Matrix4x4.cpp
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#include "Matrix4x4.h"
#include "Vector3.h"
#include "Math.h"
//#define _EULE_NO_INTRINSICS_
#ifndef _EULE_NO_INTRINSICS_
#include <immintrin.h>
#endif
using namespace Eule;
Matrix4x4::Matrix4x4()
{
// Create identity matrix
for (std::size_t i = 0; i < 4; i++)
for (std::size_t j = 0; j < 4; j++)
v[i][j] = double(i == j);
return;
}
Matrix4x4::Matrix4x4(const Matrix4x4& other)
{
v = other.v;
return;
}
Matrix4x4::Matrix4x4(Matrix4x4&& other) noexcept
{
v = std::move(other.v);
return;
}
Matrix4x4 Matrix4x4::operator*(const Matrix4x4& other) const
{
Matrix4x4 newMatrix;
newMatrix.p = 1;
#ifndef _EULE_NO_INTRINSICS_
/* <= Matrix3x3 multiplication => */
// Load matrix components
__m256d __va1 = _mm256_set_pd(v[0][0], v[0][0], v[0][0], v[1][0]);
__m256d __va2 = _mm256_set_pd(v[1][0], v[1][0], v[2][0], v[2][0]);
__m256d __oa1 = _mm256_set_pd(other[0][0], other[0][1], other[0][2], other[0][0]);
__m256d __oa2 = _mm256_set_pd(other[0][1], other[0][2], other[0][0], other[0][1]);
__m256d __vb1 = _mm256_set_pd(v[0][1], v[0][1], v[0][1], v[1][1]);
__m256d __vb2 = _mm256_set_pd(v[1][1], v[1][1], v[2][1], v[2][1]);
__m256d __ob1 = _mm256_set_pd(other[1][0], other[1][1], other[1][2], other[1][0]);
__m256d __ob2 = _mm256_set_pd(other[1][1], other[1][2], other[1][0], other[1][1]);
__m256d __vc1 = _mm256_set_pd(v[0][2], v[0][2], v[0][2], v[1][2]);
__m256d __vc2 = _mm256_set_pd(v[1][2], v[1][2], v[2][2], v[2][2]);
__m256d __oc1 = _mm256_set_pd(other[2][0], other[2][1], other[2][2], other[2][0]);
__m256d __oc2 = _mm256_set_pd(other[2][1], other[2][2], other[2][0], other[2][1]);
// Initialize sums
__m256d __sum1 = _mm256_set1_pd(0);
__m256d __sum2 = _mm256_set1_pd(0);
// Let's multiply-add them together
// First, the first block
__sum1 = _mm256_fmadd_pd(__va1, __oa1, __sum1);
__sum1 = _mm256_fmadd_pd(__vb1, __ob1, __sum1);
__sum1 = _mm256_fmadd_pd(__vc1, __oc1, __sum1);
// Then the second block
__sum2 = _mm256_fmadd_pd(__va2, __oa2, __sum2);
__sum2 = _mm256_fmadd_pd(__vb2, __ob2, __sum2);
__sum2 = _mm256_fmadd_pd(__vc2, __oc2, __sum2);
// Retrieve results
double sum1[4];
double sum2[4];
_mm256_storeu_pd(sum1, __sum1);
_mm256_storeu_pd(sum2, __sum2);
// Apply results
// Block 1
newMatrix[0][0] = sum1[3];
newMatrix[0][1] = sum1[2];
newMatrix[0][2] = sum1[1];
newMatrix[1][0] = sum1[0];
// Block 2
newMatrix[1][1] = sum2[3];
newMatrix[1][2] = sum2[2];
newMatrix[2][0] = sum2[1];
newMatrix[2][1] = sum2[0];
// Does not fit in the intrinsic calculation. Might just calculate 'by hand'.
newMatrix[2][2] = (v[2][0] * other[0][2]) + (v[2][1] * other[1][2]) + (v[2][2] * other[2][2]);
/* <= Translation component => */
// Load translation components into registers
__m256d __transSelf = _mm256_set_pd(0, l, h, d);
__m256d __transOther = _mm256_set_pd(0, other.l, other.h, other.d);
// Let's add them
__m256d __sum = _mm256_add_pd(__transSelf, __transOther);
// Retrieve results
double sum[4];
_mm256_storeu_pd(sum, __sum);
// Apply them
newMatrix.d = sum[0];
newMatrix.h = sum[1];
newMatrix.l = sum[2];
#else
// Rotation, Scaling
newMatrix[0][0] = (v[0][0] * other[0][0]) + (v[0][1] * other[1][0]) + (v[0][2] * other[2][0]);
newMatrix[0][1] = (v[0][0] * other[0][1]) + (v[0][1] * other[1][1]) + (v[0][2] * other[2][1]);
newMatrix[0][2] = (v[0][0] * other[0][2]) + (v[0][1] * other[1][2]) + (v[0][2] * other[2][2]);
newMatrix[1][0] = (v[1][0] * other[0][0]) + (v[1][1] * other[1][0]) + (v[1][2] * other[2][0]);
newMatrix[1][1] = (v[1][0] * other[0][1]) + (v[1][1] * other[1][1]) + (v[1][2] * other[2][1]);
newMatrix[1][2] = (v[1][0] * other[0][2]) + (v[1][1] * other[1][2]) + (v[1][2] * other[2][2]);
newMatrix[2][0] = (v[2][0] * other[0][0]) + (v[2][1] * other[1][0]) + (v[2][2] * other[2][0]);
newMatrix[2][1] = (v[2][0] * other[0][1]) + (v[2][1] * other[1][1]) + (v[2][2] * other[2][1]);
newMatrix[2][2] = (v[2][0] * other[0][2]) + (v[2][1] * other[1][2]) + (v[2][2] * other[2][2]);
// Translation
newMatrix[0][3] = v[0][3] + other[0][3];
newMatrix[1][3] = v[1][3] + other[1][3];
newMatrix[2][3] = v[2][3] + other[2][3];
#endif
return newMatrix;
}
void Matrix4x4::operator*=(const Matrix4x4& other)
{
*this = *this * other;
return;
}
Matrix4x4 Matrix4x4::operator/(const Matrix4x4& other) const
{
return *this * other.Inverse3x3();
}
void Matrix4x4::operator/=(const Matrix4x4& other)
{
*this = *this * other.Inverse3x3();
return;
}
Matrix4x4 Matrix4x4::operator*(const double scalar) const
{
Matrix4x4 m;
#ifndef _EULE_NO_INTRINSICS_
// Load matrix rows
__m256d __row0 = _mm256_set_pd(v[0][3], v[0][2], v[0][1], v[0][0]);
__m256d __row1 = _mm256_set_pd(v[1][3], v[1][2], v[1][1], v[1][0]);
__m256d __row2 = _mm256_set_pd(v[2][3], v[2][2], v[2][1], v[2][0]);
__m256d __row3 = _mm256_set_pd(v[3][3], v[3][2], v[3][1], v[3][0]);
// Load scalar
__m256d __scalar = _mm256_set1_pd(scalar);
// Scale values
__m256d __sr0 = _mm256_mul_pd(__row0, __scalar);
__m256d __sr1 = _mm256_mul_pd(__row1, __scalar);
__m256d __sr2 = _mm256_mul_pd(__row2, __scalar);
__m256d __sr3 = _mm256_mul_pd(__row3, __scalar);
// Extract results
_mm256_storeu_pd(m.v[0].data(), __sr0);
_mm256_storeu_pd(m.v[1].data(), __sr1);
_mm256_storeu_pd(m.v[2].data(), __sr2);
_mm256_storeu_pd(m.v[3].data(), __sr3);
#else
for (std::size_t x = 0; x < 4; x++)
for (std::size_t y = 0; y < 4; y++)
m[x][y] = v[x][y] * scalar;
#endif
return m;
}
void Matrix4x4::operator*=(const double scalar)
{
*this = *this * scalar;
return;
}
Matrix4x4 Matrix4x4::operator/(const double denominator) const
{
const double precomputeDivision = 1.0 / denominator;
return *this * precomputeDivision;
}
void Matrix4x4::operator/=(const double denominator)
{
*this = *this / denominator;
return;
}
Matrix4x4 Matrix4x4::operator+(const Matrix4x4& other) const
{
Matrix4x4 m;
#ifndef _EULE_NO_INTRINSICS_
// Load matrix rows
__m256d __row0a = _mm256_set_pd(v[0][3], v[0][2], v[0][1], v[0][0]);
__m256d __row1a = _mm256_set_pd(v[1][3], v[1][2], v[1][1], v[1][0]);
__m256d __row2a = _mm256_set_pd(v[2][3], v[2][2], v[2][1], v[2][0]);
__m256d __row3a = _mm256_set_pd(v[3][3], v[3][2], v[3][1], v[3][0]);
__m256d __row0b = _mm256_set_pd(other[0][3], other[0][2], other[0][1], other[0][0]);
__m256d __row1b = _mm256_set_pd(other[1][3], other[1][2], other[1][1], other[1][0]);
__m256d __row2b = _mm256_set_pd(other[2][3], other[2][2], other[2][1], other[2][0]);
__m256d __row3b = _mm256_set_pd(other[3][3], other[3][2], other[3][1], other[3][0]);
// Add rows
__m256d __sr0 = _mm256_add_pd(__row0a, __row0b);
__m256d __sr1 = _mm256_add_pd(__row1a, __row1b);
__m256d __sr2 = _mm256_add_pd(__row2a, __row2b);
__m256d __sr3 = _mm256_add_pd(__row3a, __row3b);
// Extract results
_mm256_storeu_pd(m.v[0].data(), __sr0);
_mm256_storeu_pd(m.v[1].data(), __sr1);
_mm256_storeu_pd(m.v[2].data(), __sr2);
_mm256_storeu_pd(m.v[3].data(), __sr3);
#else
for (std::size_t x = 0; x < 4; x++)
for (std::size_t y = 0; y < 4; y++)
m[x][y] = v[x][y] + other[x][y];
#endif
return m;
}
void Matrix4x4::operator+=(const Matrix4x4& other)
{
#ifndef _EULE_NO_INTRINSICS_
// Doing it again is a tad directer, and thus faster. We avoid an intermittent Matrix4x4 instance
// Load matrix rows
__m256d __row0a = _mm256_set_pd(v[0][3], v[0][2], v[0][1], v[0][0]);
__m256d __row1a = _mm256_set_pd(v[1][3], v[1][2], v[1][1], v[1][0]);
__m256d __row2a = _mm256_set_pd(v[2][3], v[2][2], v[2][1], v[2][0]);
__m256d __row3a = _mm256_set_pd(v[3][3], v[3][2], v[3][1], v[3][0]);
__m256d __row0b = _mm256_set_pd(other[0][3], other[0][2], other[0][1], other[0][0]);
__m256d __row1b = _mm256_set_pd(other[1][3], other[1][2], other[1][1], other[1][0]);
__m256d __row2b = _mm256_set_pd(other[2][3], other[2][2], other[2][1], other[2][0]);
__m256d __row3b = _mm256_set_pd(other[3][3], other[3][2], other[3][1], other[3][0]);
// Add rows
__m256d __sr0 = _mm256_add_pd(__row0a, __row0b);
__m256d __sr1 = _mm256_add_pd(__row1a, __row1b);
__m256d __sr2 = _mm256_add_pd(__row2a, __row2b);
__m256d __sr3 = _mm256_add_pd(__row3a, __row3b);
// Extract results
_mm256_storeu_pd(v[0].data(), __sr0);
_mm256_storeu_pd(v[1].data(), __sr1);
_mm256_storeu_pd(v[2].data(), __sr2);
_mm256_storeu_pd(v[3].data(), __sr3);
#else
*this = *this + other;
#endif
return;
}
Matrix4x4 Matrix4x4::operator-(const Matrix4x4& other) const
{
Matrix4x4 m;
#ifndef _EULE_NO_INTRINSICS_
// Load matrix rows
__m256d __row0a = _mm256_set_pd(v[0][3], v[0][2], v[0][1], v[0][0]);
__m256d __row1a = _mm256_set_pd(v[1][3], v[1][2], v[1][1], v[1][0]);
__m256d __row2a = _mm256_set_pd(v[2][3], v[2][2], v[2][1], v[2][0]);
__m256d __row3a = _mm256_set_pd(v[3][3], v[3][2], v[3][1], v[3][0]);
__m256d __row0b = _mm256_set_pd(other[0][3], other[0][2], other[0][1], other[0][0]);
__m256d __row1b = _mm256_set_pd(other[1][3], other[1][2], other[1][1], other[1][0]);
__m256d __row2b = _mm256_set_pd(other[2][3], other[2][2], other[2][1], other[2][0]);
__m256d __row3b = _mm256_set_pd(other[3][3], other[3][2], other[3][1], other[3][0]);
// Subtract rows
__m256d __sr0 = _mm256_sub_pd(__row0a, __row0b);
__m256d __sr1 = _mm256_sub_pd(__row1a, __row1b);
__m256d __sr2 = _mm256_sub_pd(__row2a, __row2b);
__m256d __sr3 = _mm256_sub_pd(__row3a, __row3b);
// Extract results
_mm256_storeu_pd(m.v[0].data(), __sr0);
_mm256_storeu_pd(m.v[1].data(), __sr1);
_mm256_storeu_pd(m.v[2].data(), __sr2);
_mm256_storeu_pd(m.v[3].data(), __sr3);
#else
for (std::size_t x = 0; x < 4; x++)
for (std::size_t y = 0; y < 4; y++)
m[x][y] = v[x][y] - other[x][y];
#endif
return m;
}
void Matrix4x4::operator-=(const Matrix4x4& other)
{
#ifndef _EULE_NO_INTRINSICS_
// Doing it again is a tad directer, and thus faster. We avoid an intermittent Matrix4x4 instance
// Load matrix rows
__m256d __row0a = _mm256_set_pd(v[0][3], v[0][2], v[0][1], v[0][0]);
__m256d __row1a = _mm256_set_pd(v[1][3], v[1][2], v[1][1], v[1][0]);
__m256d __row2a = _mm256_set_pd(v[2][3], v[2][2], v[2][1], v[2][0]);
__m256d __row3a = _mm256_set_pd(v[3][3], v[3][2], v[3][1], v[3][0]);
__m256d __row0b = _mm256_set_pd(other[0][3], other[0][2], other[0][1], other[0][0]);
__m256d __row1b = _mm256_set_pd(other[1][3], other[1][2], other[1][1], other[1][0]);
__m256d __row2b = _mm256_set_pd(other[2][3], other[2][2], other[2][1], other[2][0]);
__m256d __row3b = _mm256_set_pd(other[3][3], other[3][2], other[3][1], other[3][0]);
// Subtract rows
__m256d __sr0 = _mm256_sub_pd(__row0a, __row0b);
__m256d __sr1 = _mm256_sub_pd(__row1a, __row1b);
__m256d __sr2 = _mm256_sub_pd(__row2a, __row2b);
__m256d __sr3 = _mm256_sub_pd(__row3a, __row3b);
// Extract results
_mm256_storeu_pd(v[0].data(), __sr0);
_mm256_storeu_pd(v[1].data(), __sr1);
_mm256_storeu_pd(v[2].data(), __sr2);
_mm256_storeu_pd(v[3].data(), __sr3);
#else
* this = *this - other;
#endif
return;
}
std::array<double, 4>& Matrix4x4::operator[](std::size_t y)
{
return v[y];
}
const std::array<double, 4>& Matrix4x4::operator[](std::size_t y) const
{
return v[y];
}
void Matrix4x4::operator=(const Matrix4x4& other)
{
v = other.v;
return;
}
void Matrix4x4::operator=(Matrix4x4&& other) noexcept
{
v = std::move(other.v);
return;
}
bool Matrix4x4::operator==(const Matrix4x4& other)
{
return v == other.v;
}
bool Matrix4x4::operator!=(const Matrix4x4& other)
{
return !operator==(other);
}
const Vector3d Matrix4x4::GetTranslationComponent() const
{
return Vector3d(d, h, l);
}
void Matrix4x4::SetTranslationComponent(const Vector3d& trans)
{
d = trans.x;
h = trans.y;
l = trans.z;
return;
}
Matrix4x4 Matrix4x4::DropTranslationComponents() const
{
Matrix4x4 m(*this);
m.d = 0;
m.h = 0;
m.l = 0;
return m;
}
Matrix4x4 Matrix4x4::Transpose3x3() const
{
Matrix4x4 trans(*this); // Keep other cells
for (std::size_t i = 0; i < 3; i++)
for (std::size_t j = 0; j < 3; j++)
trans[j][i] = v[i][j];
return trans;
}
Matrix4x4 Matrix4x4::Transpose4x4() const
{
Matrix4x4 trans;
for (std::size_t i = 0; i < 4; i++)
for (std::size_t j = 0; j < 4; j++)
trans[j][i] = v[i][j];
return trans;
}
Matrix4x4 Matrix4x4::Multiply4x4(const Matrix4x4& o) const
{
Matrix4x4 m;
m[0][0] = (v[0][0]*o[0][0]) + (v[0][1]*o[1][0]) + (v[0][2]*o[2][0]) + (v[0][3]*o[3][0]);
m[0][1] = (v[0][0]*o[0][1]) + (v[0][1]*o[1][1]) + (v[0][2]*o[2][1]) + (v[0][3]*o[3][1]);
m[0][2] = (v[0][0]*o[0][2]) + (v[0][1]*o[1][2]) + (v[0][2]*o[2][2]) + (v[0][3]*o[3][2]);
m[0][3] = (v[0][0]*o[0][3]) + (v[0][1]*o[1][3]) + (v[0][2]*o[2][3]) + (v[0][3]*o[3][3]);
m[1][0] = (v[1][0]*o[0][0]) + (v[1][1]*o[1][0]) + (v[1][2]*o[2][0]) + (v[1][3]*o[3][0]);
m[1][1] = (v[1][0]*o[0][1]) + (v[1][1]*o[1][1]) + (v[1][2]*o[2][1]) + (v[1][3]*o[3][1]);
m[1][2] = (v[1][0]*o[0][2]) + (v[1][1]*o[1][2]) + (v[1][2]*o[2][2]) + (v[1][3]*o[3][2]);
m[1][3] = (v[1][0]*o[0][3]) + (v[1][1]*o[1][3]) + (v[1][2]*o[2][3]) + (v[1][3]*o[3][3]);
m[2][0] = (v[2][0]*o[0][0]) + (v[2][1]*o[1][0]) + (v[2][2]*o[2][0]) + (v[2][3]*o[3][0]);
m[2][1] = (v[2][0]*o[0][1]) + (v[2][1]*o[1][1]) + (v[2][2]*o[2][1]) + (v[2][3]*o[3][1]);
m[2][2] = (v[2][0]*o[0][2]) + (v[2][1]*o[1][2]) + (v[2][2]*o[2][2]) + (v[2][3]*o[3][2]);
m[2][3] = (v[2][0]*o[0][3]) + (v[2][1]*o[1][3]) + (v[2][2]*o[2][3]) + (v[2][3]*o[3][3]);
m[3][0] = (v[3][0]*o[0][0]) + (v[3][1]*o[1][0]) + (v[3][2]*o[2][0]) + (v[3][3]*o[3][0]);
m[3][1] = (v[3][0]*o[0][1]) + (v[3][1]*o[1][1]) + (v[3][2]*o[2][1]) + (v[3][3]*o[3][1]);
m[3][2] = (v[3][0]*o[0][2]) + (v[3][1]*o[1][2]) + (v[3][2]*o[2][2]) + (v[3][3]*o[3][2]);
m[3][3] = (v[3][0]*o[0][3]) + (v[3][1]*o[1][3]) + (v[3][2]*o[2][3]) + (v[3][3]*o[3][3]);
return m;
}
Matrix4x4 Matrix4x4::GetCofactors(std::size_t p, std::size_t q, std::size_t n) const
{
if (n > 4)
throw std::runtime_error("Dimension out of range! 0 <= n <= 4");
Matrix4x4 cofs;
std::size_t i = 0;
std::size_t j = 0;
for (std::size_t y = 0; y < n; y++)
for (std::size_t x = 0; x < n; x++)
{
if ((y != p) && (x != q))
{
cofs[i][j] = v[y][x];
j++;
}
if (j == n - 1)
{
j = 0;
i++;
}
}
return cofs;
}
/*
* BEGIN_REF
* https://www.geeksforgeeks.org/adjoint-inverse-matrix/
*/
double Matrix4x4::Determinant(std::size_t n) const
{
if (n > 4)
throw std::runtime_error("Dimension out of range! 0 <= n <= 4");
double d = 0;
double sign = 1;
if (n == 1)
return v[0][0];
for (std::size_t x = 0; x < n; x++)
{
Matrix4x4 cofs = GetCofactors(0, x, n);
d += sign * v[0][x] * cofs.Determinant(n - 1);
sign = -sign;
}
return d;
}
Matrix4x4 Matrix4x4::Adjoint(std::size_t n) const
{
if (n > 4)
throw std::runtime_error("Dimension out of range! 0 <= n <= 4");
Matrix4x4 adj;
double sign = 1;
for (std::size_t i = 0; i < n; i++)
for (std::size_t j = 0; j < n; j++)
{
Matrix4x4 cofs = GetCofactors(i, j, n);
// sign of adj[j][i] positive if sum of row
// and column indexes is even.
sign = ((i + j) % 2 == 0) ? 1 : -1;
// Interchanging rows and columns to get the
// transpose of the cofactor matrix
adj[j][i] = sign * (cofs.Determinant(n - 1));
}
return adj;
}
Matrix4x4 Matrix4x4::Inverse3x3() const
{
Matrix4x4 inv;
double det = Determinant(3);
if (det == 0.0)
throw std::runtime_error("Matrix3x3 not inversible!");
Matrix4x4 adj = Adjoint(3);
for (std::size_t i = 0; i < 3; i++)
for (std::size_t j = 0; j < 3; j++)
inv[i][j] = adj[i][j] / det;
inv.SetTranslationComponent(-GetTranslationComponent());
return inv;
}
Matrix4x4 Matrix4x4::Inverse4x4() const
{
Matrix4x4 inv;
double det = Determinant(4);
if (det == 0.0)
throw std::runtime_error("Matrix4x4 not inversible!");
Matrix4x4 adj = Adjoint(4);
for (std::size_t i = 0; i < 4; i++)
for (std::size_t j = 0; j < 4; j++)
inv[i][j] = adj[i][j] / det;
return inv;
}
/*
* END REF
*/
bool Matrix4x4::IsInversible3x3() const
{
return (Determinant(3) != 0);
}
bool Matrix4x4::IsInversible4x4() const
{
return (Determinant(4) != 0);
}
bool Matrix4x4::Similar(const Matrix4x4& other, double epsilon) const
{
for (std::size_t i = 0; i < 4; i++)
for (std::size_t j = 0; j < 4; j++)
if (!Math::Similar(v[i][j], other[i][j], epsilon))
return false;
return true;
}
namespace Eule
{
std::ostream& operator<<(std::ostream& os, const Matrix4x4& m)
{
os << std::endl;
for (std::size_t y = 0; y < 4; y++)
{
for (std::size_t x = 0; x < 4; x++)
os << " | " << m[y][x];
os << " |" << std::endl;
}
return os;
}
std::wostream& operator<<(std::wostream& os, const Matrix4x4& m)
{
os << std::endl;
for (std::size_t y = 0; y < 4; y++)
{
for (std::size_t x = 0; x < 4; x++)
os << L" | " << m[y][x];
os << L" |" << std::endl;
}
return os;
}
}
Eule::Matrix4x4::j
double & j
Definition: Matrix4x4.h:137
Eule::Matrix4x4::Inverse4x4
Matrix4x4 Inverse4x4() const
Will return the full 4x4-inverse of this matrix.
Definition: Matrix4x4.cpp:577
Eule::Matrix4x4::Adjoint
Matrix4x4 Adjoint(std::size_t n) const
Will return the adjoint of this matrix, by dimension n.
Definition: Matrix4x4.cpp:533
Eule::Matrix4x4::operator==
bool operator==(const Matrix4x4 &other)
Definition: Matrix4x4.cpp:397
Eule::Matrix4x4::operator+
Matrix4x4 operator+(const Matrix4x4 &other) const
Cellwise addition.
Definition: Matrix4x4.cpp:221
Eule::Matrix4x4::i
double & i
Definition: Matrix4x4.h:136
Eule::Matrix4x4::operator-=
void operator-=(const Matrix4x4 &other)
Cellwise subtraction.
Definition: Matrix4x4.cpp:338
Eule::Matrix4x4::Transpose4x4
Matrix4x4 Transpose4x4() const
Will return the 4x4 transpose of this matrix.
Definition: Matrix4x4.cpp:440
Eule::Matrix4x4::operator!=
bool operator!=(const Matrix4x4 &other)
Definition: Matrix4x4.cpp:402
Eule::Vector3< double >
Eule::Matrix4x4::operator[]
std::array< double, 4 > & operator[](std::size_t y)
Definition: Matrix4x4.cpp:375
Eule::Matrix4x4::DropTranslationComponents
Matrix4x4 DropTranslationComponents() const
Will return this Matrix4x4 with d,h,l being set to 0.
Definition: Matrix4x4.cpp:420
Eule::Matrix4x4::operator*=
void operator*=(const Matrix4x4 &other)
Definition: Matrix4x4.cpp:147
Eule::Matrix4x4::Inverse3x3
Matrix4x4 Inverse3x3() const
Will return the 3x3-inverse of this matrix.
Definition: Matrix4x4.cpp:558
Eule::Matrix4x4::operator/
Matrix4x4 operator/(const Matrix4x4 &other) const
Definition: Matrix4x4.cpp:153
Eule::Matrix4x4::v
std::array< std::array< double, 4 >, 4 > v
Array holding the matrices values.
Definition: Matrix4x4.h:44
Eule::Matrix4x4::operator*
Matrix4x4 operator*(const Matrix4x4 &other) const
Definition: Matrix4x4.cpp:34
Math.h
Eule::Vector3d
Vector3< double > Vector3d
Definition: Matrix4x4.h:9
Matrix4x4.h
Eule::Matrix4x4::operator=
void operator=(const Matrix4x4 &other)
Definition: Matrix4x4.cpp:385
Eule::Vector3::z
T z
Definition: Vector3.h:96
Eule::Matrix4x4
A matrix 4x4 class representing a 3d transformation.
Definition: Matrix4x4.h:36
Eule::Matrix4x4::IsInversible4x4
bool IsInversible4x4() const
Will check if the entire matrix is inversible.
Definition: Matrix4x4.cpp:603
Eule::Matrix4x4::Similar
bool Similar(const Matrix4x4 &other, double epsilon=0.00001) const
Will compare if two matrices are similar to a certain epsilon value.
Definition: Matrix4x4.cpp:608
Eule::Matrix4x4::operator/=
void operator/=(const Matrix4x4 &other)
Definition: Matrix4x4.cpp:158
Eule::Vector3::x
T x
Definition: Vector3.h:94
Eule::Matrix4x4::p
double & p
Definition: Matrix4x4.h:143
Eule::Matrix4x4::IsInversible3x3
bool IsInversible3x3() const
Will check if the 3x3-component is inversible.
Definition: Matrix4x4.cpp:598
Eule::Matrix4x4::Transpose3x3
Matrix4x4 Transpose3x3() const
Will return the 3x3 transpose of this matrix.
Definition: Matrix4x4.cpp:429
Eule::operator<<
std::ostream & operator<<(std::ostream &os, const Matrix4x4 &m)
Definition: Matrix4x4.cpp:620
Eule::Matrix4x4::l
double & l
Definition: Matrix4x4.h:139
Eule::Matrix4x4::operator-
Matrix4x4 operator-(const Matrix4x4 &other) const
Cellwise subtraction.
Definition: Matrix4x4.cpp:298
Eule::Matrix4x4::Determinant
double Determinant(std::size_t n) const
Will return the determinant, by dimension n.
Definition: Matrix4x4.cpp:511
Vector3.h
Eule::Math::Similar
static constexpr bool Similar(const double a, const double b, const double epsilon=0.00001)
Compares two double values with a given accuracy.
Eule::Matrix4x4::operator+=
void operator+=(const Matrix4x4 &other)
Cellwise addition.
Definition: Matrix4x4.cpp:261
Eule::Matrix4x4::Matrix4x4
Matrix4x4()
Definition: Matrix4x4.cpp:12
Eule::Matrix4x4::SetTranslationComponent
void SetTranslationComponent(const Vector3d &trans)
Will set d,h,l from a Vector3d(x,y,z)
Definition: Matrix4x4.cpp:412
Eule::Matrix4x4::Multiply4x4
Matrix4x4 Multiply4x4(const Matrix4x4 &o) const
Will return the Matrix4x4 of an actual 4x4 multiplication. operator* only does a 3x3.
Definition: Matrix4x4.cpp:451
Eule::Matrix4x4::o
double & o
Definition: Matrix4x4.h:142
Eule::Matrix4x4::m
double & m
Definition: Matrix4x4.h:140
Eule::Matrix4x4::GetCofactors
Matrix4x4 GetCofactors(std::size_t p, std::size_t q, std::size_t n) const
Will return the cofactors of this matrix, by dimension n.
Definition: Matrix4x4.cpp:478
Eule::Matrix4x4::GetTranslationComponent
const Vector3d GetTranslationComponent() const
Will return d,h,l as a Vector3d(x,y,z)
Definition: Matrix4x4.cpp:407
Eule::Matrix4x4::n
double & n
Definition: Matrix4x4.h:141
Eule::Matrix4x4::h
double & h
Definition: Matrix4x4.h:135
Eule
Definition: Collider.h:4
Eule::Matrix4x4::d
double & d
Definition: Matrix4x4.h:131
Eule::Vector3::y
T y
Definition: Vector3.h:95