spat::Transformation< Valtype > Class Template Reference

Homogenous transformation matrix. More...

#include <C:/Trend/Development/Trax3/Code/spat/Matrix.h>

Inheritance diagram for spat::Transformation< Valtype >:

Public Types
using	Basetype = typename SquareMatrix<Valtype,4>::Basetype
Public Types inherited from spat::SquareMatrix< Valtype, 4 >
using	Basetype
	Utmost base type of this SquareMatrix.
Public Types inherited from spat::Matrix< Valtype, nColsAndRows, nColsAndRows >
typedef Valtype	value_type

Public Member Functions
template<typename Valtype2>
Transformation< Valtype > &	operator= (const Rotation< Valtype2 > &rot) noexcept
template<typename Valtype2, typename ValtypeT2>
Transformation< Valtype > &	operator= (const Frame< Valtype2, ValtypeT2 > &frame) noexcept
Construction
Parameters rot Construct pure rotational transformation matrix Construct from matrix frame Construct from frame so that this transformation transforms coordinates, local to the frame into coordinates in the system the frame is defined.
	Transformation (const SquareMatrix< Valtype, 4 > &matrix)
	Transformation (SquareMatrix< Valtype, 4 > &&matrix) noexcept
	Transformation (const Basetype &matrix)
	Transformation (Basetype &&matrix) noexcept
template<typename Valtype2>
	Transformation (const Rotation< Valtype2 > &rot)
template<typename Valtype2, typename ValtypeT2>
	Transformation (const Frame< Valtype2, ValtypeT2 > &frame)
	Transformation (const std::initializer_list< Valtype > &elements)
Assignment
Parameters rot Assign pure rotational transformation frame Assign frame local to parent transformation
template<typename Valtype2>
Transformation &	operator= (const Rotation< Valtype2 > &rot) noexcept
template<typename Valtype2, typename ValtypeT2>
Transformation &	operator= (const Frame< Valtype2, ValtypeT2 > &frame) noexcept
Transformation
template<typename Valtype2>
PositionH< Valtype2 >	operator* (const PositionH< Valtype2 > &p) const noexcept
template<typename Valtype2>
Position< Valtype2 >	operator* (const Position< Valtype2 > &pos) const noexcept
template<typename Valtype2>
Vector< Valtype2 >	operator* (const Vector< Valtype2 > &vec) const noexcept
CreateTranslation
Creates a matrix that has the effect of a translation. Parameters translation Translation vector tx x - translation. ty y - translation. tz z - translation.
void	CreateTranslation (const Vector< Valtype > &translation) noexcept
void	CreateTranslation (Valtype tx, Valtype ty, Valtype tz) noexcept
CreateRotation
Creates a matrix that has the effect of a rotation. Parameters rotation Rotation vector rx x - component of rotation vector. ry y - component of rotation vector. rz z - component of rotation vector.
void	CreateRotation (const Vector< Valtype > &rotation)
void	CreateRotation (Valtype rx, Valtype ry, Valtype rz)
CreateScaling
Creates a matrix that has the effect of a scaling. Parameters scaling Scaling vector rx x - component of scaling vector. ry y - component of scaling vector. rz z - component of scaling vector.
void	CreateScaling (const Vector< Valtype > &scaling) noexcept
void	CreateScaling (Valtype sx, Valtype sy, Valtype sz) noexcept
CreateMirror
Creates a matrix that has the effect of mirroring on a plane, described by mirror.
template<typename Valtype2>
void	CreateMirror (const VectorBundle< Valtype2, Valtype > &mirror)
	Create a view matrix that transforms to camera space.
void	LookAt (const Position< Valtype > &at, const Position< Valtype > &eye, const Vector< Valtype > &up) noexcept
	Create a view matrix that transforms to camera space.
void	CreateViewport (Valtype Width, Valtype Height, Valtype MinZ, Valtype MaxZ, Valtype LeftMargin=0.0f, Valtype TopMargin=0.0f) noexcept
	Creates a viewport projection.
bool	CreateCameraProjection (Valtype fovy, Valtype Aspect, Valtype zn, Valtype zf) noexcept
	Creates camera projection transformation.
bool	CreateOrthographicProjection (Valtype width, Valtype height, Valtype znear, Valtype zfar) noexcept
	Creates orthographic projection transformation.
Vector< Valtype >	TransformVector (const Vector< Valtype > &vec) const noexcept
	Vector transformation. Use it for difference vectors between positions or dynamic vectors like velocities and accellerations.
void	GetTranslation (Transformation &T) const noexcept
	Kovariant vector use this for face normals or vectors denoting a rotation orientation.
bool	GeRotation (Transformation &R) const noexcept
	Calculates a rotational part of the transformation so that T * R * S == *this.
bool	GetScaling (Transformation &S) const noexcept
	Calculates a scaling part of the transformation so that T * R * S == *this.
bool	Dismantle (Transformation &T, Transformation &R, Transformation &S) const noexcept
	Calculates translational, rotational and scaling part of the transformation so that T * R * S == *this.
bool	IsValid () const noexcept
	Tests wether the matrix is a valid homogenous transformation.
Public Member Functions inherited from spat::SquareMatrix< Valtype, 4 >
Matrix &	operator= (const Matrix &matrix) noexcept
Matrix &	operator= (Matrix &&matrix) noexcept
Matrix &	operator= (const std::initializer_list< Valtype > &elements) noexcept
const Valtype &	operator() (unsigned short col, unsigned short row) const noexcept
Valtype &	operator() (unsigned short col, unsigned short row) noexcept
void	SetIdentity () noexcept
	Sets the matrix to the identity matrix (i.e. all 1 in diagonal, 0 for everything else).
bool	IsIdentity (Valtype epsilon=0) const noexcept
bool	IsDiagonal () const noexcept
bool	IsSymmetric (Valtype epsilon=0) const noexcept
SquareMatrix &	Transpose () noexcept
	Change colums and rows.
SquareMatrix &	Invert ()
	Invert matrix so that M*I == Identity.
Valtype	Trace () const noexcept
	Trace of the matrix, wich is the sum of all element with same indices.
Public Member Functions inherited from spat::Matrix< Valtype, nColsAndRows, nColsAndRows >
void	SetNull () noexcept
	Sets all elements to 0.
constexpr unsigned short	Cols () const noexcept
	Number of columns.
constexpr unsigned short	Rows () const noexcept
	Number of rows.
bool	IsEqual (const Matrix &matrix, Valtype delta=0) const noexcept
	Test elements for equality up to delta distance.
bool	operator== (const Matrix &matrix) const noexcept
	Comparison for equality.
bool	operator!= (const Matrix &matrix) const noexcept
	Comparison for inequality.
void	operator*= (Valtype skalar) noexcept
	Matrix * Skalar multiplication.
void	operator*= (const Matrix< Valtype, nCols, nCols > &matrix)
	Matrix multiplication.
void	operator/= (Valtype skalar) noexcept
	Matrix / Skalar division.
void	operator+= (const Matrix &matrix) noexcept
	Matrix addition.
void	operator-= (const Matrix &matrix) noexcept
	Matrix subtraction.
const Valtype *	ptr () const noexcept
	Pointer accessor for direct copying. The memory layout is column-major order.
Matrix< Valtype, nCols-1, nRows-1 >	SubMatrix (unsigned short c, unsigned short r) const
	Extracts the submatrix of mat wich results from omitting the row r and collumn c.
	Matrix (const Matrix &matrix)
	Matrix (Matrix &&matrix) noexcept
	Matrix (const std::initializer_list< Valtype > &elements)
Matrix &	operator= (const Matrix &matrix) noexcept
Matrix &	operator= (Matrix &&matrix) noexcept
Matrix &	operator= (const std::initializer_list< Valtype > &elements) noexcept
const Valtype &	operator() (unsigned short col, unsigned short row) const noexcept
Valtype &	operator() (unsigned short col, unsigned short row) noexcept

Detailed Description

template<typename Valtype>
class spat::Transformation< Valtype >

Homogenous transformation matrix.

Member Function Documentation

CreateCameraProjection()

template<typename Valtype>

bool spat::Transformation< Valtype >::CreateCameraProjection ( Valtype fovy, Valtype Aspect, Valtype zn, Valtype zf )

noexcept

Creates camera projection transformation.

Parameters

fovy	Field of view angle.
Aspect	Width to height aspect of opening angles.
zn	Distance to the near plane of the camera frustum.
zf	Distance to the far plane of the camera frustum.

GetTranslation()

template<typename Valtype>

void spat::Transformation< Valtype >::GetTranslation ( Transformation< Valtype > & T ) const

noexcept

Kovariant vector use this for face normals or vectors denoting a rotation orientation.

Calculates a translational part of the transformation so that T * R * S == *this.

TransformVector()

template<typename Valtype>

Vector< Valtype > spat::Transformation< Valtype >::TransformVector ( const Vector< Valtype > & vec ) const

noexcept

Vector transformation. Use it for difference vectors between positions or dynamic vectors like velocities and accellerations.

If you want to transform normal vectors be aware that due to the nature of this kind of vector beeing orthogonal to a plane you have to use the inverse transposed matrix.

M: Transformation matrix for coordinates. Q: Transformation matrix for normals. D = P2 - P1: Vector between two arbitrary points in a plane. D' = P2' - P1' = M * P2 - M * P1 = M * D: Transformed vector D. N: Normal on that plane.

Now its N*D = 0 for all D since N is orthogonal to the plane. But with the transformed vectors the same condition must hold: N'*D' = 0. -> Q*N*M*D = 0 -> N*Qt*M*D = 0 (Qt is the transposed of Q) since this must hold for all D (or lets put it the other way: to be on the safe side) Qt*M = IdentityMatrix must hold. hence Q = Transposed(Inverse(M)) = Inverse(Transposed(M))

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The documentation for this class was generated from the following file:

• C:/Trend/Development/Trax3/Code/spat/Matrix.h