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matrix4.h
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matrix4.h
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#ifndef MATRIX4_H_INCLUDED
#define MATRIX4_H_INCLUDED
#include "matrixn.h"
#include "vector3d.h"
#include "base_maths.h"
namespace Geometry
{
//
// Interface
//
template< typename Scalar>
class Matrix4 : public MatrixN<Scalar, 4>
{
public:
const static size_t sColumns = 4;
const static size_t sRows = 4;
typedef Scalar ScalarType;
typedef Matrix4<Scalar> MatrixType;
typedef MatrixN<Scalar,4> BaseType;
Matrix4()
: BaseType(uninitialised)
{
this->BecomeIdentity();
}
// explictly uninitialised construction
explicit Matrix4(const Uninitialised&)
: BaseType(uninitialised)
{ }
Matrix4(const typename BaseType::BaseType& rhs)
: BaseType(rhs)
{ }
explicit Matrix4(const Scalar data[sRows*sColumns])
: BaseType(data)
{ }
Matrix4(std::initializer_list<Scalar> data)
: BaseType(data)
{ }
Matrix4(
const VectorN<Scalar,3>& x,
const VectorN<Scalar,3>& y,
const VectorN<Scalar,3>& z);
static Matrix4 RotationAroundX(Scalar r);
void BecomeRotationAroundX(Scalar r);
static Matrix4 RotationAroundY(Scalar r);
void BecomeRotationAroundY(Scalar r);
static Matrix4 RotationAroundZ(Scalar r);
void BecomeRotationAroundZ(Scalar r);
static Matrix4 RotationFromEuler(const VectorN<Scalar,3>& r);
void BecomeRotationFromEuler(const VectorN<Scalar,3>& r);
static Matrix4 RotationAround(const VectorN<Scalar,3>& axis, Scalar r);
void BecomeRotationAround(const VectorN<Scalar,3>& axis, Scalar r);
static Matrix4 RotationAlign(const Vector3d<Scalar>& v1, const Vector3d<Scalar>& v2);
void BecomeRotationAlign( const Vector3d<Scalar>& v1, const Vector3d<Scalar>& v2);
};
//
// Free-functions
//
// ---
//
// Member Functions
//
// basis vectors
template< typename Scalar>
Matrix4<Scalar>::Matrix4(
const VectorN<Scalar,3>& x,
const VectorN<Scalar,3>& y,
const VectorN<Scalar,3>& z)
{
this->mData[ 0] = x[0];
this->mData[ 1] = x[1];
this->mData[ 2] = x[2];
this->mData[ 3] = 0;
this->mData[ 4] = y[0];
this->mData[ 5] = y[1];
this->mData[ 6] = y[2];
this->mData[ 7] = 0;
this->mData[ 8] = z[0];
this->mData[ 9] = z[1];
this->mData[10] = z[2];
this->mData[11] = 0;
this->mData[12] = 0;
this->mData[13] = 0;
this->mData[14] = 0;
this->mData[15] = 1;
}
// static
template< typename Scalar>
Matrix4<Scalar> Matrix4<Scalar>::RotationAroundX(Scalar r)
{
Matrix4<Scalar> result(uninitialised);
result.BecomeRotationAroundX(r);
return result;
}
template< typename Scalar>
void Matrix4<Scalar>::BecomeRotationAroundX(Scalar r)
{
Scalar cr = Cos(r);
Scalar sr = Sin(r);
// | 1 0 0 0 |
// | 0 cos(A) -sin(A) 0 |
// | 0 sin(A) cos(A) 0 |
// | 0 0 0 1 |
this->mData[ 0] = 1;
this->mData[ 1] = 0;
this->mData[ 2] = 0;
this->mData[ 3] = 0;
this->mData[ 4] = 0;
this->mData[ 5] = cr;
this->mData[ 6] = -sr;
this->mData[ 7] = 0;
this->mData[ 8] = 0;
this->mData[ 9] = sr;
this->mData[10] = cr;
this->mData[11] = 0;
this->mData[12] = 0;
this->mData[13] = 0;
this->mData[14] = 0;
this->mData[15] = 1;
}
// static
template< typename Scalar>
Matrix4<Scalar> Matrix4<Scalar>::RotationAroundY(Scalar r)
{
Matrix4<Scalar> result(uninitialised);
result.BecomeRotationAroundY(r);
return result;
}
template< typename Scalar>
void Matrix4<Scalar>::BecomeRotationAroundY(Scalar r)
{
Scalar cr = Cos(r);
Scalar sr = Sin(r);
// | cos(A) 0 sin(A) 0 |
// | 0 1 0 0 |
// | -sin(A) 0 cos(A) 0 |
// | 0 0 0 1 |
this->mData[ 0] = cr;
this->mData[ 1] = 0;
this->mData[ 2] = sr;
this->mData[ 3] = 0;
this->mData[ 4] = 0;
this->mData[ 5] = 1;
this->mData[ 6] = 0;
this->mData[ 7] = 0;
this->mData[ 8] = -sr;
this->mData[ 9] = 0;
this->mData[10] = cr;
this->mData[11] = 0;
this->mData[12] = 0;
this->mData[13] = 0;
this->mData[14] = 0;
this->mData[15] = 1;
}
// static
template< typename Scalar>
Matrix4<Scalar> Matrix4<Scalar>::RotationAroundZ(Scalar r)
{
Matrix4<Scalar> result(uninitialised);
result.BecomeRotationAroundZ(r);
return result;
}
template< typename Scalar>
void Matrix4<Scalar>::BecomeRotationAroundZ(Scalar r)
{
Scalar cr = Cos(r);
Scalar sr = Sin(r);
// cos(spin), -sin(spin), 0, 0,
this->mData[ 0] = cr;
this->mData[ 1] = -sr;
this->mData[ 2] = 0;
this->mData[ 3] = 0;
// sin(spin), cos(spin), 0, 0,
this->mData[ 4] = sr;
this->mData[ 5] = cr;
this->mData[ 6] = 0;
this->mData[ 7] = 0;
// 0, 0, 1, 0,
this->mData[ 8] = 0;
this->mData[ 9] = 0;
this->mData[10] = 1;
this->mData[11] = 0;
// 0, 0, 0, 1
this->mData[12] = 0;
this->mData[13] = 0;
this->mData[14] = 0;
this->mData[15] = 1;
}
// static
template< typename Scalar>
Matrix4<Scalar> Matrix4<Scalar>::RotationFromEuler(const VectorN<Scalar,3>& r)
{
Matrix4<Scalar> result(uninitialised);
result.RotationFromEuler(r);
return result;
}
template< typename Scalar>
void Matrix4<Scalar>::BecomeRotationFromEuler(const VectorN<Scalar,3>& r)
{
Scalar A = Cos(r.Get(0));
Scalar B = Sin(r.Get(0));
Scalar C = Cos(r.Get(1));
Scalar D = Sin(r.Get(1));
Scalar E = Cos(r.Get(2));
Scalar F = Sin(r.Get(2));
Scalar AD = A * D;
Scalar BD = B * D;
this->mData[0] = C * E;
this->mData[1] = -C * F;
this->mData[2] = D;
this->mData[4] = BD * E + A * F;
this->mData[5] = -BD * F + A * E;
this->mData[6] = -B * C;
this->mData[8] = -AD * E + B * F;
this->mData[9] = AD * F + B * E;
this->mData[10] = A * C;
this->mData[3] = this->mData[7] = this->mData[11] = this->mData[12] = this->mData[13] = this->mData[14] = 0;
this->mData[15] = 1;
}
// static
template< typename Scalar>
Matrix4<Scalar> Matrix4<Scalar>::RotationAround(const VectorN<Scalar,3>& axis, Scalar r)
{
Matrix4<Scalar> result(uninitialised);
result.BecomeRotationAround(axis, r);
return result;
}
template< typename Scalar>
void Matrix4<Scalar>::BecomeRotationAround(const VectorN<Scalar,3>& axis, Scalar r)
{
const Scalar rcos = Cos(r);
const Scalar rsin = Sin(r);
const Scalar rcosr = 1-rcos;
(*this)[0][0] = rcos + axis[0]*axis[0]*rcosr;
(*this)[1][0] = axis[2] * rsin + axis[1]*axis[0]*rcosr;
//(*this)[2][0] = -axis[1] * rsin + axis[2]*axis[0]*rcosr;
(*this)[2][0] = 0;
(*this)[0][1] = -axis[2] * rsin + axis[0]*axis[1]*rcosr;
(*this)[1][1] = rcos + axis[1]*axis[1]*rcosr;
//(*this)[2][1] = axis[0] * rsin + axis[2]*axis[1]*rcosr;
(*this)[2][1] = 0;
(*this)[0][2] = axis[1] * rsin + axis[0]*axis[2]*rcosr;
(*this)[1][2] = -axis[0] * rsin + axis[1]*axis[2]*rcosr;
(*this)[2][2] = rcos + axis[2]*axis[2]*rcosr;
(*this)[2][3] = 0;
(*this)[0][3] = 0;
(*this)[1][3] = 0;
(*this)[2][3] = 0;
(*this)[3][3] = 1;
}
// thanks to the incredible work here:
// https://gist.github.com/kevinmoran/b45980723e53edeb8a5a43c49f134724
// static
template< typename Scalar>
Matrix4<Scalar> Matrix4<Scalar>::RotationAlign(
const Vector3d<Scalar>& v1,
const Vector3d<Scalar>& v2)
{
Matrix4<Scalar> result(uninitialised);
result.BecomeRotationAlign(v1, v2);
return result;
}
template< typename Scalar>
void Matrix4<Scalar>::BecomeRotationAlign(
const Vector3d<Scalar>& v1,
const Vector3d<Scalar>& v2)
{
// vec3 axis = cross( v1, v2 );
auto axis = CrossProduct( v1, v2 );
// const float cosA = dot( v1, v2 );
auto cosA = Vector3d<Scalar>::DotProduct( v1, v2 );
// const float k = 1.0f / (1.0f + cosA);
const double k = 1.0 / (1.0 + cosA);
const int x=0; const int y=1; const int z=2;
(*this)[0][0] = (axis[x] * axis[x] * k) + cosA;
(*this)[0][1] = (axis[y] * axis[x] * k) - axis[z];
(*this)[0][2] = (axis[z] * axis[x] * k) + axis[y];
(*this)[0][3] = 0;
(*this)[1][0] = (axis[x] * axis[y] * k) + axis[z];
(*this)[1][1] = (axis[y] * axis[y] * k) + cosA;
(*this)[1][2] = (axis[z] * axis[y] * k) - axis[x];
(*this)[1][3] = 0;
(*this)[2][0] = (axis[x] * axis[z] * k) - axis[y];
(*this)[2][1] = (axis[y] * axis[z] * k) + axis[x];
(*this)[2][2] = (axis[z] * axis[z] * k) + cosA;
(*this)[2][3] = 0;
(*this)[3][0] = 0;
(*this)[3][1] = 0;
(*this)[3][2] = 0;
(*this)[3][3] = 1;
}
}//namespace Geometry
#endif