 467 | RotationOnly(const Matrix4x4& x)
|
---|
| 468 | {
|
---|
| 469 | Matrix4x4 M = x;
|
---|
| 470 | M.x[3][0] = M.x[3][1] = M.x[3][2] = 0;
|
---|
| 471 | return M;
|
---|
| 472 | }
|
---|
| 473 |
|
---|
| 474 | // Add corresponding elements of the two matrices.
|
---|
| 475 | Matrix4x4&
|
---|
| 476 | Matrix4x4::operator+= (const Matrix4x4& A)
|
---|
| 477 | {
|
---|
| 478 | for (int i = 0; i < 4; i++)
|
---|
| 479 | for (int j = 0; j < 4; j++)
|
---|
| 480 | x[i][j] += A.x[i][j];
|
---|
| 481 | return *this;
|
---|
| 482 | }
|
---|
| 483 |
|
---|
| 484 | // Subtract corresponding elements of the matrices.
|
---|
| 485 | Matrix4x4&
|
---|
| 486 | Matrix4x4::operator-= (const Matrix4x4& A)
|
---|
| 487 | {
|
---|
| 488 | for (int i = 0; i < 4; i++)
|
---|
| 489 | for (int j = 0; j < 4; j++)
|
---|
| 490 | x[i][j] -= A.x[i][j];
|
---|
| 491 | return *this;
|
---|
| 492 | }
|
---|
| 493 |
|
---|
| 494 | // Scale each element of the matrix by A.
|
---|
| 495 | Matrix4x4&
|
---|
| 496 | Matrix4x4::operator*= (float A)
|
---|
| 497 | {
|
---|
| 498 | for (int i = 0; i < 4; i++)
|
---|
| 499 | for (int j = 0; j < 4; j++)
|
---|
| 500 | x[i][j] *= A;
|
---|
| 501 | return *this;
|
---|
| 502 | }
|
---|
| 503 |
|
---|
| 504 | // Multiply two matrices.
|
---|
| 505 | Matrix4x4&
|
---|
| 506 | Matrix4x4::operator*= (const Matrix4x4& A)
|
---|
| 507 | {
|
---|
| 508 | Matrix4x4 ret = *this;
|
---|
| 509 |
|
---|
| 510 | for (int i = 0; i < 4; i++)
|
---|
| 511 | for (int j = 0; j < 4; j++) {
|
---|
| 512 | float subt = 0;
|
---|
| 513 | for (int k = 0; k < 4; k++)
|
---|
| 514 | subt += ret.x[i][k] * A.x[k][j];
|
---|
| 515 | x[i][j] = subt;
|
---|
| 516 | }
|
---|
| 517 | return *this;
|
---|
| 518 | }
|
---|
| 519 |
|
---|
| 520 | // Add corresponding elements of the matrices.
|
---|
| 521 | Matrix4x4
|
---|
| 522 | operator+ (const Matrix4x4& A, const Matrix4x4& B)
|
---|
| 523 | {
|
---|
| 524 | Matrix4x4 ret;
|
---|
| 525 |
|
---|
| 526 | for (int i = 0; i < 4; i++)
|
---|
| 527 | for (int j = 0; j < 4; j++)
|
---|
| 528 | ret.x[i][j] = A.x[i][j] + B.x[i][j];
|
---|
| 529 | return ret;
|
---|
| 530 | }
|
---|
| 531 |
|
---|
| 532 | // Subtract corresponding elements of the matrices.
|
---|
| 533 | Matrix4x4
|
---|
| 534 | operator- (const Matrix4x4& A, const Matrix4x4& B)
|
---|
| 535 | {
|
---|
| 536 | Matrix4x4 ret;
|
---|
| 537 |
|
---|
| 538 | for (int i = 0; i < 4; i++)
|
---|
| 539 | for (int j = 0; j < 4; j++)
|
---|
| 540 | ret.x[i][j] = A.x[i][j] - B.x[i][j];
|
---|
| 541 | return ret;
|
---|
| 542 | }
|
---|
| 543 |
|
---|
| 544 | // Multiply matrices.
|
---|
| 545 | Matrix4x4
|
---|
| 546 | operator* (const Matrix4x4& A, const Matrix4x4& B)
|
---|
| 547 | {
|
---|
| 548 | Matrix4x4 ret;
|
---|
| 549 |
|
---|
| 550 | for (int i = 0; i < 4; i++)
|
---|
| 551 | for (int j = 0; j < 4; j++) {
|
---|
| 552 | float subt = 0;
|
---|
| 553 | for (int k = 0; k < 4; k++)
|
---|
| 554 | subt += A.x[i][k] * B.x[k][j];
|
---|
| 555 | ret.x[i][j] = subt;
|
---|
| 556 | }
|
---|
| 557 | return ret;
|
---|
| 558 | }
|
---|
| 559 |
|
---|
| 560 | // Transform a vector by a matrix.
|
---|
| 561 | Vector3
|
---|
| 562 | operator* (const Matrix4x4& M, const Vector3& v)
|
---|
| 563 | {
|
---|
| 564 | Vector3 ret;
|
---|
| 565 | float denom;
|
---|
| 566 |
|
---|
| 567 | ret.x = v.x * M.x[0][0] + v.y * M.x[1][0] + v.z * M.x[2][0] + M.x[3][0];
|
---|
| 568 | ret.y = v.x * M.x[0][1] + v.y * M.x[1][1] + v.z * M.x[2][1] + M.x[3][1];
|
---|
| 569 | ret.z = v.x * M.x[0][2] + v.y * M.x[1][2] + v.z * M.x[2][2] + M.x[3][2];
|
---|
[2939] | 570 | denom = v.x * M.x[0][3] + v.y * M.x[1][3] + v.z * M.x[2][3] + M.x[3][3];
|
---|
| 571 |
|
---|
[2746] | 572 | if (denom != 1.0)
|
---|
| 573 | ret /= denom;
|
---|
| 574 | return ret;
|
---|
| 575 | }
|
---|
| 576 |
|
---|
[2944] | 577 |
|
---|
| 578 | Vector3 Matrix4x4::Transform(float &w, const Vector3 &v, float h) const
|
---|
| 579 | {
|
---|
| 580 | Vector3 ret;
|
---|
[2953] | 581 |
|
---|
[2944] | 582 | ret.x = v.x * x[0][0] + v.y * x[1][0] + v.z * x[2][0] + h * x[3][0];
|
---|
| 583 | ret.y = v.x * x[0][1] + v.y * x[1][1] + v.z * x[2][1] + h * x[3][1];
|
---|
| 584 | ret.z = v.x * x[0][2] + v.y * x[1][2] + v.z * x[2][2] + h * x[3][2];
|
---|
| 585 | w = v.x * x[0][3] + v.y * x[1][3] + v.z * x[2][3] + h * x[3][3];
|
---|
| 586 |
|
---|
| 587 | return ret;
|
---|
| 588 | }
|
---|
| 589 |
|
---|
| 590 |
|
---|
[2746] | 591 | // Apply the rotation portion of a matrix to a vector.
|
---|
| 592 | Vector3
|
---|
| 593 | RotateOnly(const Matrix4x4& M, const Vector3& v)
|
---|
| 594 | {
|
---|
| 595 | Vector3 ret;
|
---|
| 596 | float denom;
|
---|
| 597 |
|
---|
| 598 | ret.x = v.x * M.x[0][0] + v.y * M.x[1][0] + v.z * M.x[2][0];
|
---|
| 599 | ret.y = v.x * M.x[0][1] + v.y * M.x[1][1] + v.z * M.x[2][1];
|
---|
| 600 | ret.z = v.x * M.x[0][2] + v.y * M.x[1][2] + v.z * M.x[2][2];
|
---|
| 601 | denom = M.x[0][3] + M.x[1][3] + M.x[2][3] + M.x[3][3];
|
---|
| 602 | if (denom != 1.0)
|
---|
| 603 | ret /= denom;
|
---|
| 604 | return ret;
|
---|
| 605 | }
|
---|
| 606 |
|
---|
| 607 | // Scale each element of the matrix by B.
|
---|
| 608 | Matrix4x4
|
---|
| 609 | operator* (const Matrix4x4& A, float B)
|
---|
| 610 | {
|
---|
| 611 | Matrix4x4 ret;
|
---|
| 612 |
|
---|
| 613 | for (int i = 0; i < 4; i++)
|
---|
| 614 | for (int j = 0; j < 4; j++)
|
---|
| 615 | ret.x[i][j] = A.x[i][j] * B;
|
---|
| 616 | return ret;
|
---|
| 617 | }
|
---|
| 618 |
|
---|
| 619 | // Overloaded << for C++-style output.
|
---|
| 620 | ostream&
|
---|
| 621 | operator<< (ostream& s, const Matrix4x4& M)
|
---|
| 622 | {
|
---|
| 623 | for (int i = 0; i < 4; i++) { // y
|
---|
| 624 | for (int j = 0; j < 4; j++) { // x
|
---|
| 625 | // x y
|
---|
[3078] | 626 | s << M.x[j][i];
|
---|
[2746] | 627 | }
|
---|
| 628 | s << '\n';
|
---|
| 629 | }
|
---|
| 630 | return s;
|
---|
| 631 | }
|
---|
| 632 |
|
---|
[2752] | 633 |
|
---|
| 634 | Vector3 PlaneRotate(const Matrix4x4& tform, const Vector3& p)
|
---|
[2746] | 635 | {
|
---|
| 636 | // I sure hope that matrix is invertible...
|
---|
| 637 | Matrix4x4 use = Transpose(Invert(tform));
|
---|
| 638 |
|
---|
| 639 | return RotateOnly(use, p);
|
---|
| 640 | }
|
---|
| 641 |
|
---|
| 642 | // Transform a normal
|
---|
[2752] | 643 | Vector3 TransformNormal(const Matrix4x4& tform, const Vector3& n)
|
---|
[2746] | 644 | {
|
---|
| 645 | Matrix4x4 use = NormalTransformMatrix(tform);
|
---|
| 646 |
|
---|
| 647 | return RotateOnly(use, n);
|
---|
| 648 | }
|
---|
| 649 |
|
---|
[3062] | 650 |
|
---|
| 651 | Matrix4x4 NormalTransformMatrix(const Matrix4x4 &tform)
|
---|
[2746] | 652 | {
|
---|
| 653 | Matrix4x4 m = tform;
|
---|
| 654 | // for normal translation vector must be zero!
|
---|
| 655 | m.x[3][0] = m.x[3][1] = m.x[3][2] = 0.0;
|
---|
| 656 | // I sure hope that matrix is invertible...
|
---|
| 657 | return Transpose(Invert(m));
|
---|
| 658 | }
|
---|
| 659 |
|
---|
| 660 |
|
---|
| 661 | Vector3 GetTranslation(const Matrix4x4 &M)
|
---|
| 662 | {
|
---|
| 663 | return Vector3(M.x[3][0], M.x[3][1], M.x[3][2]);
|
---|
| 664 | }
|
---|
| 665 |
|
---|
[2913] | 666 |
|
---|
| 667 | Matrix4x4 GetFittingProjectionMatrix(const AxisAlignedBox3 &box)
|
---|
| 668 | {
|
---|
| 669 | Matrix4x4 m;
|
---|
| 670 |
|
---|
[2916] | 671 | m.x[0][0] = 2.0f / (box.Max()[0] - box.Min()[0]);
|
---|
| 672 | m.x[0][1] = .0f;
|
---|
| 673 | m.x[0][2] = .0f;
|
---|
| 674 | m.x[0][3] = .0f;
|
---|
| 675 |
|
---|
| 676 | m.x[1][0] = .0f;
|
---|
| 677 | m.x[1][1] = 2.0f / (box.Max()[1] - box.Min()[1]);
|
---|
| 678 | m.x[1][2] = .0f;
|
---|
| 679 | m.x[1][3] = .0f;
|
---|
| 680 |
|
---|
| 681 | m.x[2][0] = .0f;
|
---|
| 682 | m.x[2][1] = .0f;
|
---|
| 683 | m.x[2][2] = 2.0f / (box.Max()[2] - box.Min()[2]);
|
---|
| 684 | m.x[2][3] = .0f;
|
---|
| 685 |
|
---|
| 686 | m.x[3][0] = -(box.Max()[0] + box.Min()[0]) / (box.Max()[0] - box.Min()[0]);
|
---|
| 687 | m.x[3][1] = -(box.Max()[1] + box.Min()[1]) / (box.Max()[1] - box.Min()[1]);
|
---|
| 688 | m.x[3][2] = -(box.Max()[2] + box.Min()[2]) / (box.Max()[2] - box.Min()[2]);
|
---|
| 689 | m.x[3][3] = 1.0f;
|
---|
| 690 |
|
---|
| 691 | return m;
|
---|
[2917] | 692 | }
|
---|
[2916] | 693 |
|
---|
[2917] | 694 |
|
---|
[3062] | 695 | /** The resultig matrix that is equal to the result of glFrustum
|
---|
[2939] | 696 | */
|
---|
[2920] | 697 | Matrix4x4 GetFrustum(float left, float right,
|
---|
| 698 | float bottom, float top,
|
---|
| 699 | float near, float far)
|
---|
[2915] | 700 | {
|
---|
| 701 | Matrix4x4 m;
|
---|
| 702 |
|
---|
| 703 | const float xDif = 1.0f / (right - left);
|
---|
| 704 | const float yDif = 1.0f / (top - bottom);
|
---|
| 705 | const float zDif = 1.0f / (near - far);
|
---|
| 706 |
|
---|
| 707 | m.x[0][0] = 2.0f * near * xDif;
|
---|
[2913] | 708 | m.x[0][1] = .0f;
|
---|
[2915] | 709 | m.x[0][2] = .0f;
|
---|
| 710 | m.x[0][3] = .0f;
|
---|
[2913] | 711 |
|
---|
[2915] | 712 | m.x[1][0] = .0f;
|
---|
| 713 | m.x[1][1] = 2.0f * near * yDif;
|
---|
[2913] | 714 | m.x[1][2] = .0f;
|
---|
| 715 | m.x[1][3] = .0f;
|
---|
| 716 |
|
---|
[2915] | 717 | m.x[2][0] = (right + left) * xDif;
|
---|
| 718 | m.x[2][1] = (top + bottom)* yDif;
|
---|
| 719 | m.x[2][2] = (far + near) * zDif;
|
---|
| 720 | m.x[2][3] = -1.0f;
|
---|
| 721 |
|
---|
| 722 | m.x[3][0] = .0f;
|
---|
| 723 | m.x[3][1] = .0f;
|
---|
| 724 | m.x[3][2] = 2.0f * near * far * zDif;
|
---|
| 725 | m.x[3][3] = .0f;
|
---|
[2917] | 726 |
|
---|
| 727 | return m;
|
---|
[2913] | 728 | }
|
---|
| 729 |
|
---|
| 730 |
|
---|
[2917] | 731 | Matrix4x4 LookAt(const Vector3 &pos, const Vector3 &dir, const Vector3& up)
|
---|
| 732 | {
|
---|
| 733 | const Vector3 nDir = Normalize(dir);
|
---|
| 734 | Vector3 nUp = Normalize(up);
|
---|
[2915] | 735 |
|
---|
[2917] | 736 | Vector3 nRight = Normalize(CrossProd(nDir, nUp));
|
---|
| 737 | nUp = Normalize(CrossProd(nRight, nDir));
|
---|
| 738 |
|
---|
[2940] | 739 | Matrix4x4 m(nRight.x, nRight.y, nRight.z, 0,
|
---|
| 740 | nUp.x, nUp.y, nUp.z, 0,
|
---|
| 741 | -nDir.x, -nDir.y, -nDir.z, 0,
|
---|
| 742 | 0, 0, 0, 1);
|
---|
[2932] | 743 |
|
---|
[2934] | 744 | // note: left handed system => we go into positive z
|
---|
[2940] | 745 | m.x[3][0] = -DotProd(nRight, pos);
|
---|
| 746 | m.x[3][1] = -DotProd(nUp, pos);
|
---|
[2942] | 747 | m.x[3][2] = DotProd(nDir, pos);
|
---|
[2934] | 748 |
|
---|
| 749 | return m;
|
---|
| 750 | }
|
---|
| 751 |
|
---|
| 752 |
|
---|
[3102] | 753 | /** The resulting matrix is equal to the result of glOrtho
|
---|
[3062] | 754 | */
|
---|
[3102] | 755 | Matrix4x4 GetOrtho(float left, float right, float bottom, float top, float near, float far)
|
---|
[3062] | 756 | {
|
---|
| 757 | Matrix4x4 m;
|
---|
| 758 |
|
---|
| 759 | const float xDif = 1.0f / (right - left);
|
---|
| 760 | const float yDif = 1.0f / (top - bottom);
|
---|
| 761 | const float zDif = 1.0f / (far - near);
|
---|
| 762 |
|
---|
| 763 | m.x[0][0] = 2.0f * xDif;
|
---|
| 764 | m.x[0][1] = .0f;
|
---|
| 765 | m.x[0][2] = .0f;
|
---|
| 766 | m.x[0][3] = .0f;
|
---|
| 767 |
|
---|
| 768 | m.x[1][0] = .0f;
|
---|
| 769 | m.x[1][1] = 2.0f * yDif;
|
---|
| 770 | m.x[1][2] = .0f;
|
---|
| 771 | m.x[1][3] = .0f;
|
---|
| 772 |
|
---|
| 773 | m.x[2][0] = .0f;
|
---|
| 774 | m.x[2][1] = .0f;
|
---|
| 775 | m.x[2][2] = -2.0f * zDif;
|
---|
| 776 | m.x[2][3] = .0f;
|
---|
| 777 |
|
---|
[3103] | 778 | m.x[3][0] = -(right + left) * xDif;
|
---|
| 779 | m.x[3][1] = -(top + bottom) * yDif;
|
---|
| 780 | m.x[3][2] = -(far + near) * zDif;
|
---|
[3062] | 781 | m.x[3][3] = 1.0f;
|
---|
| 782 |
|
---|
| 783 | return m;
|
---|
| 784 | }
|
---|
| 785 |
|
---|
| 786 | /** The resultig matrix that is equal to the result of gluPerspective
|
---|
| 787 | */
|
---|
| 788 | Matrix4x4 GetPerspective(float fov, float aspect, float near, float far)
|
---|
| 789 | {
|
---|
| 790 | Matrix4x4 m;
|
---|
| 791 |
|
---|
| 792 | const float x = 1.0f / tan(fov * 0.5f);
|
---|
| 793 | const float zDif = 1.0f / (near - far);
|
---|
| 794 |
|
---|
| 795 | m.x[0][0] = x / aspect;
|
---|
| 796 | m.x[0][1] = .0f;
|
---|
| 797 | m.x[0][2] = .0f;
|
---|
| 798 | m.x[0][3] = .0f;
|
---|
| 799 |
|
---|
| 800 | m.x[1][0] = .0f;
|
---|
| 801 | m.x[1][1] = x;
|
---|
| 802 | m.x[1][2] = .0f;
|
---|
| 803 | m.x[1][3] = .0f;
|
---|
| 804 |
|
---|
| 805 | m.x[2][0] = .0f;
|
---|
| 806 | m.x[2][1] = .0f;
|
---|
| 807 | m.x[2][2] = (far + near) * zDif;
|
---|
| 808 | m.x[2][3] = -1.0f;
|
---|
| 809 |
|
---|
| 810 | m.x[3][0] = .0f;
|
---|
| 811 | m.x[3][1] = .0f;
|
---|
| 812 | m.x[3][2] = 2.0f *(far * near) * zDif;
|
---|
| 813 | m.x[3][3] = 0.0f;
|
---|
| 814 |
|
---|
| 815 | return m;
|
---|
| 816 | }
|
---|
| 817 |
|
---|
| 818 |
|
---|
[2751] | 819 | } |
---|