Forward and inverse 4x4 matrices of an invertible perspective transformation. More...

#include <dmap4d.h>

Public Member Functions
void	InitIdentity ()
	Initialize and identity mapping. More...

void	InitFrom (DMatrix4dCR forwardMatrix, DMatrix4dCR inverseMatrix)
	Direct initialization from matrices. More...

bool	InitFromRanges (DPoint3dCR loAP, DPoint3dCR hiAP, DPoint3dCR loBP, DPoint3dCR hiBP)
	Initialize a transform which translates and scales along principle axes so box loAP..hiAP maps to box loBP..hiBP. More...

void	InitFromRotation (double c, double s, double vx, double vy, double vz)
	Initialize a rotation about axis vx,vy,vz by angle whose cosine and sine are (proportional to) c and s. More...

void	InitFromQuadrantRotation (int multiple, double vx, double vy, double vz)
	Rotate about vx,yv,vz by an integer multiple of 90 degrees. More...

void	InitFromRotation (double radians, double vx, double vy, double vz)
	Initialize a rotation by angle in radians about axis vx,vy,vz. More...

void	InitFromScale (double ax, double ay, double az)
	Initialize a pure scaling transformation. More...

void	InitFromPrincipleProjection (double height, int axis)
	Initialize a transform that is a (noninvertible) projection to a principle plane. More...

void	InitFromScale (double a)
	Initialize a uniform scaling transformation. More...

void	InitFromTranslation (double tx, double ty, double tz)
	Initialize a translation transform. More...

bool	InitFromTaper (double taper)
	Initialize a transform with perspective entries for a (nonzero) taper in the z direction. More...

bool	InitFromTransform (TransformCR transform, bool invert)

bool	InitFromSkewBox (DPoint4dCR point0001, DPoint4dCR point1001, DPoint4dCR point0101, DPoint4dCR point0010)
	Fill a mapping between a unit prism and homogeneous skew space. More...

void	ZFrustum (double z0, double zetaHalf)

void	InverseOf (DMap4dCR B)
	Sets pA to the inverse of B. More...

void	SandwichOf (DMap4dCR A, DMap4dCR B, DMap4dCR C)
	Form the product C * Binv * A * B * Cinv. More...

void	SandwichOfBABinverse (DMap4dCR A, DMap4dCR B)
	Form the product B * A * BInv A NULL for B or C skips that part. More...

void	SandwichOfBinverseAB (DMap4dCR A, DMap4dCR B)
	Form the product Binv * A * B. More...

void	InitProduct (DMap4dCR A, DMap4dCR B)
	Multiply transforms. More...

void	InitProduct (DMap4dCR A, bool invertA, DMap4dCR B, bool invertB)
	Multiply transforms, selecting optional forward or inverse for each. More...

bool	IsIndependent (int xChange, int yChange, int zChange)
	Checks if the mapping is strictly a scale/translate in specified directions. More...

bool	IsSingular () const
	Test if a transform is singular. More...

bool	IsAffine () const
	Test if a transform is affiine. More...

bool	IsPerspective () const
	Test if a transform is perspective. More...

void	Explode (RotMatrixR matrix, DPoint3dR translation, DPoint4dR perspective, bool inverse) const
	Copy various parts of the 4x4 matrix to separate data structures. More...

bool	IsIdentity () const

Static Public Member Functions
static DMap4d	FromIdentity ()
	Initialize and identity mapping. More...

static DMap4d	From (DMatrix4dCR forwardMatrix, DMatrix4dCR inverseMatrix)
	Direct initialization from matrices. More...

static DMap4d	FromRotation (double c, double s, double vx, double vy, double vz)
	Initialize a rotation about axis vx,vy,vz by angle whose cosine and sine are (proportional to) c and s. More...

static DMap4d	FromQuadrantRotation (int multiple, double vx, double vy, double vz)
	Rotate about vx,yv,vz by an integer multiple of 90 degrees. More...

static DMap4d	FromRotation (double radians, double vx, double vy, double vz)
	Initialize a rotation by angle in radians about axis vx,vy,vz. More...

static DMap4d	FromScale (double ax, double ay, double az)
	Initialize a pure scaling transformation. More...

static DMap4d	FromPrincipleProjection (double height, int axis)
	Initialize a transform that is a (noninvertible) projection to a principle plane. More...

static DMap4d	FromScale (double a)
	Initialize a uniform scaling transformation. More...

static DMap4d	FromTranslation (double tx, double ty, double tz)
	Initialize a translation transform. More...

Public Attributes
DMatrix4d	M0
	Forward transformation. More...

DMatrix4d	M1
	Inverse transformation. More...

int	mask
	Internal state data. More...

Detailed Description

Forward and inverse 4x4 matrices of an invertible perspective transformation.

Member Function Documentation

void Explode	(	RotMatrixR	matrix,
		DPoint3dR	translation,
		DPoint4dR	perspective,
		bool	inverse
	)		const

Copy various parts of the 4x4 matrix to separate data structures.

Parameters

[out]	matrix	upper 3x3
[out]	translation	last column (above diagonal)
[out]	perspective	last row (including diagonal)
[in]	inverse	false for forward part, true for inverse

Remarks: The separate pieces do not "mean" much if there is perspective.

static DMap4d From	(	DMatrix4dCR	forwardMatrix,
		DMatrix4dCR	inverseMatrix
	)

static

Direct initialization from matrices.

Caller is responsible for correct inverse relationship.

Parameters

[in]	forwardMatrix	"forward" matrix.
[in]	inverseMatrix	"inverse" matrix.

static DMap4d FromIdentity ( )

static

Initialize and identity mapping.

static DMap4d FromPrincipleProjection	(	double	height,
		int	axis
	)

static

Initialize a transform that is a (noninvertible) projection to a principle plane.

Parameters

[in]	height	distance of plane from origin
[in]	axis	0,1,2 for x,y,z normal

static DMap4d FromQuadrantRotation	(	int	multiple,
		double	vx,
		double	vy,
		double	vz
	)

static

Rotate about vx,yv,vz by an integer multiple of 90 degrees.

Providing the angle as an integer allows exact table lookup without approximation of pi.

Parameters

[in]	multiple	rotation angle is multiple * 90 degrees
[in]	vx	x component of rotation axis
[in]	vy	y component of rotation axis
[in]	vz	z component of rotation axis

static DMap4d FromRotation	(	double	c,
		double	s,
		double	vx,
		double	vy,
		double	vz
	)

static

Initialize a rotation about axis vx,vy,vz by angle whose cosine and sine are (proportional to) c and s.

Parameters

[in]	c	cosine of angle
[in]	s	sine of angle
[in]	vx	x component of rotation axis
[in]	vy	y component of rotation axis
[in]	vz	z component of rotation axis

static DMap4d FromRotation	(	double	radians,
		double	vx,
		double	vy,
		double	vz
	)

static

Initialize a rotation by angle in radians about axis vx,vy,vz.

Parameters

[in]	radians	angle in degrees
[in]	vx	x component of rotation axis
[in]	vy	y component of rotation axis
[in]	vz	z component of rotation axis

static DMap4d FromScale	(	double	ax,
		double	ay,
		double	az
	)

static

Initialize a pure scaling transformation.

If any scale factor is zero, the corresponding inverse entry is also zero.

Parameters

[in]	ax	x scale factor
[in]	ay	y scale factor
[in]	az	z scale factor

static DMap4d FromScale ( double a )

static

Initialize a uniform scaling transformation.

Parameters

[in] a scale factor

static DMap4d FromTranslation	(	double	tx,
		double	ty,
		double	tz
	)

static

Initialize a translation transform.

Parameters

[in]	tx	x component of translation
[in]	ty	y component of translation
[in]	tz	z component of translation

void InitFrom	(	DMatrix4dCR	forwardMatrix,
		DMatrix4dCR	inverseMatrix
	)

Direct initialization from matrices.

Caller is responsible for correct inverse relationship.

Parameters

[in]	forwardMatrix	"forward" matrix.
[in]	inverseMatrix	"inverse" matrix.

void InitFromPrincipleProjection	(	double	height,
		int	axis
	)

Initialize a transform that is a (noninvertible) projection to a principle plane.

Parameters

[in]	height	distance of plane from origin
[in]	axis	0,1,2 for x,y,z normal

void InitFromQuadrantRotation	(	int	multiple,
		double	vx,
		double	vy,
		double	vz
	)

Rotate about vx,yv,vz by an integer multiple of 90 degrees.

Providing the angle as an integer allows exact table lookup without approximation of pi.

Parameters

[in]	multiple	rotation angle is multiple * 90 degrees
[in]	vx	x component of rotation axis
[in]	vy	y component of rotation axis
[in]	vz	z component of rotation axis

bool InitFromRanges	(	DPoint3dCR	loAP,
		DPoint3dCR	hiAP,
		DPoint3dCR	loBP,
		DPoint3dCR	hiBP
	)

Initialize a transform which translates and scales along principle axes so box loAP..hiAP maps to box loBP..hiBP.

Parameters

[in]	loAP	corner of box A
[in]	hiAP	diagonally opposite corner of box A
[in]	loBP	corner of box B
[in]	hiBP	diagonally opposite corner of box B

Returns: int

void InitFromRotation	(	double	c,
		double	s,
		double	vx,
		double	vy,
		double	vz
	)

Initialize a rotation about axis vx,vy,vz by angle whose cosine and sine are (proportional to) c and s.

Parameters

[in]	c	cosine of angle
[in]	s	sine of angle
[in]	vx	x component of rotation axis
[in]	vy	y component of rotation axis
[in]	vz	z component of rotation axis

void InitFromRotation	(	double	radians,
		double	vx,
		double	vy,
		double	vz
	)

Initialize a rotation by angle in radians about axis vx,vy,vz.

Parameters

[in]	radians	angle in degrees
[in]	vx	x component of rotation axis
[in]	vy	y component of rotation axis
[in]	vz	z component of rotation axis

void InitFromScale	(	double	ax,
		double	ay,
		double	az
	)

Initialize a pure scaling transformation.

If any scale factor is zero, the corresponding inverse entry is also zero.

Parameters

[in]	ax	x scale factor
[in]	ay	y scale factor
[in]	az	z scale factor

void InitFromScale ( double a )

Initialize a uniform scaling transformation.

Parameters

[in] a scale factor

bool InitFromSkewBox	(	DPoint4dCR	point0001,
		DPoint4dCR	point1001,
		DPoint4dCR	point0101,
		DPoint4dCR	point0010
	)

Fill a mapping between a unit prism and homogeneous skew space.

Example use: We want to map a unit rectangle from font space to screen, under a full perspective mapping. That is, given font space point (x,y) we want A * (x,y,0,1)^T = the visible pixel. Also, given pixel (i,j) we want Ainverse * (i,j,0,1) to map back into font space. A long time ago, we were told points P0,P1,P2 which are the preperspective points that correspond to font space (0,0), (1,0), and (0,1). Since then, P00, P10, P01 have been through a homogeneous transformation. (For instance, there may be 'weight' of other than 1 on each one.) The transformed (homogeneous) points are Q00, Q10, Q01 In device space, we do a projection in the z direction. Hence we need a 4th point Qz=(0,0,1,0). Build this matrix by calling jmdlDMap4d_fillHomogeneousSkewFrame (pHMap, Q00, Q10,Q01,Qz)

Parameters

point0001	0001 in the unit space maps here
point1001	1001 in the unit space maps here
point0101	0100 in the unit space maps here
point0010	0010 in the unit space maps here

Returns: true if the 4 points are independent

bool InitFromTaper ( double taper )

Initialize a transform with perspective entries for a (nonzero) taper in the z direction.

Parameters

[in] taper taper fraction

Returns: true if an invertible map was constructed.

bool InitFromTransform	(	TransformCR	transform,
		bool	invert
	)

Parameters

[in]	transform	affine transformation 3x4 matrix
[in]	invert	true to treat this matrix as the inverse of the mapping, false if forward.

Returns: true if the Transfrom was invertible.

void InitFromTranslation	(	double	tx,
		double	ty,
		double	tz
	)

Initialize a translation transform.

Parameters

[in]	tx	x component of translation
[in]	ty	y component of translation
[in]	tz	z component of translation

void InitIdentity ( )

Initialize and identity mapping.

void InitProduct	(	DMap4dCR	A,
		DMap4dCR	B
	)

Multiply transforms.

Parameters

[in]	A	transform A
[in]	B	transform B

void InitProduct	(	DMap4dCR	A,
		bool	invertA,
		DMap4dCR	B,
		bool	invertB
	)

Multiply transforms, selecting optional forward or inverse for each.

Parameters

[in]	A	transform A
[in]	invertA	if true, use invese of A
[in]	B	transform B
[in]	invertB	if true, use invese of B

void InverseOf ( DMap4dCR B )

Sets pA to the inverse of B.

Parameters

[in] B original mapping

bool IsAffine ( ) const

Test if a transform is affiine.

Returns: true if the mapping is affine.

bool IsIdentity ( ) const

Returns: true if the mapping is an identity

bool IsIndependent	(	int	xChange,
		int	yChange,
		int	zChange
	)

Checks if the mapping is strictly a scale/translate in specified directions.

Parameters

[in]	xChange	1 if x may change, 0 if it must stay fixed
[in]	yChange	1 if y may change, 0 if it must stay fixed
[in]	zChange	1 if z may change, 0 if it must stay fixed

Returns: true if independence tests are satisfied.

bool IsPerspective ( ) const

Test if a transform is perspective.

Returns: true if the mapping contains perspective.

bool IsSingular ( ) const

Test if a transform is singular.

Returns: true if the mapping is singular

void SandwichOf	(	DMap4dCR	A,
		DMap4dCR	B,
		DMap4dCR	C
	)

Form the product C * Binv * A * B * Cinv.

Parameters

[in]	A	inside term of sandwich
[in]	B	middle term of sandwich
[in]	C	outer term of sandwich

void SandwichOfBABinverse	(	DMap4dCR	A,
		DMap4dCR	B
	)

Form the product B * A * BInv A NULL for B or C skips that part.

Parameters

[in]	A	inside term of sandwich
[in]	B	outer term of sandwich

void SandwichOfBinverseAB	(	DMap4dCR	A,
		DMap4dCR	B
	)

Form the product Binv * A * B.

Parameters

[in]	A	inside term of sandwich
[in]	B	outer term of sandwich

void ZFrustum	(	double	z0,
		double	zetaHalf
	)

Parameters

[in]	z0	reference z. Normalized projective coordinate is 0 at this z
[in]	zetaHalf	controls rate of growth of normalized projective z. Projective z at z0/k is k-1*zetahalf, i.e. is zetahalf at z0/2

Member Data Documentation

DMatrix4d M0

Forward transformation.

DMatrix4d M1

Inverse transformation.

int mask

Internal state data.

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

dmap4d.h

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Member Function Documentation

Member Data Documentation