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Diffstat (limited to 'shared/Matrices.cpp')
-rw-r--r-- | shared/Matrices.cpp | 581 |
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diff --git a/shared/Matrices.cpp b/shared/Matrices.cpp new file mode 100644 index 0000000..582b285 --- /dev/null +++ b/shared/Matrices.cpp @@ -0,0 +1,581 @@ +/////////////////////////////////////////////////////////////////////////////// +// Matrice.cpp +// =========== +// NxN Matrix Math classes +// +// The elements of the matrix are stored as column major order. +// | 0 2 | | 0 3 6 | | 0 4 8 12 | +// | 1 3 | | 1 4 7 | | 1 5 9 13 | +// | 2 5 8 | | 2 6 10 14 | +// | 3 7 11 15 | +// +// AUTHOR: Song Ho Ahn (song.ahn@gmail.com) +// CREATED: 2005-06-24 +// UPDATED: 2014-09-21 +// +// Copyright (C) 2005 Song Ho Ahn +/////////////////////////////////////////////////////////////////////////////// + +#include <cmath> +#include <algorithm> +#include "Matrices.h" + +const float DEG2RAD = 3.141593f / 180; +const float EPSILON = 0.00001f; + + + +/////////////////////////////////////////////////////////////////////////////// +// transpose 2x2 matrix +/////////////////////////////////////////////////////////////////////////////// +Matrix2& Matrix2::transpose() +{ + std::swap(m[1], m[2]); + return *this; +} + + + +/////////////////////////////////////////////////////////////////////////////// +// return the determinant of 2x2 matrix +/////////////////////////////////////////////////////////////////////////////// +float Matrix2::getDeterminant() +{ + return m[0] * m[3] - m[1] * m[2]; +} + + + +/////////////////////////////////////////////////////////////////////////////// +// inverse of 2x2 matrix +// If cannot find inverse, set identity matrix +/////////////////////////////////////////////////////////////////////////////// +Matrix2& Matrix2::invert() +{ + float determinant = getDeterminant(); + if(fabs(determinant) <= EPSILON) + { + return identity(); + } + + float tmp = m[0]; // copy the first element + float invDeterminant = 1.0f / determinant; + m[0] = invDeterminant * m[3]; + m[1] = -invDeterminant * m[1]; + m[2] = -invDeterminant * m[2]; + m[3] = invDeterminant * tmp; + + return *this; +} + + + +/////////////////////////////////////////////////////////////////////////////// +// transpose 3x3 matrix +/////////////////////////////////////////////////////////////////////////////// +Matrix3& Matrix3::transpose() +{ + std::swap(m[1], m[3]); + std::swap(m[2], m[6]); + std::swap(m[5], m[7]); + + return *this; +} + + + +/////////////////////////////////////////////////////////////////////////////// +// return determinant of 3x3 matrix +/////////////////////////////////////////////////////////////////////////////// +float Matrix3::getDeterminant() +{ + return m[0] * (m[4] * m[8] - m[5] * m[7]) - + m[1] * (m[3] * m[8] - m[5] * m[6]) + + m[2] * (m[3] * m[7] - m[4] * m[6]); +} + + + +/////////////////////////////////////////////////////////////////////////////// +// inverse 3x3 matrix +// If cannot find inverse, set identity matrix +/////////////////////////////////////////////////////////////////////////////// +Matrix3& Matrix3::invert() +{ + float determinant, invDeterminant; + float tmp[9]; + + tmp[0] = m[4] * m[8] - m[5] * m[7]; + tmp[1] = m[2] * m[7] - m[1] * m[8]; + tmp[2] = m[1] * m[5] - m[2] * m[4]; + tmp[3] = m[5] * m[6] - m[3] * m[8]; + tmp[4] = m[0] * m[8] - m[2] * m[6]; + tmp[5] = m[2] * m[3] - m[0] * m[5]; + tmp[6] = m[3] * m[7] - m[4] * m[6]; + tmp[7] = m[1] * m[6] - m[0] * m[7]; + tmp[8] = m[0] * m[4] - m[1] * m[3]; + + // check determinant if it is 0 + determinant = m[0] * tmp[0] + m[1] * tmp[3] + m[2] * tmp[6]; + if(fabs(determinant) <= EPSILON) + { + return identity(); // cannot inverse, make it idenety matrix + } + + // divide by the determinant + invDeterminant = 1.0f / determinant; + m[0] = invDeterminant * tmp[0]; + m[1] = invDeterminant * tmp[1]; + m[2] = invDeterminant * tmp[2]; + m[3] = invDeterminant * tmp[3]; + m[4] = invDeterminant * tmp[4]; + m[5] = invDeterminant * tmp[5]; + m[6] = invDeterminant * tmp[6]; + m[7] = invDeterminant * tmp[7]; + m[8] = invDeterminant * tmp[8]; + + return *this; +} + + + +/////////////////////////////////////////////////////////////////////////////// +// transpose 4x4 matrix +/////////////////////////////////////////////////////////////////////////////// +Matrix4& Matrix4::transpose() +{ + std::swap(m[1], m[4]); + std::swap(m[2], m[8]); + std::swap(m[3], m[12]); + std::swap(m[6], m[9]); + std::swap(m[7], m[13]); + std::swap(m[11], m[14]); + + return *this; +} + + + +/////////////////////////////////////////////////////////////////////////////// +// inverse 4x4 matrix +/////////////////////////////////////////////////////////////////////////////// +Matrix4& Matrix4::invert() +{ + // If the 4th row is [0,0,0,1] then it is affine matrix and + // it has no projective transformation. + if(m[3] == 0 && m[7] == 0 && m[11] == 0 && m[15] == 1) + this->invertAffine(); + else + { + this->invertGeneral(); + /*@@ invertProjective() is not optimized (slower than generic one) + if(fabs(m[0]*m[5] - m[1]*m[4]) > EPSILON) + this->invertProjective(); // inverse using matrix partition + else + this->invertGeneral(); // generalized inverse + */ + } + + return *this; +} + + + +/////////////////////////////////////////////////////////////////////////////// +// compute the inverse of 4x4 Euclidean transformation matrix +// +// Euclidean transformation is translation, rotation, and reflection. +// With Euclidean transform, only the position and orientation of the object +// will be changed. Euclidean transform does not change the shape of an object +// (no scaling). Length and angle are reserved. +// +// Use inverseAffine() if the matrix has scale and shear transformation. +// +// M = [ R | T ] +// [ --+-- ] (R denotes 3x3 rotation/reflection matrix) +// [ 0 | 1 ] (T denotes 1x3 translation matrix) +// +// y = M*x -> y = R*x + T -> x = R^-1*(y - T) -> x = R^T*y - R^T*T +// (R is orthogonal, R^-1 = R^T) +// +// [ R | T ]-1 [ R^T | -R^T * T ] (R denotes 3x3 rotation matrix) +// [ --+-- ] = [ ----+--------- ] (T denotes 1x3 translation) +// [ 0 | 1 ] [ 0 | 1 ] (R^T denotes R-transpose) +/////////////////////////////////////////////////////////////////////////////// +Matrix4& Matrix4::invertEuclidean() +{ + // transpose 3x3 rotation matrix part + // | R^T | 0 | + // | ----+-- | + // | 0 | 1 | + float tmp; + tmp = m[1]; m[1] = m[4]; m[4] = tmp; + tmp = m[2]; m[2] = m[8]; m[8] = tmp; + tmp = m[6]; m[6] = m[9]; m[9] = tmp; + + // compute translation part -R^T * T + // | 0 | -R^T x | + // | --+------- | + // | 0 | 0 | + float x = m[12]; + float y = m[13]; + float z = m[14]; + m[12] = -(m[0] * x + m[4] * y + m[8] * z); + m[13] = -(m[1] * x + m[5] * y + m[9] * z); + m[14] = -(m[2] * x + m[6] * y + m[10]* z); + + // last row should be unchanged (0,0,0,1) + + return *this; +} + + + +/////////////////////////////////////////////////////////////////////////////// +// compute the inverse of a 4x4 affine transformation matrix +// +// Affine transformations are generalizations of Euclidean transformations. +// Affine transformation includes translation, rotation, reflection, scaling, +// and shearing. Length and angle are NOT preserved. +// M = [ R | T ] +// [ --+-- ] (R denotes 3x3 rotation/scale/shear matrix) +// [ 0 | 1 ] (T denotes 1x3 translation matrix) +// +// y = M*x -> y = R*x + T -> x = R^-1*(y - T) -> x = R^-1*y - R^-1*T +// +// [ R | T ]-1 [ R^-1 | -R^-1 * T ] +// [ --+-- ] = [ -----+---------- ] +// [ 0 | 1 ] [ 0 + 1 ] +/////////////////////////////////////////////////////////////////////////////// +Matrix4& Matrix4::invertAffine() +{ + // R^-1 + Matrix3 r(m[0],m[1],m[2], m[4],m[5],m[6], m[8],m[9],m[10]); + r.invert(); + m[0] = r[0]; m[1] = r[1]; m[2] = r[2]; + m[4] = r[3]; m[5] = r[4]; m[6] = r[5]; + m[8] = r[6]; m[9] = r[7]; m[10]= r[8]; + + // -R^-1 * T + float x = m[12]; + float y = m[13]; + float z = m[14]; + m[12] = -(r[0] * x + r[3] * y + r[6] * z); + m[13] = -(r[1] * x + r[4] * y + r[7] * z); + m[14] = -(r[2] * x + r[5] * y + r[8] * z); + + // last row should be unchanged (0,0,0,1) + //m[3] = m[7] = m[11] = 0.0f; + //m[15] = 1.0f; + + return * this; +} + + + +/////////////////////////////////////////////////////////////////////////////// +// inverse matrix using matrix partitioning (blockwise inverse) +// It devides a 4x4 matrix into 4 of 2x2 matrices. It works in case of where +// det(A) != 0. If not, use the generic inverse method +// inverse formula. +// M = [ A | B ] A, B, C, D are 2x2 matrix blocks +// [ --+-- ] det(M) = |A| * |D - ((C * A^-1) * B)| +// [ C | D ] +// +// M^-1 = [ A' | B' ] A' = A^-1 - (A^-1 * B) * C' +// [ ---+--- ] B' = (A^-1 * B) * -D' +// [ C' | D' ] C' = -D' * (C * A^-1) +// D' = (D - ((C * A^-1) * B))^-1 +// +// NOTE: I wrap with () if it it used more than once. +// The matrix is invertable even if det(A)=0, so must check det(A) before +// calling this function, and use invertGeneric() instead. +/////////////////////////////////////////////////////////////////////////////// +Matrix4& Matrix4::invertProjective() +{ + // partition + Matrix2 a(m[0], m[1], m[4], m[5]); + Matrix2 b(m[8], m[9], m[12], m[13]); + Matrix2 c(m[2], m[3], m[6], m[7]); + Matrix2 d(m[10], m[11], m[14], m[15]); + + // pre-compute repeated parts + a.invert(); // A^-1 + Matrix2 ab = a * b; // A^-1 * B + Matrix2 ca = c * a; // C * A^-1 + Matrix2 cab = ca * b; // C * A^-1 * B + Matrix2 dcab = d - cab; // D - C * A^-1 * B + + // check determinant if |D - C * A^-1 * B| = 0 + //NOTE: this function assumes det(A) is already checked. if |A|=0 then, + // cannot use this function. + float determinant = dcab[0] * dcab[3] - dcab[1] * dcab[2]; + if(fabs(determinant) <= EPSILON) + { + return identity(); + } + + // compute D' and -D' + Matrix2 d1 = dcab; // (D - C * A^-1 * B) + d1.invert(); // (D - C * A^-1 * B)^-1 + Matrix2 d2 = -d1; // -(D - C * A^-1 * B)^-1 + + // compute C' + Matrix2 c1 = d2 * ca; // -D' * (C * A^-1) + + // compute B' + Matrix2 b1 = ab * d2; // (A^-1 * B) * -D' + + // compute A' + Matrix2 a1 = a - (ab * c1); // A^-1 - (A^-1 * B) * C' + + // assemble inverse matrix + m[0] = a1[0]; m[4] = a1[2]; /*|*/ m[8] = b1[0]; m[12]= b1[2]; + m[1] = a1[1]; m[5] = a1[3]; /*|*/ m[9] = b1[1]; m[13]= b1[3]; + /*-----------------------------+-----------------------------*/ + m[2] = c1[0]; m[6] = c1[2]; /*|*/ m[10]= d1[0]; m[14]= d1[2]; + m[3] = c1[1]; m[7] = c1[3]; /*|*/ m[11]= d1[1]; m[15]= d1[3]; + + return *this; +} + + + +/////////////////////////////////////////////////////////////////////////////// +// compute the inverse of a general 4x4 matrix using Cramer's Rule +// If cannot find inverse, return indentity matrix +// M^-1 = adj(M) / det(M) +/////////////////////////////////////////////////////////////////////////////// +Matrix4& Matrix4::invertGeneral() +{ + // get cofactors of minor matrices + float cofactor0 = getCofactor(m[5],m[6],m[7], m[9],m[10],m[11], m[13],m[14],m[15]); + float cofactor1 = getCofactor(m[4],m[6],m[7], m[8],m[10],m[11], m[12],m[14],m[15]); + float cofactor2 = getCofactor(m[4],m[5],m[7], m[8],m[9], m[11], m[12],m[13],m[15]); + float cofactor3 = getCofactor(m[4],m[5],m[6], m[8],m[9], m[10], m[12],m[13],m[14]); + + // get determinant + float determinant = m[0] * cofactor0 - m[1] * cofactor1 + m[2] * cofactor2 - m[3] * cofactor3; + if(fabs(determinant) <= EPSILON) + { + return identity(); + } + + // get rest of cofactors for adj(M) + float cofactor4 = getCofactor(m[1],m[2],m[3], m[9],m[10],m[11], m[13],m[14],m[15]); + float cofactor5 = getCofactor(m[0],m[2],m[3], m[8],m[10],m[11], m[12],m[14],m[15]); + float cofactor6 = getCofactor(m[0],m[1],m[3], m[8],m[9], m[11], m[12],m[13],m[15]); + float cofactor7 = getCofactor(m[0],m[1],m[2], m[8],m[9], m[10], m[12],m[13],m[14]); + + float cofactor8 = getCofactor(m[1],m[2],m[3], m[5],m[6], m[7], m[13],m[14],m[15]); + float cofactor9 = getCofactor(m[0],m[2],m[3], m[4],m[6], m[7], m[12],m[14],m[15]); + float cofactor10= getCofactor(m[0],m[1],m[3], m[4],m[5], m[7], m[12],m[13],m[15]); + float cofactor11= getCofactor(m[0],m[1],m[2], m[4],m[5], m[6], m[12],m[13],m[14]); + + float cofactor12= getCofactor(m[1],m[2],m[3], m[5],m[6], m[7], m[9], m[10],m[11]); + float cofactor13= getCofactor(m[0],m[2],m[3], m[4],m[6], m[7], m[8], m[10],m[11]); + float cofactor14= getCofactor(m[0],m[1],m[3], m[4],m[5], m[7], m[8], m[9], m[11]); + float cofactor15= getCofactor(m[0],m[1],m[2], m[4],m[5], m[6], m[8], m[9], m[10]); + + // build inverse matrix = adj(M) / det(M) + // adjugate of M is the transpose of the cofactor matrix of M + float invDeterminant = 1.0f / determinant; + m[0] = invDeterminant * cofactor0; + m[1] = -invDeterminant * cofactor4; + m[2] = invDeterminant * cofactor8; + m[3] = -invDeterminant * cofactor12; + + m[4] = -invDeterminant * cofactor1; + m[5] = invDeterminant * cofactor5; + m[6] = -invDeterminant * cofactor9; + m[7] = invDeterminant * cofactor13; + + m[8] = invDeterminant * cofactor2; + m[9] = -invDeterminant * cofactor6; + m[10]= invDeterminant * cofactor10; + m[11]= -invDeterminant * cofactor14; + + m[12]= -invDeterminant * cofactor3; + m[13]= invDeterminant * cofactor7; + m[14]= -invDeterminant * cofactor11; + m[15]= invDeterminant * cofactor15; + + return *this; +} + + + +/////////////////////////////////////////////////////////////////////////////// +// return determinant of 4x4 matrix +/////////////////////////////////////////////////////////////////////////////// +float Matrix4::getDeterminant() +{ + return m[0] * getCofactor(m[5],m[6],m[7], m[9],m[10],m[11], m[13],m[14],m[15]) - + m[1] * getCofactor(m[4],m[6],m[7], m[8],m[10],m[11], m[12],m[14],m[15]) + + m[2] * getCofactor(m[4],m[5],m[7], m[8],m[9], m[11], m[12],m[13],m[15]) - + m[3] * getCofactor(m[4],m[5],m[6], m[8],m[9], m[10], m[12],m[13],m[14]); +} + + + +/////////////////////////////////////////////////////////////////////////////// +// compute cofactor of 3x3 minor matrix without sign +// input params are 9 elements of the minor matrix +// NOTE: The caller must know its sign. +/////////////////////////////////////////////////////////////////////////////// +float Matrix4::getCofactor(float m0, float m1, float m2, + float m3, float m4, float m5, + float m6, float m7, float m8) +{ + return m0 * (m4 * m8 - m5 * m7) - + m1 * (m3 * m8 - m5 * m6) + + m2 * (m3 * m7 - m4 * m6); +} + + + +/////////////////////////////////////////////////////////////////////////////// +// translate this matrix by (x, y, z) +/////////////////////////////////////////////////////////////////////////////// +Matrix4& Matrix4::translate(const Vector3& v) +{ + return translate(v.x, v.y, v.z); +} + +Matrix4& Matrix4::translate(float x, float y, float z) +{ + m[0] += m[3] * x; m[4] += m[7] * x; m[8] += m[11]* x; m[12]+= m[15]* x; + m[1] += m[3] * y; m[5] += m[7] * y; m[9] += m[11]* y; m[13]+= m[15]* y; + m[2] += m[3] * z; m[6] += m[7] * z; m[10]+= m[11]* z; m[14]+= m[15]* z; + + return *this; +} + + + +/////////////////////////////////////////////////////////////////////////////// +// uniform scale +/////////////////////////////////////////////////////////////////////////////// +Matrix4& Matrix4::scale(float s) +{ + return scale(s, s, s); +} + +Matrix4& Matrix4::scale(float x, float y, float z) +{ + m[0] *= x; m[4] *= x; m[8] *= x; m[12] *= x; + m[1] *= y; m[5] *= y; m[9] *= y; m[13] *= y; + m[2] *= z; m[6] *= z; m[10]*= z; m[14] *= z; + return *this; +} + + + +/////////////////////////////////////////////////////////////////////////////// +// build a rotation matrix with given angle(degree) and rotation axis, then +// multiply it with this object +/////////////////////////////////////////////////////////////////////////////// +Matrix4& Matrix4::rotate(float angle, const Vector3& axis) +{ + return rotate(angle, axis.x, axis.y, axis.z); +} + +Matrix4& Matrix4::rotate(float angle, float x, float y, float z) +{ + float c = cosf(angle * DEG2RAD); // cosine + float s = sinf(angle * DEG2RAD); // sine + float c1 = 1.0f - c; // 1 - c + float m0 = m[0], m4 = m[4], m8 = m[8], m12= m[12], + m1 = m[1], m5 = m[5], m9 = m[9], m13= m[13], + m2 = m[2], m6 = m[6], m10= m[10], m14= m[14]; + + // build rotation matrix + float r0 = x * x * c1 + c; + float r1 = x * y * c1 + z * s; + float r2 = x * z * c1 - y * s; + float r4 = x * y * c1 - z * s; + float r5 = y * y * c1 + c; + float r6 = y * z * c1 + x * s; + float r8 = x * z * c1 + y * s; + float r9 = y * z * c1 - x * s; + float r10= z * z * c1 + c; + + // multiply rotation matrix + m[0] = r0 * m0 + r4 * m1 + r8 * m2; + m[1] = r1 * m0 + r5 * m1 + r9 * m2; + m[2] = r2 * m0 + r6 * m1 + r10* m2; + m[4] = r0 * m4 + r4 * m5 + r8 * m6; + m[5] = r1 * m4 + r5 * m5 + r9 * m6; + m[6] = r2 * m4 + r6 * m5 + r10* m6; + m[8] = r0 * m8 + r4 * m9 + r8 * m10; + m[9] = r1 * m8 + r5 * m9 + r9 * m10; + m[10]= r2 * m8 + r6 * m9 + r10* m10; + m[12]= r0 * m12+ r4 * m13+ r8 * m14; + m[13]= r1 * m12+ r5 * m13+ r9 * m14; + m[14]= r2 * m12+ r6 * m13+ r10* m14; + + return *this; +} + +Matrix4& Matrix4::rotateX(float angle) +{ + float c = cosf(angle * DEG2RAD); + float s = sinf(angle * DEG2RAD); + float m1 = m[1], m2 = m[2], + m5 = m[5], m6 = m[6], + m9 = m[9], m10= m[10], + m13= m[13], m14= m[14]; + + m[1] = m1 * c + m2 *-s; + m[2] = m1 * s + m2 * c; + m[5] = m5 * c + m6 *-s; + m[6] = m5 * s + m6 * c; + m[9] = m9 * c + m10*-s; + m[10]= m9 * s + m10* c; + m[13]= m13* c + m14*-s; + m[14]= m13* s + m14* c; + + return *this; +} + +Matrix4& Matrix4::rotateY(float angle) +{ + float c = cosf(angle * DEG2RAD); + float s = sinf(angle * DEG2RAD); + float m0 = m[0], m2 = m[2], + m4 = m[4], m6 = m[6], + m8 = m[8], m10= m[10], + m12= m[12], m14= m[14]; + + m[0] = m0 * c + m2 * s; + m[2] = m0 *-s + m2 * c; + m[4] = m4 * c + m6 * s; + m[6] = m4 *-s + m6 * c; + m[8] = m8 * c + m10* s; + m[10]= m8 *-s + m10* c; + m[12]= m12* c + m14* s; + m[14]= m12*-s + m14* c; + + return *this; +} + +Matrix4& Matrix4::rotateZ(float angle) +{ + float c = cosf(angle * DEG2RAD); + float s = sinf(angle * DEG2RAD); + float m0 = m[0], m1 = m[1], + m4 = m[4], m5 = m[5], + m8 = m[8], m9 = m[9], + m12= m[12], m13= m[13]; + + m[0] = m0 * c + m1 *-s; + m[1] = m0 * s + m1 * c; + m[4] = m4 * c + m5 *-s; + m[5] = m4 * s + m5 * c; + m[8] = m8 * c + m9 *-s; + m[9] = m8 * s + m9 * c; + m[12]= m12* c + m13*-s; + m[13]= m12* s + m13* c; + + return *this; +} |