Description

The Transf3d class represents a general affine or projective transformation in 3D space.

The transform is represented by a 4x4 matrix, the last row being the projective coefficients and are set to (0,0,0,1) for affine transformations.

To transform a point or a vector, pre-multiply it by a Transf3d matrix.

#include <Transf3d.h>

Public Types
enum	ProjectionType { kParallelProjection, kPerspectiveProjection }

Public Member Functions
	Transf3d ()
	The constructor creates an identity transform. More...

	Transf3d (const Point3d &origin, const Vector3d &xDir, const Vector3d &yDir, const Vector3d &zDir, bool bKeepScalingFactors=false)
	The constructor creates a transform from an origin and directions of x, y and z axes. More...

	Transf3d (const Point3d &origin, const Vector3d &xDir, const Vector3d &yDir)
	The constructor creates a rigid motion transform from an origin and direction of x and y axis. More...

	Transf3d (const Line3d &axis)
	The constructor creates a rigid motion transform from an origin (axis.point) and the direction of the z axis (axis.vector). More...

	Transf3d (const Point3d &origin)
	The constructor creates a rigid motion transform from an origin. More...

void	setValue (size_t i1, size_t i2, double newValue)
	Set the Transf3d data at the (i1, i2) position to newValue. More...

void	addValue (size_t i1, size_t i2, double newValue)
	Adds newValue to the Transf3d data at the (i1, i2) position. More...

double	operator() (size_t i1, size_t i2) const
	Returns the Transf3d data at the (i1, i2) position. More...

Point3d	operator* (const Point3d &) const
	Transform points, vectors and other transforms. More...

Vector3d	operator* (const Vector3d &) const

UnitVector3d	operator* (const UnitVector3d &) const
	This normalizes the result of the transformation (it doesn't stretch the vector)! More...

Transf3d	operator* (const Transf3d &) const

Line3d	operator* (const Line3d &l) const

Transf3d &	operator*= (const Transf3d &)

void	getCoordSystem (Point3d &origin, Vector3d &xDir, Vector3d &yDir, Vector3d &zDir) const

Point3d	origin () const

void	setOrigin (Point3d const &pt)
	Set the origin of the CoordSystem. More...

Vector3d	xDir () const
	Returns the x component of the affine part of the transformation. More...

Vector3d	yDir () const
	Returns the y component of the affine part of the transformation. More...

Vector3d	zDir () const
	Returns the z component of the affine part of the transformation. More...

bool	project (const Point3d &p, Point3d &out) const
	Project a point, using the full 4x4 matrix, including the projectiv part. More...

	Transf3d (ProjectionType type, const Point3d &fromPt, const Point3d &toPt=Point3d(0, 0, 0), const Vector3d &upDir=Vector3d(0, 0, 0))
	Create a general projection transformation (this is how to create a projection transformation to be passed to the Body::hideDisplay() method). More...

Transf3d	affineInverseTranspose () const
	Transposes the affine part of the inverse of the transformation. More...

Transf3d	invert () const

bool	isValid () const

bool	isOrthogonal () const
	No shear. More...

bool	isEqualScalingOrthogonal () const
	No shear, no nonequal scaling. More...

bool	isRigidTransform () const
	no shear, scaling, or mirroring. More...

Vector3d	stretchVector () const

bool	isMirror () const

bool	isPerspective () const

bool	isIdentity () const

bool	isEqual (const Transf3d &t, double dTol=WSM_MACHINE_TOL) const
	Returns true if the transformations are equal. More...

bool	isRotation90DegreeMultiple () const
	Returns true if taking the bounding box of transformed points is the same as transforming the bounding box of the points. More...

void	SetAllFlags () const
	Sets all the flags. More...

const double *	data () const
	Returns a pointer to the double array containing the transform. More...

Static Public Member Functions
static Transf3d	translation (const Vector3d &)
	Create special transformations. More...

static Transf3d	rotation (const Line3d &axis, double angle)

static Transf3d	scaling (const Point3d &fixedPt, double factor)

static Transf3d	scaling (const Point3d &fixedPt, const Vector3d &xyzFactors)

static Transf3d	stretching (const Line3d &axis)

static Transf3d	mirroring (const Plane &)

static Transf3d	projectOn (const Plane &projPlane, const Vector3d &projDir=Vector3d::kNull)

static Transf3d	createOrthogonalSnappedTransform (Point3d origin, double dGlobalScale, Vector3d const &xDir, Vector3d const &yDir, Vector3d const &zDir)
	Creates an orthogonal coordinate system that preserves the axial scaling that may exist in the given vectors. More...

static Transf3d	align (const Point3d &src1, const Point3d &src2, const Point3d &src3, const Point3d &dst1, const Point3d &dst2, const Point3d &dst3)
	The transformation maps points as follows: More...

static Transf3d	align (const Point3d &src1, const Vector3d &src2, const Vector3d &src3, const Point3d &dst1, const Vector3d &dst2, const Vector3d &dst3)
	The transformation maps points and vectors as follows: More...

static Transf3d	align (const Point3d &src1, const Vector3d &src2, const Point3d &dst1, const Vector3d &dst2)

Static Public Attributes
static const Transf3d	kFrontView
	Some ready to use projection transformations. More...

static const Transf3d	kBackView

static const Transf3d	kTopView

static const Transf3d	kBottomView

static const Transf3d	kLeftView

static const Transf3d	kRightView

static const Transf3d	kIsometricView

static const Transf3d	kDimetricView

static const Transf3d	kIdentity

Member Enumeration Documentation

enum WSM::Transf3d::ProjectionType

Enumerator
kParallelProjection
kPerspectiveProjection

Constructor & Destructor Documentation

WSM::Transf3d::Transf3d ( )

inline

The constructor creates an identity transform.

WSM::Transf3d::Transf3d	(	const Point3d &	origin,
		const Vector3d &	xDir,
		const Vector3d &	yDir,
		const Vector3d &	zDir,
		bool	bKeepScalingFactors = `false`
	)

The constructor creates a transform from an origin and directions of x, y and z axes.

Note if bKeepScalingFactors is true does not normalize x, y, and z axes before construction. Also note that orthogonality of x, y, and z is not checked.

WSM::Transf3d::Transf3d	(	const Point3d &	origin,
		const Vector3d &	xDir,
		const Vector3d &	yDir
	)

The constructor creates a rigid motion transform from an origin and direction of x and y axis.

If yDir is not perpendicular to xDir, yDir will be adjusted.

WSM::Transf3d::Transf3d ( const Line3d & axis )

The constructor creates a rigid motion transform from an origin (axis.point) and the direction of the z axis (axis.vector).

The directions of the x and y axes are determined according to the AutoCAD's arbitrary axis algorithm.

WSM::Transf3d::Transf3d ( const Point3d & origin )

The constructor creates a rigid motion transform from an origin.

The x, y and z axis are aligned with the world x, y and z axis.

WSM::Transf3d::Transf3d	(	ProjectionType	type,
		const Point3d &	fromPt,
		const Point3d &	toPt = `Point3d(0, 0, 0)`,
		const Vector3d &	upDir = `Vector3d(0, 0, 0)`
	)

Create a general projection transformation (this is how to create a projection transformation to be passed to the Body::hideDisplay() method).

Member Function Documentation

void WSM::Transf3d::addValue	(	size_t	i1,
		size_t	i2,
		double	newValue
	)

Adds newValue to the Transf3d data at the (i1, i2) position.

Transf3d WSM::Transf3d::affineInverseTranspose ( ) const

Transposes the affine part of the inverse of the transformation.

static Transf3d WSM::Transf3d::align	(	const Point3d &	src1,
		const Point3d &	src2,
		const Point3d &	src3,
		const Point3d &	dst1,
		const Point3d &	dst2,
		const Point3d &	dst3
	)

static

The transformation maps points as follows:

Point src1 maps to point dst1 Vector (src1,src2) maps to vector (dst1,dst2) Plane (src1,src2,src3) maps to plane (dst1,dst2,dst3)

static Transf3d WSM::Transf3d::align	(	const Point3d &	src1,
		const Vector3d &	src2,
		const Vector3d &	src3,
		const Point3d &	dst1,
		const Vector3d &	dst2,
		const Vector3d &	dst3
	)

static

The transformation maps points and vectors as follows:

Point src1 maps to point dst1 Vector src2 maps to vector dst2 Plane (src1,src2,src3) maps to plane (dst1,dst2,dst3)

static Transf3d WSM::Transf3d::align	(	const Point3d &	src1,
		const Vector3d &	src2,
		const Point3d &	dst1,
		const Vector3d &	dst2
	)

static

static Transf3d WSM::Transf3d::createOrthogonalSnappedTransform	(	Point3d	origin,
		double	dGlobalScale,
		Vector3d const &	xDir,
		Vector3d const &	yDir,
		Vector3d const &	zDir
	)

static

Creates an orthogonal coordinate system that preserves the axial scaling that may exist in the given vectors.

The following snaps are applied in the given order for values which are close to the snap value. Origin components are snapped to 0. The global scale is snapped to 1, and then applied to the individual axis vectors. The lengths of the axes are snapped to 1. The X, Y and Z lengths are snapped together. The X and Y vectors are snapped to the principal axes and principal planes. The Z vector is then recomputed as the cross of the snapped X and Y axes, and the Y vector is recomputed as the cross of the new Z and snapped X axes.

const double* WSM::Transf3d::data ( ) const

inline

Returns a pointer to the double array containing the transform.

void WSM::Transf3d::getCoordSystem	(	Point3d &	origin,
		Vector3d &	xDir,
		Vector3d &	yDir,
		Vector3d &	zDir
	)		const

Transf3d WSM::Transf3d::invert ( ) const

bool WSM::Transf3d::isEqual	(	const Transf3d &	t,
		double	dTol = `WSM_MACHINE_TOL`
	)		const

inline

Returns true if the transformations are equal.

bool WSM::Transf3d::isEqualScalingOrthogonal ( ) const

No shear, no nonequal scaling.

bool WSM::Transf3d::isIdentity ( ) const

bool WSM::Transf3d::isMirror ( ) const

bool WSM::Transf3d::isOrthogonal ( ) const

No shear.

bool WSM::Transf3d::isPerspective ( ) const

bool WSM::Transf3d::isRigidTransform ( ) const

no shear, scaling, or mirroring.

bool WSM::Transf3d::isRotation90DegreeMultiple ( ) const

Returns true if taking the bounding box of transformed points is the same as transforming the bounding box of the points.

bool WSM::Transf3d::isValid ( ) const

static Transf3d WSM::Transf3d::mirroring ( const Plane & )

static

double WSM::Transf3d::operator()	(	size_t	i1,
		size_t	i2
	)		const

inline

Returns the Transf3d data at the (i1, i2) position.

Point3d WSM::Transf3d::operator* ( const Point3d & ) const

Transform points, vectors and other transforms.

Vector3d WSM::Transf3d::operator* ( const Vector3d & ) const

UnitVector3d WSM::Transf3d::operator* ( const UnitVector3d & ) const

This normalizes the result of the transformation (it doesn't stretch the vector)!

Transf3d WSM::Transf3d::operator* ( const Transf3d & ) const

Line3d WSM::Transf3d::operator* ( const Line3d & l ) const

Transf3d& WSM::Transf3d::operator*= ( const Transf3d & )

Point3d WSM::Transf3d::origin ( ) const

bool WSM::Transf3d::project	(	const Point3d &	p,
		Point3d &	out
	)		const

Project a point, using the full 4x4 matrix, including the projectiv part.

Returns false if the point couldn't be projected by the perspective transform because it lied behind the view point.

static Transf3d WSM::Transf3d::projectOn	(	const Plane &	projPlane,
		const Vector3d &	projDir = `Vector3d::kNull`
	)

static

static Transf3d WSM::Transf3d::rotation	(	const Line3d &	axis,
		double	angle
	)

static

static Transf3d WSM::Transf3d::scaling	(	const Point3d &	fixedPt,
		double	factor
	)

static

static Transf3d WSM::Transf3d::scaling	(	const Point3d &	fixedPt,
		const Vector3d &	xyzFactors
	)

static

void WSM::Transf3d::SetAllFlags ( ) const

Sets all the flags.

Note this is only required if you want the isXXX methods to truly be read only.

void WSM::Transf3d::setOrigin ( Point3d const & pt )

Set the origin of the CoordSystem.

void WSM::Transf3d::setValue	(	size_t	i1,
		size_t	i2,
		double	newValue
	)

Set the Transf3d data at the (i1, i2) position to newValue.

static Transf3d WSM::Transf3d::stretching ( const Line3d & axis )

static

Vector3d WSM::Transf3d::stretchVector ( ) const

static Transf3d WSM::Transf3d::translation ( const Vector3d & )

static

Create special transformations.

Vector3d WSM::Transf3d::xDir ( ) const

Returns the x component of the affine part of the transformation.

Not necessarily length 1.

Vector3d WSM::Transf3d::yDir ( ) const

Returns the y component of the affine part of the transformation.

Not necessarily length 1.

Vector3d WSM::Transf3d::zDir ( ) const

Returns the z component of the affine part of the transformation.

Not necessarily length 1.

Member Data Documentation

const Transf3d WSM::Transf3d::kBackView

static

const Transf3d WSM::Transf3d::kBottomView

static

const Transf3d WSM::Transf3d::kDimetricView

static

const Transf3d WSM::Transf3d::kFrontView

static

Some ready to use projection transformations.

const Transf3d WSM::Transf3d::kIdentity

static

const Transf3d WSM::Transf3d::kIsometricView

static

const Transf3d WSM::Transf3d::kLeftView

static

const Transf3d WSM::Transf3d::kRightView

static

const Transf3d WSM::Transf3d::kTopView

static

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

WSM/Transf3d.h

Description

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation