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