| 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 | namespace CHCDemoEngine
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| 9 | {
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| 10 |
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| 11 | Matrix4x4::Matrix4x4()
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| 12 | {}
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| 13 |
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| 14 |
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| 15 | Matrix4x4::Matrix4x4(const Vector3 &a, const Vector3 &b, const Vector3 &c)
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| 16 | {
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| 17 | // first index is column [x], the second is row [y]
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| 18 | x[0][0] = a.x;
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| 19 | x[1][0] = b.x;
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| 20 | x[2][0] = c.x;
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| 21 | x[3][0] = 0.0f;
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| 22 |
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| 23 | x[0][1] = a.y;
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| 24 | x[1][1] = b.y;
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| 25 | x[2][1] = c.y;
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| 26 | x[3][1] = 0.0f;
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| 27 |
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| 28 | x[0][2] = a.z;
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| 29 | x[1][2] = b.z;
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| 30 | x[2][2] = c.z;
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| 31 | x[3][2] = 0.0f;
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| 32 |
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| 33 | x[0][3] = 0.0f;
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| 34 | x[1][3] = 0.0f;
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| 35 | x[2][3] = 0.0f;
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| 36 | x[3][3] = 1.0f;
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| 37 | }
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| 38 |
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| 39 |
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| 40 | void Matrix4x4::SetColumns(const Vector3 &a, const Vector3 &b, const Vector3 &c)
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| 41 | {
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| 42 | // first index is column [x], the second is row [y]
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| 43 | x[0][0] = a.x;
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| 44 | x[1][0] = a.y;
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| 45 | x[2][0] = a.z;
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| 46 | x[3][0] = 0.0f;
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| 47 |
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| 48 | x[0][1] = b.x;
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| 49 | x[1][1] = b.y;
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| 50 | x[2][1] = b.z;
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| 51 | x[3][1] = 0.0f;
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| 52 |
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| 53 | x[0][2] = c.x;
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| 54 | x[1][2] = c.y;
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| 55 | x[2][2] = c.z;
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| 56 | x[3][2] = 0.0f;
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| 57 |
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| 58 | x[0][3] = 0.0f;
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| 59 | x[1][3] = 0.0f;
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| 60 | x[2][3] = 0.0f;
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| 61 | x[3][3] = 1.0f;
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| 62 | }
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| 63 |
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| 64 | // full constructor
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| 65 | Matrix4x4::Matrix4x4(float x11, float x12, float x13, float x14,
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| 66 | float x21, float x22, float x23, float x24,
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| 67 | float x31, float x32, float x33, float x34,
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| 68 | float x41, float x42, float x43, float x44)
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| 69 | {
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| 70 | // first index is column [x], the second is row [y]
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| 71 | x[0][0] = x11;
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| 72 | x[1][0] = x12;
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| 73 | x[2][0] = x13;
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| 74 | x[3][0] = x14;
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| 75 |
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| 76 | x[0][1] = x21;
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| 77 | x[1][1] = x22;
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| 78 | x[2][1] = x23;
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| 79 | x[3][1] = x24;
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| 80 |
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| 81 | x[0][2] = x31;
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| 82 | x[1][2] = x32;
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| 83 | x[2][2] = x33;
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| 84 | x[3][2] = x34;
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| 85 |
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| 86 | x[0][3] = x41;
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| 87 | x[1][3] = x42;
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| 88 | x[2][3] = x43;
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| 89 | x[3][3] = x44;
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| 90 | }
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| 91 |
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| 92 |
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| 93 | float Matrix4x4::Det3x3() const
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| 94 | {
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| 95 | return (x[0][0]*x[1][1]*x[2][2] + \
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| 96 | x[1][0]*x[2][1]*x[0][2] + \
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| 97 | x[2][0]*x[0][1]*x[1][2] - \
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| 98 | x[2][0]*x[1][1]*x[0][2] - \
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| 99 | x[0][0]*x[2][1]*x[1][2] - \
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| 100 | x[1][0]*x[0][1]*x[2][2]);
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| 101 | }
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| 102 |
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| 103 |
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| 104 |
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| 105 | // inverse matrix computation gauss_jacobiho method .. from N.R. in C
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| 106 | // if matrix is regular = computatation successfull = returns 0
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| 107 | // in case of singular matrix returns 1
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| 108 | int Matrix4x4::Invert()
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| 109 | {
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| 110 | int indxc[4],indxr[4],ipiv[4];
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| 111 | int i,icol,irow,j,k,l,ll,n;
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| 112 | float big,dum,pivinv,temp;
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| 113 | // satisfy the compiler
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| 114 | icol = irow = 0;
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| 115 |
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| 116 | // the size of the matrix
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| 117 | n = 4;
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| 118 |
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| 119 | for ( j = 0 ; j < n ; j++) /* zero pivots */
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| 120 | ipiv[j] = 0;
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| 121 |
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| 122 | for ( i = 0; i < n; i++)
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| 123 | {
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| 124 | big = 0.0;
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| 125 | for (j = 0 ; j < n ; j++)
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| 126 | if (ipiv[j] != 1)
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| 127 | for ( k = 0 ; k<n ; k++)
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| 128 | {
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| 129 | if (ipiv[k] == 0)
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| 130 | {
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| 131 | if (fabs(x[k][j]) >= big)
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| 132 | {
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| 133 | big = fabs(x[k][j]);
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| 134 | irow = j;
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| 135 | icol = k;
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| 136 | }
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| 137 | }
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| 138 | else
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| 139 | if (ipiv[k] > 1)
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| 140 | return 1; /* singular matrix */
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| 141 | }
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| 142 | ++(ipiv[icol]);
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| 143 | if (irow != icol)
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| 144 | {
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| 145 | for ( l = 0 ; l<n ; l++)
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| 146 | {
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| 147 | temp = x[l][icol];
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| 148 | x[l][icol] = x[l][irow];
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| 149 | x[l][irow] = temp;
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| 150 | }
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| 151 | }
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| 152 | indxr[i] = irow;
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| 153 | indxc[i] = icol;
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| 154 | if (x[icol][icol] == 0.0)
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| 155 | return 1; /* singular matrix */
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| 156 |
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| 157 | pivinv = 1.0f / x[icol][icol];
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| 158 | x[icol][icol] = 1.0f ;
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| 159 | for ( l = 0 ; l<n ; l++)
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| 160 | x[l][icol] = x[l][icol] * pivinv ;
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| 161 |
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| 162 | for (ll = 0 ; ll < n ; ll++)
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| 163 | if (ll != icol)
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| 164 | {
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| 165 | dum = x[icol][ll];
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| 166 | x[icol][ll] = 0.0;
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| 167 | for ( l = 0 ; l<n ; l++)
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| 168 | x[l][ll] = x[l][ll] - x[l][icol] * dum ;
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| 169 | }
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| 170 | }
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| 171 | for ( l = n; l--; )
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| 172 | {
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| 173 | if (indxr[l] != indxc[l])
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| 174 | for ( k = 0; k<n ; k++)
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| 175 | {
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| 176 | temp = x[indxr[l]][k];
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| 177 | x[indxr[l]][k] = x[indxc[l]][k];
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| 178 | x[indxc[l]][k] = temp;
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| 179 | }
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| 180 | }
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| 181 |
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| 182 | return 0 ; // matrix is regular .. inversion has been succesfull
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| 183 | }
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| 184 |
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| 185 |
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| 186 | // Invert the given matrix using the above inversion routine.
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| 187 | Matrix4x4 Invert(const Matrix4x4& M)
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| 188 | {
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| 189 | Matrix4x4 InvertMe = M;
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| 190 | InvertMe.Invert();
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| 191 | return InvertMe;
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| 192 | }
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| 193 |
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| 194 |
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| 195 | // Transpose the matrix.
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| 196 | void Matrix4x4::Transpose()
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| 197 | {
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| 198 | for (int i = 0; i < 4; i++)
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| 199 | for (int j = i; j < 4; j++)
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| 200 | if (i != j) {
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| 201 | float temp = x[i][j];
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| 202 | x[i][j] = x[j][i];
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| 203 | x[j][i] = temp;
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| 204 | }
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| 205 | }
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| 206 |
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| 207 |
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| 208 | // Transpose the given matrix using the transpose routine above.
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| 209 | Matrix4x4 Transpose(const Matrix4x4& M)
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| 210 | {
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| 211 | Matrix4x4 TransposeMe = M;
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| 212 | TransposeMe.Transpose();
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| 213 | return TransposeMe;
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| 214 | }
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| 215 |
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| 216 |
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| 217 | // Construct an identity matrix.
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| 218 | Matrix4x4 IdentityMatrix()
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| 219 | {
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| 220 | Matrix4x4 M;
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| 221 |
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| 222 | for (int i = 0; i < 4; i++)
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| 223 | for (int j = 0; j < 4; j++)
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| 224 | M.x[i][j] = (i == j) ? 1.0f : 0.0f;
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| 225 | return M;
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| 226 | }
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| 227 |
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| 228 |
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| 229 | // Construct a zero matrix.
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| 230 | Matrix4x4 ZeroMatrix()
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| 231 | {
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| 232 | Matrix4x4 M;
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| 233 | for (int i = 0; i < 4; i++)
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| 234 | for (int j = 0; j < 4; j++)
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| 235 | M.x[i][j] = 0;
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| 236 | return M;
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| 237 | }
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| 238 |
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| 239 | // Construct a translation matrix given the location to translate to.
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| 240 | Matrix4x4
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| 241 | TranslationMatrix(const Vector3& Location)
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| 242 | {
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| 243 | Matrix4x4 M = IdentityMatrix();
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| 244 | M.x[3][0] = Location.x;
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| 245 | M.x[3][1] = Location.y;
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| 246 | M.x[3][2] = Location.z;
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| 247 | return M;
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| 248 | }
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| 249 |
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| 250 | // Construct a rotation matrix. Rotates Angle radians about the
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| 251 | // X axis.
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| 252 | Matrix4x4
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| 253 | RotationXMatrix(float Angle)
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| 254 | {
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| 255 | Matrix4x4 M = IdentityMatrix();
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| 256 | float Cosine = cos(Angle);
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| 257 | float Sine = sin(Angle);
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| 258 | M.x[1][1] = Cosine;
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| 259 | M.x[2][1] = -Sine;
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| 260 | M.x[1][2] = Sine;
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| 261 | M.x[2][2] = Cosine;
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| 262 | return M;
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| 263 | }
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| 264 |
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| 265 | // Construct a rotation matrix. Rotates Angle radians about the
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| 266 | // Y axis.
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| 267 | Matrix4x4 RotationYMatrix(float angle)
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| 268 | {
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| 269 | Matrix4x4 m = IdentityMatrix();
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| 270 |
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| 271 | float cosine = cos(angle);
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| 272 | float sine = sin(angle);
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| 273 |
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| 274 | m.x[0][0] = cosine;
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| 275 | m.x[2][0] = -sine;
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| 276 | m.x[0][2] = sine;
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| 277 | m.x[2][2] = cosine;
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| 278 |
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| 279 | return m;
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| 280 | }
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| 281 |
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| 282 |
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| 283 | // Construct a rotation matrix. Rotates Angle radians about the
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| 284 | // Z axis.
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| 285 | Matrix4x4 RotationZMatrix(float angle)
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| 286 | {
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| 287 | Matrix4x4 m = IdentityMatrix();
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| 288 |
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| 289 | float cosine = cos(angle);
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| 290 | float sine = sin(angle);
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| 291 |
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| 292 | m.x[0][0] = cosine;
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| 293 | m.x[1][0] = -sine;
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| 294 | m.x[0][1] = sine;
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| 295 | m.x[1][1] = cosine;
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| 296 |
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| 297 | return m;
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| 298 | }
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| 299 |
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| 300 |
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| 301 | // Construct a yaw-pitch-roll rotation matrix. Rotate Yaw
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| 302 | // radians about the XY axis, rotate Pitch radians in the
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| 303 | // plane defined by the Yaw rotation, and rotate Roll radians
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| 304 | // about the axis defined by the previous two angles.
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| 305 | Matrix4x4 RotationYPRMatrix(float Yaw, float Pitch, float Roll)
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| 306 | {
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| 307 | Matrix4x4 M;
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| 308 | float ch = cos(Yaw);
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| 309 | float sh = sin(Yaw);
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| 310 | float cp = cos(Pitch);
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| 311 | float sp = sin(Pitch);
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| 312 | float cr = cos(Roll);
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| 313 | float sr = sin(Roll);
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| 314 |
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| 315 | M.x[0][0] = ch * cr + sh * sp * sr;
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| 316 | M.x[1][0] = -ch * sr + sh * sp * cr;
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| 317 | M.x[2][0] = sh * cp;
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| 318 | M.x[0][1] = sr * cp;
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| 319 | M.x[1][1] = cr * cp;
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| 320 | M.x[2][1] = -sp;
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| 321 | M.x[0][2] = -sh * cr - ch * sp * sr;
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| 322 | M.x[1][2] = sr * sh + ch * sp * cr;
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| 323 | M.x[2][2] = ch * cp;
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| 324 | for (int i = 0; i < 4; i++)
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| 325 | M.x[3][i] = M.x[i][3] = 0;
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| 326 | M.x[3][3] = 1;
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| 327 |
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| 328 | return M;
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| 329 | }
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| 330 |
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| 331 | // Construct a rotation of a given angle about a given axis.
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| 332 | // Derived from Eric Haines's SPD (Standard Procedural
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| 333 | // Database).
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| 334 | Matrix4x4 RotationAxisMatrix(const Vector3& axis, float angle)
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| 335 | {
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| 336 | Matrix4x4 M;
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| 337 |
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| 338 | float cosine = cos(angle);
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| 339 | float sine = sin(angle);
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| 340 | float one_minus_cosine = 1 - cosine;
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| 341 |
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| 342 | M.x[0][0] = axis.x * axis.x + (1.0f - axis.x * axis.x) * cosine;
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| 343 | M.x[0][1] = axis.x * axis.y * one_minus_cosine + axis.z * sine;
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| 344 | M.x[0][2] = axis.x * axis.z * one_minus_cosine - axis.y * sine;
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| 345 | M.x[0][3] = 0;
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| 346 |
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| 347 | M.x[1][0] = axis.x * axis.y * one_minus_cosine - axis.z * sine;
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| 348 | M.x[1][1] = axis.y * axis.y + (1.0f - axis.y * axis.y) * cosine;
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| 349 | M.x[1][2] = axis.y * axis.z * one_minus_cosine + axis.x * sine;
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| 350 | M.x[1][3] = 0;
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| 351 |
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| 352 | M.x[2][0] = axis.x * axis.z * one_minus_cosine + axis.y * sine;
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| 353 | M.x[2][1] = axis.y * axis.z * one_minus_cosine - axis.x * sine;
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| 354 | M.x[2][2] = axis.z * axis.z + (1.0f - axis.z * axis.z) * cosine;
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| 355 | M.x[2][3] = 0;
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| 356 |
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| 357 | M.x[3][0] = 0;
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| 358 | M.x[3][1] = 0;
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| 359 | M.x[3][2] = 0;
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| 360 | M.x[3][3] = 1;
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| 361 |
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| 362 | return M;
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| 363 | }
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| 364 |
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| 365 |
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| 366 | // Constructs the rotation matrix that rotates 'vec1' to 'vec2'
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| 367 | Matrix4x4 RotationVectorsMatrix(const Vector3 &vecStart, const Vector3 &vecTo)
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| 368 | {
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| 369 | Vector3 vec = CrossProd(vecStart, vecTo);
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| 370 |
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| 371 | if (Magnitude(vec) > Limits::Small) {
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| 372 | // vector exist, compute angle
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| 373 | float angle = acos(DotProd(vecStart, vecTo));
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| 374 | // normalize for sure
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| 375 | vec.Normalize();
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| 376 | return RotationAxisMatrix(vec, angle);
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| 377 | }
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| 378 |
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| 379 | // opposite or colinear vectors
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| 380 | Matrix4x4 ret = IdentityMatrix();
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| 381 | if (DotProd(vecStart, vecTo) < 0.0f)
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| 382 | ret *= -1.0f; // opposite vectors
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| 383 |
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| 384 | return ret;
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| 385 | }
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| 386 |
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| 387 |
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| 388 | // Construct a scale matrix given the X, Y, and Z parameters
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| 389 | // to scale by. To scale uniformly, let X==Y==Z.
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| 390 | Matrix4x4 ScaleMatrix(float X, float Y, float Z)
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| 391 | {
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| 392 | Matrix4x4 M = IdentityMatrix();
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| 393 |
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| 394 | M.x[0][0] = X;
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| 395 | M.x[1][1] = Y;
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| 396 | M.x[2][2] = Z;
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| 397 |
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| 398 | return M;
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| 399 | }
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| 400 |
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| 401 |
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| 402 | // Construct a rotation matrix that makes the x, y, z axes
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| 403 | // correspond to the vectors given.
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| 404 | Matrix4x4 GenRotation(const Vector3 &x, const Vector3 &y, const Vector3 &z)
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| 405 | {
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| 406 | Matrix4x4 M = IdentityMatrix();
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| 407 |
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| 408 | // x y
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|---|
| 409 | M.x[0][0] = x.x;
|
|---|
| 410 | M.x[1][0] = x.y;
|
|---|
| 411 | M.x[2][0] = x.z;
|
|---|
| 412 |
|
|---|
| 413 | M.x[0][1] = y.x;
|
|---|
| 414 | M.x[1][1] = y.y;
|
|---|
| 415 | M.x[2][1] = y.z;
|
|---|
| 416 |
|
|---|
| 417 | M.x[0][2] = z.x;
|
|---|
| 418 | M.x[1][2] = z.y;
|
|---|
| 419 | M.x[2][2] = z.z;
|
|---|
| 420 |
|
|---|
| 421 | return M;
|
|---|
| 422 | }
|
|---|
| 423 |
|
|---|
| 424 | // Construct a quadric matrix. After Foley et al. pp. 528-529.
|
|---|
| 425 | Matrix4x4
|
|---|
| 426 | QuadricMatrix(float a, float b, float c, float d, float e,
|
|---|
| 427 | float f, float g, float h, float j, float k)
|
|---|
| 428 | {
|
|---|
| 429 | Matrix4x4 M;
|
|---|
| 430 |
|
|---|
| 431 | M.x[0][0] = a; M.x[0][1] = d; M.x[0][2] = f; M.x[0][3] = g;
|
|---|
| 432 | M.x[1][0] = d; M.x[1][1] = b; M.x[1][2] = e; M.x[1][3] = h;
|
|---|
| 433 | M.x[2][0] = f; M.x[2][1] = e; M.x[2][2] = c; M.x[2][3] = j;
|
|---|
| 434 | M.x[3][0] = g; M.x[3][1] = h; M.x[3][2] = j; M.x[3][3] = k;
|
|---|
| 435 |
|
|---|
| 436 | return M;
|
|---|
| 437 | }
|
|---|
| 438 |
|
|---|
| 439 | // Construct various "mirror" matrices, which flip coordinate
|
|---|
| 440 | // signs in the various axes specified.
|
|---|
| 441 | Matrix4x4
|
|---|
| 442 | MirrorX()
|
|---|
| 443 | {
|
|---|
| 444 | Matrix4x4 M = IdentityMatrix();
|
|---|
| 445 | M.x[0][0] = -1;
|
|---|
| 446 | return M;
|
|---|
| 447 | }
|
|---|
| 448 |
|
|---|
| 449 | Matrix4x4
|
|---|
| 450 | MirrorY()
|
|---|
| 451 | {
|
|---|
| 452 | Matrix4x4 M = IdentityMatrix();
|
|---|
| 453 | M.x[1][1] = -1;
|
|---|
| 454 | return M;
|
|---|
| 455 | }
|
|---|
| 456 |
|
|---|
| 457 | Matrix4x4
|
|---|
| 458 | MirrorZ()
|
|---|
| 459 | {
|
|---|
| 460 | Matrix4x4 M = IdentityMatrix();
|
|---|
| 461 | M.x[2][2] = -1;
|
|---|
| 462 | return M;
|
|---|
| 463 | }
|
|---|
| 464 |
|
|---|
| 465 | Matrix4x4
|
|---|
| 466 | RotationOnly(const Matrix4x4& x)
|
|---|
| 467 | {
|
|---|
| 468 | Matrix4x4 M = x;
|
|---|
| 469 | M.x[3][0] = M.x[3][1] = M.x[3][2] = 0;
|
|---|
| 470 | return M;
|
|---|
| 471 | }
|
|---|
| 472 |
|
|---|
| 473 | // Add corresponding elements of the two matrices.
|
|---|
| 474 | Matrix4x4&
|
|---|
| 475 | Matrix4x4::operator+= (const Matrix4x4& A)
|
|---|
| 476 | {
|
|---|
| 477 | for (int i = 0; i < 4; i++)
|
|---|
| 478 | for (int j = 0; j < 4; j++)
|
|---|
| 479 | x[i][j] += A.x[i][j];
|
|---|
| 480 | return *this;
|
|---|
| 481 | }
|
|---|
| 482 |
|
|---|
| 483 | // Subtract corresponding elements of the matrices.
|
|---|
| 484 | Matrix4x4&
|
|---|
| 485 | Matrix4x4::operator-= (const Matrix4x4& A)
|
|---|
| 486 | {
|
|---|
| 487 | for (int i = 0; i < 4; i++)
|
|---|
| 488 | for (int j = 0; j < 4; j++)
|
|---|
| 489 | x[i][j] -= A.x[i][j];
|
|---|
| 490 | return *this;
|
|---|
| 491 | }
|
|---|
| 492 |
|
|---|
| 493 | // Scale each element of the matrix by A.
|
|---|
| 494 | Matrix4x4&
|
|---|
| 495 | Matrix4x4::operator*= (float A)
|
|---|
| 496 | {
|
|---|
| 497 | for (int i = 0; i < 4; i++)
|
|---|
| 498 | for (int j = 0; j < 4; j++)
|
|---|
| 499 | x[i][j] *= A;
|
|---|
| 500 | return *this;
|
|---|
| 501 | }
|
|---|
| 502 |
|
|---|
| 503 | // Multiply two matrices.
|
|---|
| 504 | Matrix4x4&
|
|---|
| 505 | Matrix4x4::operator*= (const Matrix4x4& A)
|
|---|
| 506 | {
|
|---|
| 507 | Matrix4x4 ret = *this;
|
|---|
| 508 |
|
|---|
| 509 | for (int i = 0; i < 4; i++)
|
|---|
| 510 | for (int j = 0; j < 4; j++) {
|
|---|
| 511 | float subt = 0;
|
|---|
| 512 | for (int k = 0; k < 4; k++)
|
|---|
| 513 | subt += ret.x[i][k] * A.x[k][j];
|
|---|
| 514 | x[i][j] = subt;
|
|---|
| 515 | }
|
|---|
| 516 | return *this;
|
|---|
| 517 | }
|
|---|
| 518 |
|
|---|
| 519 | // Add corresponding elements of the matrices.
|
|---|
| 520 | Matrix4x4
|
|---|
| 521 | operator+ (const Matrix4x4& A, const Matrix4x4& B)
|
|---|
| 522 | {
|
|---|
| 523 | Matrix4x4 ret;
|
|---|
| 524 |
|
|---|
| 525 | for (int i = 0; i < 4; i++)
|
|---|
| 526 | for (int j = 0; j < 4; j++)
|
|---|
| 527 | ret.x[i][j] = A.x[i][j] + B.x[i][j];
|
|---|
| 528 | return ret;
|
|---|
| 529 | }
|
|---|
| 530 |
|
|---|
| 531 | // Subtract corresponding elements of the matrices.
|
|---|
| 532 | Matrix4x4
|
|---|
| 533 | operator- (const Matrix4x4& A, const Matrix4x4& B)
|
|---|
| 534 | {
|
|---|
| 535 | Matrix4x4 ret;
|
|---|
| 536 |
|
|---|
| 537 | for (int i = 0; i < 4; i++)
|
|---|
| 538 | for (int j = 0; j < 4; j++)
|
|---|
| 539 | ret.x[i][j] = A.x[i][j] - B.x[i][j];
|
|---|
| 540 | return ret;
|
|---|
| 541 | }
|
|---|
| 542 |
|
|---|
| 543 | // Multiply matrices.
|
|---|
| 544 | Matrix4x4
|
|---|
| 545 | operator* (const Matrix4x4& A, const Matrix4x4& B)
|
|---|
| 546 | {
|
|---|
| 547 | Matrix4x4 ret;
|
|---|
| 548 |
|
|---|
| 549 | for (int i = 0; i < 4; i++)
|
|---|
| 550 | for (int j = 0; j < 4; j++) {
|
|---|
| 551 | float subt = 0;
|
|---|
| 552 | for (int k = 0; k < 4; k++)
|
|---|
| 553 | subt += A.x[i][k] * B.x[k][j];
|
|---|
| 554 | ret.x[i][j] = subt;
|
|---|
| 555 | }
|
|---|
| 556 | return ret;
|
|---|
| 557 | }
|
|---|
| 558 |
|
|---|
| 559 | // Transform a vector by a matrix.
|
|---|
| 560 | Vector3
|
|---|
| 561 | operator* (const Matrix4x4& M, const Vector3& v)
|
|---|
| 562 | {
|
|---|
| 563 | Vector3 ret;
|
|---|
| 564 | float denom;
|
|---|
| 565 |
|
|---|
| 566 | ret.x = v.x * M.x[0][0] + v.y * M.x[1][0] + v.z * M.x[2][0] + M.x[3][0];
|
|---|
| 567 | ret.y = v.x * M.x[0][1] + v.y * M.x[1][1] + v.z * M.x[2][1] + M.x[3][1];
|
|---|
| 568 | ret.z = v.x * M.x[0][2] + v.y * M.x[1][2] + v.z * M.x[2][2] + M.x[3][2];
|
|---|
| 569 | denom = M.x[0][3] + M.x[1][3] + M.x[2][3] + M.x[3][3];
|
|---|
| 570 | if (denom != 1.0)
|
|---|
| 571 | ret /= denom;
|
|---|
| 572 | return ret;
|
|---|
| 573 | }
|
|---|
| 574 |
|
|---|
| 575 | // Apply the rotation portion of a matrix to a vector.
|
|---|
| 576 | Vector3
|
|---|
| 577 | RotateOnly(const Matrix4x4& M, const Vector3& v)
|
|---|
| 578 | {
|
|---|
| 579 | Vector3 ret;
|
|---|
| 580 | float denom;
|
|---|
| 581 |
|
|---|
| 582 | ret.x = v.x * M.x[0][0] + v.y * M.x[1][0] + v.z * M.x[2][0];
|
|---|
| 583 | ret.y = v.x * M.x[0][1] + v.y * M.x[1][1] + v.z * M.x[2][1];
|
|---|
| 584 | ret.z = v.x * M.x[0][2] + v.y * M.x[1][2] + v.z * M.x[2][2];
|
|---|
| 585 | denom = M.x[0][3] + M.x[1][3] + M.x[2][3] + M.x[3][3];
|
|---|
| 586 | if (denom != 1.0)
|
|---|
| 587 | ret /= denom;
|
|---|
| 588 | return ret;
|
|---|
| 589 | }
|
|---|
| 590 |
|
|---|
| 591 | // Scale each element of the matrix by B.
|
|---|
| 592 | Matrix4x4
|
|---|
| 593 | operator* (const Matrix4x4& A, float B)
|
|---|
| 594 | {
|
|---|
| 595 | Matrix4x4 ret;
|
|---|
| 596 |
|
|---|
| 597 | for (int i = 0; i < 4; i++)
|
|---|
| 598 | for (int j = 0; j < 4; j++)
|
|---|
| 599 | ret.x[i][j] = A.x[i][j] * B;
|
|---|
| 600 | return ret;
|
|---|
| 601 | }
|
|---|
| 602 |
|
|---|
| 603 | // Overloaded << for C++-style output.
|
|---|
| 604 | ostream&
|
|---|
| 605 | operator<< (ostream& s, const Matrix4x4& M)
|
|---|
| 606 | {
|
|---|
| 607 | for (int i = 0; i < 4; i++) { // y
|
|---|
| 608 | for (int j = 0; j < 4; j++) { // x
|
|---|
| 609 | // x y
|
|---|
| 610 | s << setprecision(4) << setw(10) << M.x[j][i];
|
|---|
| 611 | }
|
|---|
| 612 | s << '\n';
|
|---|
| 613 | }
|
|---|
| 614 | return s;
|
|---|
| 615 | }
|
|---|
| 616 |
|
|---|
| 617 |
|
|---|
| 618 | Vector3 PlaneRotate(const Matrix4x4& tform, const Vector3& p)
|
|---|
| 619 | {
|
|---|
| 620 | // I sure hope that matrix is invertible...
|
|---|
| 621 | Matrix4x4 use = Transpose(Invert(tform));
|
|---|
| 622 |
|
|---|
| 623 | return RotateOnly(use, p);
|
|---|
| 624 | }
|
|---|
| 625 |
|
|---|
| 626 | // Transform a normal
|
|---|
| 627 | Vector3 TransformNormal(const Matrix4x4& tform, const Vector3& n)
|
|---|
| 628 | {
|
|---|
| 629 | Matrix4x4 use = NormalTransformMatrix(tform);
|
|---|
| 630 |
|
|---|
| 631 | return RotateOnly(use, n);
|
|---|
| 632 | }
|
|---|
| 633 |
|
|---|
| 634 | Matrix4x4
|
|---|
| 635 | NormalTransformMatrix(const Matrix4x4 &tform)
|
|---|
| 636 | {
|
|---|
| 637 | Matrix4x4 m = tform;
|
|---|
| 638 | // for normal translation vector must be zero!
|
|---|
| 639 | m.x[3][0] = m.x[3][1] = m.x[3][2] = 0.0;
|
|---|
| 640 | // I sure hope that matrix is invertible...
|
|---|
| 641 | return Transpose(Invert(m));
|
|---|
| 642 | }
|
|---|
| 643 |
|
|---|
| 644 |
|
|---|
| 645 | Vector3 GetTranslation(const Matrix4x4 &M)
|
|---|
| 646 | {
|
|---|
| 647 | return Vector3(M.x[3][0], M.x[3][1], M.x[3][2]);
|
|---|
| 648 | }
|
|---|
| 649 |
|
|---|
| 650 | } |
|---|
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