shamanDevel
9 years ago
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c162d474c7
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#ifndef MATRIX3_H |
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#define MATRIX3_H |
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//Simple matrix library. |
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//A 3x3 matrix is represented as a float16 in row major order |
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typedef float16 mat3; |
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//All matrix functions are prefixed with mat3 or mat4 |
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//Returns the zero matrix |
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inline mat3 mat3Zero() { |
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return (float16)(0); |
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} |
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//Returns the identity matrix |
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inline mat3 mat3Identity() { |
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return (float16) |
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(1, 0, 0, 0, |
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0, 1, 0, 0, |
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0, 0, 1, 0, |
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0, 0, 0, 1); |
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} |
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inline mat3 mat3FromRows(float3 row1, float3 row2, float3 row3) { |
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return (float16) |
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(row1.x, row1.y, row1.z, 0, |
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row2.x, row2.y, row2.z, 0, |
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row3.x, row3.y, row3.z, 0, |
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0, 0, 0, 1); |
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} |
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inline mat3 mat3FromColumns(float3 col1, float3 col2, float3 col3) { |
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return (float16) |
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(col1.x, col2.x, col3.x, 0, |
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col1.y, col2.y, col3.y, 0, |
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col1.z, col2.z, col3.z, 0, |
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0, 0, 0, 1); |
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} |
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inline mat3 mat3FromDiagonal(float3 diag) { |
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return (float16) |
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(diag.x, 0, 0, 0, |
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0, diag.y, 0, 0, |
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0, 0, diag.z, 0, |
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0, 0, 0, 1); |
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} |
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//Returns the i-th row (0-based) |
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inline float3 mat3GetRow(mat3 mat, int i) { |
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if (i==0) return mat.s012; |
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else if (i==1) return mat.s456; |
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else return mat.s89a; |
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} |
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//Sets the i-th row (0-based) |
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inline mat3 mat3SetRow(mat3 mat, int i, float3 row) { |
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if (i==0) mat.s012 = row; |
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else if (i==1) mat.s456 = row; |
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else mat.s89a = row; |
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return mat; |
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} |
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//Returns the i-th column (0-based) |
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inline float3 mat3GetColumn(mat3 mat, int i) { |
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if (i==0) return mat.s048; |
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else if (i==1) return mat.s159; |
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else return mat.s26a; |
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} |
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//Sets the i-th column (0-based) |
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inline mat3 mat3SetColumn(mat3 mat, int i, float3 col) { |
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if (i==0) mat.s048 = col; |
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else if (i==1) mat.s159 = col; |
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else mat.s26a = col; |
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return mat; |
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} |
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//Returns the diagonal |
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inline float3 mat3GetDiagonal(mat3 mat) { |
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return mat.s05a; |
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} |
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//Sets the diagonal |
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inline mat3 mat3SetDiagonal(mat3 mat, float3 diag) { |
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mat.s05a = diag; |
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return mat; |
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} |
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mat3 mat3FromAngleNormalAxis(float angle, float3 axis) { |
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float fCos = cos(angle); |
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float fSin = sin(angle); |
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float fOneMinusCos = 1.0f - fCos; |
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float fX2 = axis.x * axis.x; |
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float fY2 = axis.y * axis.y; |
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float fZ2 = axis.z * axis.z; |
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float fXYM = axis.x * axis.y * fOneMinusCos; |
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float fXZM = axis.x * axis.z * fOneMinusCos; |
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float fYZM = axis.y * axis.z * fOneMinusCos; |
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float fXSin = axis.x * fSin; |
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float fYSin = axis.y * fSin; |
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float fZSin = axis.z * fSin; |
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return (float16) ( |
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fX2 * fOneMinusCos + fCos, |
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fXYM - fZSin, |
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fXZM + fYSin, |
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0, |
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fXYM + fZSin, |
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fY2 * fOneMinusCos + fCos, |
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fYZM - fXSin, |
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0, |
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fXZM - fYSin, |
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fYZM + fXSin, |
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fZ2 * fOneMinusCos + fCos, |
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0, |
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0, 0, 0, 1 |
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); |
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} |
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mat3 mat3FromAngleAxis(float angle, float3 axis) { |
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return mat3FromAngleNormalAxis(angle, normalize(axis)); |
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} |
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//Multiplies the two matrices A and B |
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inline mat3 mat3Mult(mat3 A, mat3 B) { |
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return (float16) ( |
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dot(A.s012, B.s048), |
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dot(A.s012, B.s159), |
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dot(A.s012, B.s26a), |
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0, |
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dot(A.s456, B.s048), |
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dot(A.s456, B.s159), |
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dot(A.s456, B.s26a), |
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0, |
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dot(A.s89a, B.s048), |
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dot(A.s89a, B.s159), |
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dot(A.s89a, B.s26a), |
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0, |
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0, 0, 0, 1 |
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); |
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} |
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//Computes Av (right multiply of a vector to a matrix) |
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inline float3 mat3VMult(mat3 A, float3 v) { |
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return (float3) ( |
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dot(A.s012, v), |
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dot(A.s456, v), |
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dot(A.s89a, v)); |
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} |
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//Computes vA (left multiply of a vector to a matrix) |
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inline float3 mat3VMult2(float3 v, mat3 A) { |
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return (float3) ( |
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dot(v, A.s048), |
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dot(v, A.s159), |
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dot(v, A.s26a)); |
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} |
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//Scales this matrix by a constant |
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inline mat3 mat3Scale(mat3 mat, float s) { |
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return s*mat; |
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} |
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//Transposes this matrix |
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inline mat3 mat3Transpose(mat3 mat) { |
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return mat.s048c159d26ae37bf; //magic |
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} |
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//Computes the determinant |
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inline float mat3Determinant(mat3 mat) { |
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float fCo00 = mat.s5 * mat.sa - mat.s6 * mat.s9; |
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float fCo10 = mat.s6 * mat.s8 - mat.s4 * mat.sa; |
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float fCo20 = mat.s4 * mat.s9 - mat.s5 * mat.s8; |
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float fDet = mat.s0 * fCo00 + mat.s1 * fCo10 + mat.s2 * fCo20; |
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return fDet; |
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} |
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//Creates the adjoint |
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inline mat3 mat3Adjoint(mat3 mat) { |
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return (float16) ( |
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mat.s5 * mat.sa - mat.s6 * mat.s9, |
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mat.s2 * mat.s9 - mat.s1 * mat.sa, |
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mat.s1 * mat.s6 - mat.s2 * mat.s5, |
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0, |
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mat.s6 * mat.s8 - mat.s4 * mat.sa, |
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mat.s0 * mat.sa - mat.s2 * mat.s8, |
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mat.s2 * mat.s4 - mat.s0 * mat.s6, |
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0, |
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mat.s4 * mat.s9 - mat.s5 * mat.s8, |
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mat.s1 * mat.s8 - mat.s0 * mat.s9, |
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mat.s0 * mat.s5 - mat.s1 * mat.s4, |
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0, |
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0, 0, 0, 1 |
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); |
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} |
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//Inverts this matrix |
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inline mat3 mat3Invert(mat3 mat) { |
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float det = mat3Determinant(mat); |
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if (fabs(det) <= 1.1920928955078125E-7f) return mat3Zero(); |
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mat3 m = mat3Adjoint(mat); |
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return m / det; |
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} |
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//Computes A+B |
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inline mat3 mat3Add(mat3 A, mat3 B) { |
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return A + B; |
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} |
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inline bool mat3Equals(mat3 A, mat3 B, float epsilon) { |
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return fabs(A.s0 - B.s0)<epsilon |
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&& fabs(A.s1 - B.s1)<epsilon |
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&& fabs(A.s2 - B.s2)<epsilon |
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&& fabs(A.s4 - B.s4)<epsilon |
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&& fabs(A.s5 - B.s5)<epsilon |
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&& fabs(A.s6 - B.s6)<epsilon |
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&& fabs(A.s8 - B.s8)<epsilon |
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&& fabs(A.s9 - B.s9)<epsilon |
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&& fabs(A.sa - B.sa)<epsilon; |
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} |
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#endif |
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@ -0,0 +1,12 @@ |
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#ifndef MATRIX4_H |
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#define MATRIX4_H |
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//Simple matrix library. |
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//A 4x4 matrix is represented as a float16 in row major order |
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typedef float16 mat4; |
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//All matrix functions are prefixed with mat3 or mat4 |
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#endif |
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