#include <opennurbs_xform.h>

Public Member Functions
	ON_Xform ()
	Default constructor transformation has diagonal (0,0,0,1) More...

	ON_Xform (const double *)
	from array of 16 doubles (row0,row1,row2,row3) More...

	ON_Xform (const double[4][4])
	from standard double m[4][4] More...

	ON_Xform (const float *)
	from array of 16 floats (row0,row1,row2,row3) More...

	ON_Xform (const float[4][4])
	from standard float m[4][4] More...

	ON_Xform (const ON_3dPoint &P, const ON_3dVector &X, const ON_3dVector &Y, const ON_3dVector &Z)

	ON_Xform (const ON_Matrix &)

	ON_Xform (const ON_Xform &)=default

	ON_Xform (double x)
	Constructs transformation with diagonal (x,x,x,1) More...

	~ON_Xform ()=default

void	ActOnLeft (double, double, double, double, double[4]) const

void	ActOnRight (double, double, double, double, double[4]) const

void	Affineize ()

bool	CameraToClip (bool bIsPerspective, double, double, double, double, double, double)

void	CameraToWorld (const ON_3dPoint &, const ON_3dVector &, const ON_3dVector &, const ON_3dVector &)

bool	ChangeBasis (const ON_3dPoint &P0, const ON_3dVector &X0, const ON_3dVector &Y0, const ON_3dVector &Z0, const ON_3dPoint &P1, const ON_3dVector &X1, const ON_3dVector &Y1, const ON_3dVector &Z1)

bool	ChangeBasis (const ON_3dVector &X0, const ON_3dVector &Y0, const ON_3dVector &Z0, const ON_3dVector &X1, const ON_3dVector &Y1, const ON_3dVector &Z1)

bool	ChangeBasis (const ON_Plane &plane0, const ON_Plane &plane1)

int	ClipFlag3d (const double *) const

int	ClipFlag3d (int, int, const double *, bool bTestZ=true) const

int	ClipFlag3dBox (const double , const double ) const

int	ClipFlag4d (const double *) const

int	ClipFlag4d (int, int, const double *, bool bTestZ=true) const

bool	ClipToCamera (bool bIsPerspective, double, double, double, double, double, double)
	maps -1 <= x,y,z <= 1 box to viewport frustum More...

bool	ClipToScreen (double, double, double, double, double, double)

int	Compare (const ON_Xform &other) const

ON__UINT32	CRC32 (ON__UINT32 current_remainder) const

bool	DecomposeAffine (ON_3dVector &Translation, ON_Xform &Linear) const

bool	DecomposeAffine (ON_3dVector &Translation, ON_Xform &Rotation, ON_Xform &OrthBasis, ON_3dVector &Diagonal) const

bool	DecomposeAffine (ON_Xform &Linear, ON_3dVector &Translation) const

int	DecomposeRigid (ON_3dVector &Translation, ON_Xform &Rotation, double tolerance=ON_ZERO_TOLERANCE) const

int	DecomposeSimilarity (ON_3dVector &Translation, double &dilation, ON_Xform &Rotation, double tolerance) const

bool	DecomposeSymmetric (ON_Xform &Q, ON_3dVector &diagonal) const

void	DecomposeTextureMapping (ON_3dVector &offset, ON_3dVector &repeat, ON_3dVector &rotation) const
	Convert an ON_Xform into the offset, repeat and rotation values used in ON_Texture and similar classes. More...

double	Determinant (double *minimum_pivot=nullptr) const
	If you need a slow and accurate determinant, this is the function to call. If you need a fast sign check, used SignOfDeterminant(true). More...

void	Diagonal (double d)

bool	GetEulerZYZ (double &alpha, double &beta, double &gamma) const

bool	GetKMLOrientationAnglesDegrees (double &heading_degrees, double &tilt_degrees, double &roll_degrees) const

bool	GetKMLOrientationAnglesRadians (double &heading_radians, double &tilt_radians, double &roll_radians) const

double	GetMappingXforms (ON_Xform &P_xform, ON_Xform &N_xform) const

bool	GetQuaternion (ON_Quaternion &Q) const

double	GetSurfaceNormalXform (ON_Xform &N_xform) const

double	GetSurfaceNormalXformKeepLengthAndOrientation (ON_Xform &N_xform) const

bool	GetYawPitchRoll (double &yaw, double &pitch, double &roll) const

const ON_SHA1_Hash	Hash () const

void	Identity ()
	standard transformations More...

bool	IntervalChange (int dir, ON_Interval old_interval, ON_Interval new_interval)

ON_Xform	Inverse (double *=nullptr) const

bool	Invert (double *=nullptr)

bool	IsAffine () const

bool	IsIdentity (double zero_tolerance=0.0) const

bool	IsLinear () const

bool	IsNan () const

bool	IsNotIdentity (double zero_tolerance=0.0) const

int	IsRigid (double tolerance=ON_ZERO_TOLERANCE) const

bool	IsRotation () const
	true if this is a proper rotation. More...

int	IsSimilarity () const

int	IsSimilarity (double tolerance) const

bool	IsTranslation (double zero_tolerance=0.0) const

bool	IsValid () const

bool	IsValidAndNotZeroAndNotIdentity (double zero_tolerance=0.0) const

bool	IsZero () const

bool	IsZero4x4 () const

bool	IsZero4x4 (double zero_tolerance) const

bool	IsZeroTransformation () const

bool	IsZeroTransformation (double zero_tolerance) const

void	Linearize ()

void	Mirror (ON_3dPoint point_on_mirror_plane, ON_3dVector normal_to_mirror_plane)

bool	operator!= (const ON_Xform &rhs) const

ON_2dPoint	operator* (const ON_2dPoint &) const

ON_2dVector	operator* (const ON_2dVector &) const

ON_3dPoint	operator* (const ON_3dPoint &) const

ON_3dVector	operator* (const ON_3dVector &) const

ON_4dPoint	operator* (const ON_4dPoint &) const

ON_Xform	operator* (const ON_Xform &) const

ON_Xform	operator+ (const ON_Xform &) const

ON_Xform	operator- (const ON_Xform &) const

ON_Xform &	operator= (const ON_Matrix &)
	xform = scalar results in a diagonal 3x3 with bottom row = 0,0,0,1 More...

ON_Xform &	operator= (const ON_Xform &)=default

bool	operator== (const ON_Xform &rhs) const

double *	operator[] (int)

const double *	operator[] (int) const

bool	Orthogonalize (double tol)

void	PlanarProjection (const ON_Plane &plane)

int	Rank (double *=nullptr) const

void	Rotation (const ON_3dPoint &P0, const ON_3dVector &X0, const ON_3dVector &Y0, const ON_3dVector &Z0, const ON_3dPoint &P1, const ON_3dVector &X1, const ON_3dVector &Y1, const ON_3dVector &Z1)

void	Rotation (const ON_3dVector &X0, const ON_3dVector &Y0, const ON_3dVector &Z0, const ON_3dVector &X1, const ON_3dVector &Y1, const ON_3dVector &Z1)

void	Rotation (const ON_Plane &plane0, const ON_Plane &plane1)

void	Rotation (double angle_radians, ON_3dVector rotation_axis, ON_3dPoint rotation_center)

void	Rotation (double sin_angle, double cos_angle, ON_3dVector rotation_axis, ON_3dPoint rotation_center)

void	Rotation (ON_3dVector start_dir, ON_3dVector end_dir, ON_3dPoint rotation_center)

void	RotationZYX (double yaw, double pitch, double roll)

void	RotationZYZ (double alpha, double beta, double gamma)

void	Scale (const ON_3dVector &scale_vector)

void	Scale (const ON_Plane &plane, double x_scale_factor, double y_scale_factor, double z_scale_factor)

void	Scale (double x_scale_factor, double y_scale_factor, double z_scale_factor)

void	Scale (ON_3dPoint fixed_point, double scale_factor)

bool	ScreenToClip (double, double, double, double, double, double)

void	Shear (const ON_Plane &plane, const ON_3dVector &x1, const ON_3dVector &y1, const ON_3dVector &z1)

int	SignOfDeterminant (bool bFastTest) const
	Quickly determine the sign of the determinant. Definitely good enough for graphics code. More...

void	Translation (const ON_3dVector &delta)

void	Translation (double dx, double dy, double dz)

void	Transpose ()
	matrix operations More...

void	WorldToCamera (const ON_3dPoint &, const ON_3dVector &, const ON_3dVector &, const ON_3dVector &)
	standard viewing transformations More...

Static Public Member Functions
static const ON_Xform	DiagonalTransformation (const ON_3dVector &diagonal)

static const ON_Xform	DiagonalTransformation (double d)

static const ON_Xform	DiagonalTransformation (double d0, double d1, double d2)

static const ON_Xform	MirrorTransformation (ON_PlaneEquation mirror_plane)

static const ON_Xform	RotationTransformationFromKMLAnglesDegrees (double heading_degrees, double tilt_degrees, double roll_degrees)

static const ON_Xform	RotationTransformationFromKMLAnglesRadians (double heading_radians, double tilt_radians, double roll_radians)

static const ON_Xform	ScaleTransformation (const ON_3dPoint &fixed_point, double scale_factor)

static const ON_Xform	ScaleTransformation (const ON_3dPoint &fixed_point, double x_scale_factor, double y_scale_factor, double z_scale_factor)

static const ON_Xform	ScaleTransformation (const ON_Plane &plane, double x_scale_factor, double y_scale_factor, double z_scale_factor)

static const ON_Xform	ShearTransformation (const ON_Plane &plane, const ON_3dVector &x1, const ON_3dVector &y1, const ON_3dVector &z1)

static const ON_Xform	TextureMapping (const ON_3dVector &offset, const ON_3dVector &repeat, const ON_3dVector &rotation)

static const ON_Xform	TranslationTransformation (const ON_2dVector &delta)
	Right column is (delta.x, delta.y, 0, 1). More...

static const ON_Xform	TranslationTransformation (const ON_3dVector &delta)
	Right column is (delta.x, delta.y, delta.z, 1). More...

static const ON_Xform	TranslationTransformation (double dx, double dy, double dz)
	Right column is (dx, dy, dz, 1). More...

Public Attributes
double	m_xform [4][4]

Static Public Attributes
static const ON_Xform	IdentityTransformation
	ON_Xform IdentityTransformation diagonal = (1,1,1,1) More...

static const ON_Xform	Nan
	ON_Xform::Nan - every coefficient is ON_DBL_QNAN. More...

static const ON_Xform	Unset
	ON_Xform::Unset - every coefficient is ON_UNSET_VALUE. More...

static const ON_Xform	Zero4x4
	ON_Xform::Zero4x4 - every coefficient is 0.0. More...

static const ON_Xform	ZeroTransformation
	ON_Xform ZeroTransformation diagonal = (0,0,0,1) More...

Constructor & Destructor Documentation

◆ ON_Xform() [1/9]

ON_Xform::ON_Xform ( )

Default constructor transformation has diagonal (0,0,0,1)

◆ ~ON_Xform()

ON_Xform::~ON_Xform ( )

default

◆ ON_Xform() [2/9]

ON_Xform::ON_Xform ( const ON_Xform & )

default

◆ ON_Xform() [3/9]

ON_Xform::ON_Xform ( double x )

explicit

Constructs transformation with diagonal (x,x,x,1)

◆ ON_Xform() [4/9]

ON_Xform::ON_Xform ( const double [4][4] )

explicit

from standard double m[4][4]

◆ ON_Xform() [5/9]

ON_Xform::ON_Xform ( const float [4][4] )

explicit

from standard float m[4][4]

◆ ON_Xform() [6/9]

ON_Xform::ON_Xform ( const double * )

explicit

from array of 16 doubles (row0,row1,row2,row3)

◆ ON_Xform() [7/9]

ON_Xform::ON_Xform ( const float * )

explicit

from array of 16 floats (row0,row1,row2,row3)

◆ ON_Xform() [8/9]

ON_Xform::ON_Xform ( const ON_Matrix & )

explicit

from upper left 4x4 of an

◆ ON_Xform() [9/9]

ON_Xform::ON_Xform	(	const ON_3dPoint &	P,
		const ON_3dVector &	X,
		const ON_3dVector &	Y,
		const ON_3dVector &	Z
	)

arbitrary matrix. Any missing rows/columns are set to identity.

Parameters

P	as a frame.

Member Function Documentation

◆ ActOnLeft()

void ON_Xform::ActOnLeft	(	double	,
		double	,
		double	,
		double	,
		double	[4]
	)		const

Description: Computes matrix * transpose([x,y,z,w]).

Parameters: x - [in] y - [in] z - [in] z - [in] ans - [out] = matrix * transpose([x,y,z,w])

◆ ActOnRight()

void ON_Xform::ActOnRight	(	double	,
		double	,
		double	,
		double	,
		double	[4]
	)		const

Description: Computes [x,y,z,w] * matrix.

Parameters: x - [in] y - [in] z - [in] z - [in] ans - [out] = [x,y,z,w] * matrix

◆ Affineize()

void ON_Xform::Affineize ( )

Description: Replace last row with 0 0 0 1 discarding any perspective part of this transform

◆ CameraToClip()

bool ON_Xform::CameraToClip	(	bool	bIsPerspective,
		double	,
		double	,
		double	,
		double	,
		double	,
		double
	)

Parameters

bIsPerspective maps viewport frustum to -1 <= x,y,z <= 1 box true for perspective, false for orthographic

◆ CameraToWorld()

void ON_Xform::CameraToWorld	(	const ON_3dPoint &	,
		const ON_3dVector &	,
		const ON_3dVector &	,
		const ON_3dVector &
	)

◆ ChangeBasis() [1/3]

bool ON_Xform::ChangeBasis	(	const ON_3dPoint &	P0,
		const ON_3dVector &	X0,
		const ON_3dVector &	Y0,
		const ON_3dVector &	Z0,
		const ON_3dPoint &	P1,
		const ON_3dVector &	X1,
		const ON_3dVector &	Y1,
		const ON_3dVector &	Z1
	)

Parameters: P0 - initial center X0 - initial basis X (X0,Y0,Z0 can be any 3d basis) Y0 - initial basis Y Z0 - initial basis Z P1 - final center X1 - final basis X (X1,Y1,Z1 can be any 3d basis) Y1 - final basis Y Z1 - final basis Z Remarks: Change of basis transformations and rotation transformations are often confused. This is a change of basis transformation. If Q = P0 + a0*X0 + b0*Y0 + c0*Z0 = P1 + a1*X1 + b1*Y1 + c1*Z1 then this transform will map the point (a0,b0,c0) to (a1,b1,c1)

◆ ChangeBasis() [2/3]

bool ON_Xform::ChangeBasis	(	const ON_3dVector &	X0,
		const ON_3dVector &	Y0,
		const ON_3dVector &	Z0,
		const ON_3dVector &	X1,
		const ON_3dVector &	Y1,
		const ON_3dVector &	Z1
	)

Description: Get a change of basis transformation. Parameters: X0 - initial basis X (X0,Y0,Z0 can be any 3d basis) Y0 - initial basis Y Z0 - initial basis Z X1 - final basis X (X1,Y1,Z1 can be any 3d basis) Y1 - final basis Y Z1 - final basis Z Remarks: Change of basis transformations and rotation transformations are often confused. This is a change of basis transformation. If Q = a0*X0 + b0*Y0 + c0*Z0 = a1*X1 + b1*Y1 + c1*Z1 then this transform will map the point (a0,b0,c0) to (a1,b1,c1)

◆ ChangeBasis() [3/3]

bool ON_Xform::ChangeBasis	(	const ON_Plane &	plane0,
		const ON_Plane &	plane1
	)

Description: The ChangeBasis() function is overloaded and provides several ways to compute a change of basis transformation.

Parameters: plane0 - initial plane plane1 - final plane

Returns: @untitled table true success false vectors for initial frame are not a basis

Remarks: If you have points defined with respect to planes, the version of ChangeBasis() that takes two planes computes the transformation to change coordinates from one plane to another. The predefined world plane ON_world_plane can be used as an argument.

If P = plane0.Evaluate( a0,b0,c0 ) and

(a1,b1,c1) = ChangeBasis(plane0,plane1)*ON_3dPoint(a0,b0,c0),

then P = plane1.Evaluate( a1, b1, c1 )

The version of ChangeBasis() that takes six vectors maps (a0,b0,c0) to (a1,b1,c1) where a0*X0 + b0*Y0 + c0*Z0 = a1*X1 + b1*Y1 + c1*Z1

The version of ChangeBasis() that takes six vectors with center points maps (a0,b0,c0) to (a1,b1,c1) where P0 + a0*X0 + b0*Y0 + c0*Z0 = P1 + a1*X1 + b1*Y1 + c1*Z1

The change of basis transformation is not the same as the rotation transformation that rotates one orthonormal frame to another. See ON_Xform::Rotation().

◆ ClipFlag3d() [1/2]

int ON_Xform::ClipFlag3d ( const double * ) const

Description: Computes 3d point clipping flags and returns an int with bits set to indicate if the point is outside of the clipping box.

Parameters: point - [in] 3d clipping coordinate point

Returns:
@table
bit point location 1 x < -1 2 x > +1 4 y < -1 8 y > +1 16 z < -1 32 z > +1

◆ ClipFlag3d() [2/2]

int ON_Xform::ClipFlag3d	(	int	,
		int	,
		const double *	,
		bool	bTestZ = `true`
	)		const

Parameters: count - [in] number of 3d points stride - [in] (>=3) points - [in] 3d clipping coordinate points (array of stride*count doubles) bTestZ - [in] (default=true) if false, do not test "z" coordinate

Parameters

bTestZ bTestZ

◆ ClipFlag3dBox()

int ON_Xform::ClipFlag3dBox	(	const double *	,
		const double *
	)		const

Description: Computes 3d clipping flags for a 3d bounding box and returns an int with bits set to indicate if the bounding box is outside of the clipping box.

Parameters: boxmin - [in] 3d boxmin corner boxmax - [in] 3d boxmax corner

Returns:
@table
bit box location 1 boxmax x < -1 2 boxmin x > +1 4 boxmax y < -1 8 boxmin y > +1 16 boxmax z < -1 32 boxmin z > +1

◆ ClipFlag4d() [1/2]

int ON_Xform::ClipFlag4d ( const double * ) const

Description: Computes homogeneous point clipping flags and returns an int with bits set to indicate if the point is outside of the clipping box.

Parameters: point - [in] 4d homogeneous clipping coordinate point

Returns:
@table
bit point location 1 x/w < -1 2 x/w > +1 4 y/w < -1 8 y/w > +1 16 z/w < -1 32 z/w > +1

◆ ClipFlag4d() [2/2]

int ON_Xform::ClipFlag4d	(	int	,
		int	,
		const double *	,
		bool	bTestZ = `true`
	)		const

Parameters: count - [in] number of 4d points stride - [in] (>=4) points - [in] 4d clipping coordinate points (array of stride*count doubles) bTestZ - [in] (default=true) if false, do not test "z" coordinate

Parameters

bTestZ bTestZ

◆ ClipToCamera()

bool ON_Xform::ClipToCamera	(	bool	bIsPerspective,
		double	,
		double	,
		double	,
		double	,
		double	,
		double
	)

maps -1 <= x,y,z <= 1 box to viewport frustum

Parameters

bIsPerspective true for perspective, false for orthographic

◆ ClipToScreen()

bool ON_Xform::ClipToScreen	(	double	,
		double	,
		double	,
		double	,
		double	,
		double
	)

Computes transform that maps the clipping box

      -1<x<1,-1<y<1,-1<z<1

to the screen box

     (left,right) X (bottom,top) X (near,far)

◆ Compare()

int ON_Xform::Compare ( const ON_Xform & other ) const

Description: Well ordered dictionary compare that is nan aware.

◆ CRC32()

ON__UINT32 ON_Xform::CRC32 ( ON__UINT32 current_remainder ) const

◆ DecomposeAffine() [1/3]

bool ON_Xform::DecomposeAffine	(	ON_3dVector &	Translation,
		ON_Xform &	Linear
	)		const

◆ DecomposeAffine() [2/3]

bool ON_Xform::DecomposeAffine	(	ON_3dVector &	Translation,
		ON_Xform &	Rotation,
		ON_Xform &	OrthBasis,
		ON_3dVector &	Diagonal
	)		const

Description: An affine transformation can be decomposed into a Symmetric, Rotation and Translation. Then the Symmetric component may be further decomposed as non-uniform scale in an orthonormal coordinate system.
Parameters: this - must be IsAffine(). Translation-[out] Translation vector Rotation - [out] Proper Rotation transformation OrthBasis - [out] Orthogonal Basis Diagonal - [out] diagonal elements of a DiagonalTransformation Details: DecomposeAffine(T,R,Q,diag) (*this) == TranslationTransformation(T) * R * Q * DiagonalTransformation(diag) * Q.Transpose() Returns: true if decomposition succeeds

◆ DecomposeAffine() [3/3]

bool ON_Xform::DecomposeAffine	(	ON_Xform &	Linear,
		ON_3dVector &	Translation
	)		const

◆ DecomposeRigid()

int ON_Xform::DecomposeRigid	(	ON_3dVector &	Translation,
		ON_Xform &	Rotation,
		double	tolerance = `ON_ZERO_TOLERANCE`
	)		const

Description: A rigid transformation preserves distances and orientation and can be broken into a proper rotation and a translation. An isometry transformation preserves distance and may include a reflection. Parameters: this - must be IsAffine(). Translation - [out] Translation vector Rotation - [out] Proper Rotation transformation, ie. R*Transpose(R)=I and det(R)=1 Details: If X.DecomposeRigid(T, R) is 1 then X ~ TranslationTransformation(T)*R -1 X ~ ON_Xform(-1) *TranslationTransformation(T)*R where ~ means approximates to within tolerance. DecomposeRigid will find the closest rotation to the linear part of this transformation. Returns: +1: This transformation is an rigid transformation. -1: This transformation is an orientation reversing isometry. 0 : This transformation is not an orthogonal transformation.

◆ DecomposeSimilarity()

int ON_Xform::DecomposeSimilarity	(	ON_3dVector &	Translation,
		double &	dilation,
		ON_Xform &	Rotation,
		double	tolerance
	)		const

◆ DecomposeSymmetric()

bool ON_Xform::DecomposeSymmetric	(	ON_Xform &	Q,
		ON_3dVector &	diagonal
	)		const

Description: A Symmetric linear transformation can be decomposed A = Q * Diag * Q^T where Diag is a diagonal transformation. Diag[i][i] is an eigenvalue of A and the i-th column of Q is a corresponding unit length eigenvector. Parameters: This transformation must be Linear() and Symmetric, that is *this==Transpose(). Q -[out] is set to an orthonormal matrix of eigenvectors when true is returned. diagonal -[out] is set to a vector of eigenvalues when true is returned. Details: If success then *this== Q*DiagonalTransformation(diagonal) * QT, where QT == Q.Transpose(). If L.IsLinear() and LT==L.Transpose() then LT*L is symmetric and is a common source of symmetric transformations. Return: true if success.

◆ DecomposeTextureMapping()

void ON_Xform::DecomposeTextureMapping	(	ON_3dVector &	offset,
		ON_3dVector &	repeat,
		ON_3dVector &	rotation
	)		const

Convert an ON_Xform into the offset, repeat and rotation values used in ON_Texture and similar classes.

◆ Determinant()

double ON_Xform::Determinant ( double * minimum_pivot = nullptr ) const

If you need a slow and accurate determinant, this is the function to call. If you need a fast sign check, used SignOfDeterminant(true).

Parameters

minimum_pivot If not nullptr, returns the minimum pivot

Returns: The determinant of 4x4 matrix

◆ Diagonal()

void ON_Xform::Diagonal ( double d )

Deprecated:: Use xform = ON_Xform::DiagonalTransformation(d);

◆ DiagonalTransformation() [1/3]

static const ON_Xform ON_Xform::DiagonalTransformation ( const ON_3dVector & diagonal )

static

Returns: Transformation with diagonal (d0,d1,d2,1.0).

◆ DiagonalTransformation() [2/3]

static const ON_Xform ON_Xform::DiagonalTransformation ( double d )

static

Returns: Transformation with diagonal (d,d,d,1).

◆ DiagonalTransformation() [3/3]

static const ON_Xform ON_Xform::DiagonalTransformation	(	double	d0,
		double	d1,
		double	d2
	)

static

Returns: Transformation with diagonal (d0,d1,d2,1.0).

◆ GetEulerZYZ()

bool ON_Xform::GetEulerZYZ	(	double &	alpha,
		double &	beta,
		double &	gamma
	)		const

Description: Find the Euler angles for a rotation transformation. Parameters: alpha - angle (in radians) to rotate about the Z axis beta - angle (in radians) to rotate about the Y axis gamma - angle (in radians) to rotate about the Z axis Details: When true is returned. this = RotationZYZ(alpha, beta, gamma) = R_z( alpha) * R_y(beta) * R_z(gamma) where R_*(angle) is rotation of angle radians about the corresponding *-world coordinate axis. Returns false if this is not a rotation. Notes: alpha and gamma are in the range (-pi, pi] while beta in in the range [0, pi]

◆ GetKMLOrientationAnglesDegrees()

bool ON_Xform::GetKMLOrientationAnglesDegrees	(	double &	heading_degrees,
		double &	tilt_degrees,
		double &	roll_degrees
	)		const

Description: Find the Keyhole Markup Language (KML) orientation angles (in degrees) of a rotation transformation that maps model (east,north,up) to ((1,0,0),(0,1,0),(0,0,1)). KML Earth Z axis = up, KML Earth X axis = east, KML Earth Y axis = north. NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. This is rotation direction is opposite the conventional "right hand rule." Parameters: heading_degrees - [out] angle (in degrees) of rotation around KML Earth Z axis (Earth up). NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. This is rotation direction is opposite the conventional "right hand rule." tilt_degrees - [out] angle (in degrees) of rotation around KML Earth X axis (Earth east). NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. This is rotation direction is opposite the conventional "right hand rule." roll_degrees - [out] angle (in degrees) of rotation around KML Earth Y axis (Earth north). NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. This is rotation direction is opposite the conventional "right hand rule." Returns: True if this transformation is a rotation and the KML angles are returned. False if this transformation is not a rotation, in which case all returned angle values are ON_DLB_QNAN. See Also: https://developers.google.com/kml/documentation/kmlreference#orientation

◆ GetKMLOrientationAnglesRadians()

bool ON_Xform::GetKMLOrientationAnglesRadians	(	double &	heading_radians,
		double &	tilt_radians,
		double &	roll_radians
	)		const

Description: Find the Keyhole Markup Language (KML) orientation angles (in radians) of a rotation transformation that maps model (east,north,up) to ((1,0,0),(0,1,0),(0,0,1)). KML Earth Z axis = up, KML Earth X axis = east, KML Earth Y axis = north. NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. This is rotation direction is opposite the conventional "right hand rule." Parameters: heading_radians - [out] angle (in radians) of rotation around KML Earth Z axis (Earth up). NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. This is rotation direction is opposite the conventional "right hand rule." tilt_radians - [out] angle (in radians) of rotation around KML Earth X axis (Earth east). NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. This is rotation direction is opposite the conventional "right hand rule." roll_radians - [out] angle (in radians) of rotation around KML Earth Y axis (Earth north). NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. This is rotation direction is opposite the conventional "right hand rule." Returns: True if this transformation is a rotation and the KML angles are returned. False if this transformation is not a rotation, in which case all returned angle values are ON_DLB_QNAN. See Also: https://developers.google.com/kml/documentation/kmlreference#orientation

◆ GetMappingXforms()

double ON_Xform::GetMappingXforms	(	ON_Xform &	P_xform,
		ON_Xform &	N_xform
	)		const

Description: If a texture mapping is applied to an object, the object is subsequently transformed by T, and the texture mapping needs to be recalculated, then two transforms are required to recalculate the texture mapping. Parameters: P_xform - [out] Transform to apply to points before applying the texture mapping transformation. N_xform - [out] Transform to apply to surface normals before applying the texture mapping transformation. Returns: The determinant of the "this" transformation. If non-zero, "this" is invertible and P_xform and N_xform were calculated. False if "this" is not invertible, in which case the returned P_xform and N_xform are the identity.

◆ GetQuaternion()

bool ON_Xform::GetQuaternion ( ON_Quaternion & Q ) const

Description: If *this is a proper rotation then find the equivalent quaternion.
Parameters: Q - [out] Quaternion that represents this rotation transformation Returns: True - if *this is a proper rotation

◆ GetSurfaceNormalXform()

double ON_Xform::GetSurfaceNormalXform ( ON_Xform & N_xform ) const

Description: When transforming 3d point and surface or mesh normals two different transforms must be used. If P_xform transforms the point, then the inverse transpose of P_xform must be used to transform normal vectors. Parameters: N_xform - [out] Returns: The determinant of the transformation. If non-zero, "this" is invertible and N_xform can be calculated. False if "this" is not invertible, in which case the returned N_xform = this with the right hand column and bottom row zeroed out.

◆ GetSurfaceNormalXformKeepLengthAndOrientation()

double ON_Xform::GetSurfaceNormalXformKeepLengthAndOrientation ( ON_Xform & N_xform ) const

Description: When transforming 3d point and surface or mesh normals two different transforms must be used. If P_xform transforms the point, then N_xform, the transformation that transforms unit-length and oriented normals of the face to unit-length and oriented normals of the transformed face is:

N_xform = (IsOrientationPreserving() >= 0 ? 1 : -1) * pow(Determinant(), -1/3) * Transpose(Inverse(P_xform)) Parameters: N_xform - [out] Returns: The determinant of the transformation. If non-zero, "this" is invertible and N_xform can be calculated. False if "this" is not invertible, in which case the returned N_xform = this with the right hand column and bottom row zeroed out.

◆ GetYawPitchRoll()

bool ON_Xform::GetYawPitchRoll	(	double &	yaw,
		double &	pitch,
		double &	roll
	)		const

Description: Find the Tait-Byran angles (also loosely called Euler angles) for a rotation transformation. Parameters: yaw - angle (in radians) to rotate about the Z axis pitch - angle (in radians) to rotate about the Y axis roll - angle (in radians) to rotate about the X axis Details: When true is returned.
this = RotationZYX(yaw, pitch, roll) = R_z( yaw) * R_y(pitch) * R_x(roll) where R_*(angle) is rotation of angle radians about the corresponding world coordinate axis. Returns false if this is not a rotation. Notes: roll and yaw are in the range (-pi, pi] and pitch is in [-pi/2, pi/2]

◆ Hash()

const ON_SHA1_Hash ON_Xform::Hash ( ) const

◆ Identity()

void ON_Xform::Identity ( )

standard transformations

diagonal is (1,1,1,1)

Deprecated:: Use xform = ON_Xform::IdentityTransformation;

◆ IntervalChange()

bool ON_Xform::IntervalChange	(	int	dir,
		ON_Interval	old_interval,
		ON_Interval	new_interval
	)

Description: Calculates the transformation that linearly maps old_interval to new_interval. Parameters: dir - [in] 0 = x, 1 = y, 2= z; old_interval - [in] new_interval - [in]

◆ Inverse()

ON_Xform ON_Xform::Inverse ( double * = nullptr ) const

◆ Invert()

bool ON_Xform::Invert ( double * = nullptr )

◆ IsAffine()

bool ON_Xform::IsAffine ( ) const

Description: A transformation is affine if it is valid and its last row is 0 0 0 1 If in addition its last column is ( 0, 0, 0, 1)^T then it is linear. An affine transformation can be broken into a linear transformation and a translation. Parameters: this - IsAffine() must be true for DecomposeAffine(..) to succeed Translation - [out] Translation vector Linear - [out] Linear transformation Example: A perspective transformation is not affine. Details: If X.DecomposeAffine(T, L) is true then X == TranslationTransformation(T)*L If X.DecomposeAffine(L, T) is true then X == L* TranslationTransformation(T). Note: DecomposeAffine(T,L) succeeds for all affine transformations and is a simple copying of values. DecomposeAffine(L, T), on the otherhand, may fail for affine transformations if L is not invertible and is more computationally expensive. Returns: True - if successful decomposition

◆ IsIdentity()

bool ON_Xform::IsIdentity ( double zero_tolerance = 0.0 ) const

Returns: true if matrix is the identity transformation

Remarks: An element of the matrix is "zero" if fabs(x) <= zero_tolerance. An element of the matrix is "one" if fabs(1.0-x) <= zero_tolerance. If the matrix contains a nan, false is returned.

◆ IsLinear()

bool ON_Xform::IsLinear ( ) const

◆ IsNan()

bool ON_Xform::IsNan ( ) const

Description: Test the entries of the transformation matrix to see if they are valid number. Returns: True if any coefficient in the transformation matrix is a nan.

◆ IsNotIdentity()

bool ON_Xform::IsNotIdentity ( double zero_tolerance = 0.0 ) const

Returns: true if the matrix is valid and is not the identity transformation Remarks: An element of the matrix is "zero" if fabs(x) <= zero_tolerance. An element of the matrix is "one" if fabs(1.0-x) <= zero_tolerance. If the matrix contains a nan, false is returned.

◆ IsRigid()

int ON_Xform::IsRigid ( double tolerance = ON_ZERO_TOLERANCE ) const

Description: NOTE: A better name for this function would be IsIsometry().

An "isometry" transformation is an affine transformation that preserves distances. Isometries include transformation like reflections that reverse orientation.

A "rigid" transformation is an isometry that preserves orientation and can be broken into a proper rotation and a translation.
Returns: +1: This transformation is an orientation preserving isometry transformation ("rigid and determinant = 1). -1: This transformation is an orientation reversing isometry (determinant = -1). 0 : This transformation is not an orthogonal transformation.

◆ IsRotation()

bool ON_Xform::IsRotation ( ) const

true if this is a proper rotation.

◆ IsSimilarity() [1/2]

int ON_Xform::IsSimilarity ( ) const

Description: A similarity transformation can be broken into a sequence of a dilation, translation, rotation, and a reflection. Parameters: this - must be IsAffine(). Translation - [out] Translation vector dilation - [out] dilation, (dilation <0 iff this is an orientation reversing similarity ) Rotation - [out] a proper rotation transformation ie. R*Transpose(R)=I and det(R)=1 Details: If X.DecomposeSimilarity(T, d, R, tol) !=0 then X ~ TranslationTransformation(T)*DiagonalTransformation(d)*R note when d>0 the transformation is orientation preserving. Note: If dilation<0 then DiagonalTransformation(dilation) is actually a reflection combined with a "true" dilation, i.e. DiagonalTransformation(dilation) = DiagonalTransformation(-1) * DiagonalTransformation( |diagonal| ) Returns: +1: This transformation is an orientation preserving similarity. -1: This transformation is an orientation reversing similarity. 0: This transformation is not a similarity.

◆ IsSimilarity() [2/2]

int ON_Xform::IsSimilarity ( double tolerance ) const

◆ IsTranslation()

bool ON_Xform::IsTranslation ( double zero_tolerance = 0.0 ) const

Returns: true if matrix is a pure translation

Remarks: The test for zero is fabs(x) <= zero_tolerance. The test for one is fabs(x-1) <= zero_tolerance.

◆ IsValid()

bool ON_Xform::IsValid ( ) const

Description: Test the entries of the transformation matrix to see if they are valid number. Returns: True if ON_IsValid() is true for every coefficient in the transformation matrix.

◆ IsValidAndNotZeroAndNotIdentity()

bool ON_Xform::IsValidAndNotZeroAndNotIdentity ( double zero_tolerance = 0.0 ) const

◆ IsZero()

bool ON_Xform::IsZero ( ) const

Returns: true if matrix is ON_Xform::Zero4x4, ON_Xform::ZeroTransformation, or some other type of zero. The value xform[3][3] can be anything. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 *

◆ IsZero4x4() [1/2]

bool ON_Xform::IsZero4x4 ( ) const

Returns: true if matrix is ON_Xform::Zero4x4 The value xform[3][3] must be zero. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

◆ IsZero4x4() [2/2]

bool ON_Xform::IsZero4x4 ( double zero_tolerance ) const

Returns: true if matrix is ON_Xform::Zero4x4 The value xform[3][3] must be zero. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

◆ IsZeroTransformation() [1/2]

bool ON_Xform::IsZeroTransformation ( ) const

Returns: true if matrix is ON_Xform::ZeroTransformation The value xform[3][3] must be 1. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 An element of the matrix is "zero" if fabs(x) <= zero_tolerance. IsZeroTransformation() is the same as IsZeroTransformation( 0.0 );

◆ IsZeroTransformation() [2/2]

bool ON_Xform::IsZeroTransformation ( double zero_tolerance ) const

◆ Linearize()

void ON_Xform::Linearize ( )

Description: Affineize() and replace last column with (0 0 0 1)^T discarding any translation part of this transform.

◆ Mirror()

void ON_Xform::Mirror	(	ON_3dPoint	point_on_mirror_plane,
		ON_3dVector	normal_to_mirror_plane
	)

Description: Create mirror transformation matrix. Parameters: point_on_mirror_plane - [in] point on mirror plane normal_to_mirror_plane - [in] normal to mirror plane Remarks: The mirror transform maps a point Q to Q - (2*(Q-P)oN)*N, where P = point_on_mirror_plane and N = normal_to_mirror_plane.

◆ MirrorTransformation()

static const ON_Xform ON_Xform::MirrorTransformation ( ON_PlaneEquation mirror_plane )

static

◆ operator!=()

bool ON_Xform::operator!= ( const ON_Xform & rhs ) const

◆ operator*() [1/6]

ON_2dPoint ON_Xform::operator* ( const ON_2dPoint & ) const

arbitrary matrix. Any missing rows/columns are set to identity. All non-commutative operations have "this" as left hand side and argument as right hand side. Note well: The right hand column and bottom row have an important effect when transforming a Euclidean point and have no effect when transforming a vector. Be sure you understand the differences between vectors and points when applying a 4x4 transformation.

◆ operator*() [2/6]

ON_2dVector ON_Xform::operator* ( const ON_2dVector & ) const

Note well: The right hand column and bottom row have an important effect when transforming a Euclidean point and have no effect when transforming a vector. Be sure you understand the differences between vectors and points when applying a 4x4 transformation.

◆ operator*() [3/6]

ON_3dPoint ON_Xform::operator* ( const ON_3dPoint & ) const

◆ operator*() [4/6]

ON_3dVector ON_Xform::operator* ( const ON_3dVector & ) const

◆ operator*() [5/6]

ON_4dPoint ON_Xform::operator* ( const ON_4dPoint & ) const

◆ operator*() [6/6]

ON_Xform ON_Xform::operator* ( const ON_Xform & ) const

◆ operator+()

ON_Xform ON_Xform::operator+ ( const ON_Xform & ) const

◆ operator-()

ON_Xform ON_Xform::operator- ( const ON_Xform & ) const

◆ operator=() [1/2]

ON_Xform& ON_Xform::operator= ( const ON_Matrix & )

xform = scalar results in a diagonal 3x3 with bottom row = 0,0,0,1

from upper left 4x4 of an

◆ operator=() [2/2]

ON_Xform& ON_Xform::operator= ( const ON_Xform & )

default

◆ operator==()

bool ON_Xform::operator== ( const ON_Xform & rhs ) const

◆ operator[]() [1/2]

double* ON_Xform::operator[] ( int )

◆ operator[]() [2/2]

const double* ON_Xform::operator[] ( int ) const

◆ Orthogonalize()

bool ON_Xform::Orthogonalize ( double tol )

Description: Force the linear part of this transformation to be a rotation (or a rotation with reflection). This is probably best to perform minute tweaks. Use DecomposeRigid(T,R) to find the nearest rotation

◆ PlanarProjection()

void ON_Xform::PlanarProjection ( const ON_Plane & plane )

Description: Get transformation that projects to a plane Parameters: plane - [in] plane to project to Remarks: This transformation maps a 3d point P to the point plane.ClosestPointTo(Q).

◆ Rank()

int ON_Xform::Rank ( double * = nullptr ) const

◆ Rotation() [1/6]

void ON_Xform::Rotation	(	const ON_3dPoint &	P0,
		const ON_3dVector &	X0,
		const ON_3dVector &	Y0,
		const ON_3dVector &	Z0,
		const ON_3dPoint &	P1,
		const ON_3dVector &	X1,
		const ON_3dVector &	Y1,
		const ON_3dVector &	Z1
	)

Parameters: P0 - initial frame center X0 - initial frame X Y0 - initial frame Y Z0 - initial frame Z P1 - initial frame center X1 - final frame X Y1 - final frame Y Z1 - final frame Z

◆ Rotation() [2/6]

void ON_Xform::Rotation	(	const ON_3dVector &	X0,
		const ON_3dVector &	Y0,
		const ON_3dVector &	Z0,
		const ON_3dVector &	X1,
		const ON_3dVector &	Y1,
		const ON_3dVector &	Z1
	)

Parameters: X0 - initial frame X Y0 - initial frame Y Z0 - initial frame Z X1 - final frame X Y1 - final frame Y Z1 - final frame Z

◆ Rotation() [3/6]

void ON_Xform::Rotation	(	const ON_Plane &	plane0,
		const ON_Plane &	plane1
	)

Description: Create rotation transformation that maps plane0 to plane1. Parameters: plane0 - [in] plane1 - [in]

◆ Rotation() [4/6]

void ON_Xform::Rotation	(	double	angle_radians,
		ON_3dVector	rotation_axis,
		ON_3dPoint	rotation_center
	)

Parameters: angle - rotation angle in radians rotation_axis - 3d unit axis of rotation rotation_center - 3d center of rotation

◆ Rotation() [5/6]

void ON_Xform::Rotation	(	double	sin_angle,
		double	cos_angle,
		ON_3dVector	rotation_axis,
		ON_3dPoint	rotation_center
	)

Description: The Rotation() function is overloaded and provides several ways to compute a rotation transformation. A positive rotation angle indicates a counter-clockwise (right hand rule) rotation about the axis of rotation.

Parameters: sin_angle - sin(rotation angle) cos_angle - cos(rotation angle) rotation_axis - 3d unit axis of rotation rotation_center - 3d center of rotation

Remarks: In the overloads that take frames, the frames should be right hand orthonormal frames (unit vectors with Z = X x Y).
The resulting rotation fixes the origin (0,0,0), maps initial X to final X, initial Y to final Y, and initial Z to final Z.

In the overload that takes frames with center points, if the initial and final center are equal, then that center point is the fixed point of the rotation. If the initial and final point differ, then the resulting transform is the composition of a rotation fixing P0 and translation from P0 to P1. The resulting transformation maps P0 to P1, P0+X0 to P1+X1, ...

The rotation transformations that map frames to frames are not the same as the change of basis transformations for those frames. See ON_Xform::ChangeBasis().

◆ Rotation() [6/6]

void ON_Xform::Rotation	(	ON_3dVector	start_dir,
		ON_3dVector	end_dir,
		ON_3dPoint	rotation_center
	)

Description: Calculate the minimal transformation that rotates start_dir to end_dir while fixing rotation_center.

◆ RotationTransformationFromKMLAnglesDegrees()

static const ON_Xform ON_Xform::RotationTransformationFromKMLAnglesDegrees	(	double	heading_degrees,
		double	tilt_degrees,
		double	roll_degrees
	)

static

Description: Get a rotation transformation from the Keyhole Markup Language (KML) orientation angles in degrees. (KML Earth Z axis = up, KML Earth X axis = east, KML Earth Y axis = north). KML rotations are applied in the following order: first roll, second tilt, third heading. NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. This is rotation direction is opposite the conventional "right hand rule." Parameters: heading_degrees - [in] angle (in degrees) of rotation around KML Earth Z axis (Earth up). NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. If R = RotationTransformationFromKMLAnglesDegrees(90,0,0), then R*(1,0,0) = (0,-1,0), R*(0,1,0) = (1,0,0), R*(0,0,1) = (0,0,1) tilt_degrees - [in] angle (in degrees) of rotation around KML Earth X axis (Earth east). NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. If R = RotationTransformationFromKMLAnglesDegrees(0,90,0), then R*(1,0,0) = (1,0,0), R*(0,1,0) = (0,0,-1), R*(0,0,1) = (0,1,0) roll_degrees - [in] angle (in degrees) of rotation around KML Earth Y axis (Earth north). NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. If R = RotationTransformationFromKMLAnglesDegrees(0,0,90), then R*(1,0,0) = (0,0,1), R*(0,1,0) = (0,1,0), R*(0,0,1) = (-1,0,0) Returns: If the input is valid, the rotation transformation is returned. Otherwise the ON_Xform::Nan is returned. See Also: https://developers.google.com/kml/documentation/kmlreference#orientation

◆ RotationTransformationFromKMLAnglesRadians()

static const ON_Xform ON_Xform::RotationTransformationFromKMLAnglesRadians	(	double	heading_radians,
		double	tilt_radians,
		double	roll_radians
	)

static

Description: Get a rotation transformation from the Keyhole Markup Language (KML) orientation angles in radians. (KML Earth Z axis = up, KML Earth X axis = east, KML Earth Y axis = north). KML rotations are applied in the following order: first roll, second tilt, third heading. NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. This is rotation direction is opposite the conventional "right hand rule." Parameters: heading_radians - [in] angle (in radians) of rotation around KML Earth Z axis (Earth up). NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. If R = RotationTransformationFromKMLAnglesRadians(pi/2,0,0), then R*(1,0,0) = (0,-1,0), R*(0,1,0) = (1,0,0), R*(0,0,1) = (0,0,1) tilt_radians - [in] angle (in radians) of rotation around KML Earth X axis (Earth east). NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. If R = RotationTransformationFromKMLAnglesRadians(0,pi/2,0), then R*(1,0,0) = (1,0,0), R*(0,1,0) = (0,0,-1), R*(0,0,1) = (0,1,0) roll_radians - [in] angle (in radians) of rotation around KML Earth Y axis (Earth north). NOTE WELL: In KML, positive rotations are CLOCKWISE looking down specified axis vector towards the origin. If R = RotationTransformationFromKMLAnglesRadians(0,0,pi/2), then R*(1,0,0) = (0,0,1), R*(0,1,0) = (0,1,0), R*(0,0,1) = (-1,0,0) Returns: If the input is valid, the rotation transformation is returned. Otherwise the ON_Xform::Nan is returned. See Also: https://developers.google.com/kml/documentation/kmlreference#orientation

◆ RotationZYX()

void ON_Xform::RotationZYX	(	double	yaw,
		double	pitch,
		double	roll
	)

Description: Create rotation transformation From Tait-Byran angles (also loosely known as Euler angles). Parameters: yaw - angle (in radians) to rotate about the Z axis pitch - angle (in radians) to rotate about the Y axis roll - angle (in radians) to rotate about the X axis Details: RotationZYX(yaw, pitch, roll) = R_z( yaw) * R_y(pitch) * R_x(roll) where R_*(angle) is rotation of angle radians about the corresponding world coordinate axis.

◆ RotationZYZ()

void ON_Xform::RotationZYZ	(	double	alpha,
		double	beta,
		double	gamma
	)

Description: Create rotation transformation From Euler angles. Parameters: alpha - angle (in radians) to rotate about the Z axis beta - angle (in radians) to rotate about the Y axis gamma - angle (in radians) to rotate about the Z axis Details: RotationZYZ(alpha, beta, gamma) = R_z( alpha) * R_y(beta) * R_z(gamma) where R_*(angle) is rotation of angle radians about the corresponding *-world coordinate axis.

◆ Scale() [1/4]

void ON_Xform::Scale ( const ON_3dVector & scale_vector )

Description: Create non-uniform scale transformation with the origin as the fixed point. Parameters: fixed_point - [in] scale_vector - [in] Remarks: The diagonal is (scale_vector.x, scale_vector.y, scale_vector.z, 1)

Deprecated:: Use xform = ON_Xform::DiagonalTransformation(scale_vector);

◆ Scale() [2/4]

void ON_Xform::Scale	(	const ON_Plane &	plane,
		double	x_scale_factor,
		double	y_scale_factor,
		double	z_scale_factor
	)

Description: Create non-uniform scale transformation with a specified fixed point. Parameters: plane - [in] plane.origin is the fixed point x_scale_factor - [in] plane.xaxis scale factor y_scale_factor - [in] plane.yaxis scale factor z_scale_factor - [in] plane.zaxis scale factor

Deprecated:: Use xform = ON_Xform::ScaleTransformation(plane,x_scale_factor,y_scale_factor,z_scale_factor)

◆ Scale() [3/4]

void ON_Xform::Scale	(	double	x_scale_factor,
		double	y_scale_factor,
		double	z_scale_factor
	)

Description: Create non-uniform scale transformation with the origin as a fixed point. Parameters: fixed_point - [in] x_scale_factor - [in] y_scale_factor - [in] z_scale_factor - [in] Remarks: The diagonal is (x_scale_factor, y_scale_factor, z_scale_factor, 1)

Deprecated:: Use xform = ON_Xform::DiagonalTransformation(x_scale_factor,z_scale_factor,z_scale_factor);

◆ Scale() [4/4]

void ON_Xform::Scale	(	ON_3dPoint	fixed_point,
		double	scale_factor
	)

Description: Create uniform scale transformation with a specified fixed point. Parameters: fixed_point - [in] scale_factor - [in]

Deprecated:: Use xform = ON_Xform::ScaleTransformation(fixed_point,scale_factor)

◆ ScaleTransformation() [1/3]

static const ON_Xform ON_Xform::ScaleTransformation	(	const ON_3dPoint &	fixed_point,
		double	scale_factor
	)

static

◆ ScaleTransformation() [2/3]

static const ON_Xform ON_Xform::ScaleTransformation	(	const ON_3dPoint &	fixed_point,
		double	x_scale_factor,
		double	y_scale_factor,
		double	z_scale_factor
	)

static

◆ ScaleTransformation() [3/3]

static const ON_Xform ON_Xform::ScaleTransformation	(	const ON_Plane &	plane,
		double	x_scale_factor,
		double	y_scale_factor,
		double	z_scale_factor
	)

static

Description: Create non-uniform scale transformation with a specified fixed point. Parameters: plane - [in] plane.origin is the fixed point x_scale_factor - [in] plane.xaxis scale factor y_scale_factor - [in] plane.yaxis scale factor z_scale_factor - [in] plane.zaxis scale factor

◆ ScreenToClip()

bool ON_Xform::ScreenToClip	(	double	,
		double	,
		double	,
		double	,
		double	,
		double
	)

Computes transform that maps the screen box

     (left,right) X (bottom,top) X (near,far)

to the clipping box

      -1<x<1,-1<y<1,-1<z<1

◆ Shear()

void ON_Xform::Shear	(	const ON_Plane &	plane,
		const ON_3dVector &	x1,
		const ON_3dVector &	y1,
		const ON_3dVector &	z1
	)

Deprecated:: Use xform = ON_Xform::ShearTransformation(plane,x1,y1,z1);

◆ ShearTransformation()

static const ON_Xform ON_Xform::ShearTransformation	(	const ON_Plane &	plane,
		const ON_3dVector &	x1,
		const ON_3dVector &	y1,
		const ON_3dVector &	z1
	)

static

Description: Create shear transformation. Parameters: plane - [in] plane.origin is the fixed point x1 - [in] plane.xaxis scale factor y1 - [in] plane.yaxis scale factor z1 - [in] plane.zaxis scale factor

◆ SignOfDeterminant()

int ON_Xform::SignOfDeterminant ( bool bFastTest ) const

Quickly determine the sign of the determinant. Definitely good enough for graphics code.

Parameters

bFastTest When in double, pass true. If you need a fast answer and can tolerate extremely rare wrong answers, pass true. True definitely works for all common matrices used to transform 3d objects and all common view projection matrices.

Returns: +1, 0, or -1.

◆ TextureMapping()

static const ON_Xform ON_Xform::TextureMapping	(	const ON_3dVector &	offset,
		const ON_3dVector &	repeat,
		const ON_3dVector &	rotation
	)

static

◆ Translation() [1/2]

void ON_Xform::Translation ( const ON_3dVector & delta )

Deprecated:: Use xform = ON_Xform::TranslationTransformation(delta);

◆ Translation() [2/2]

void ON_Xform::Translation	(	double	dx,
		double	dy,
		double	dz
	)

Deprecated:: Use xform = ON_Xform::TranslationTransformation(dx,dy,dz);

◆ TranslationTransformation() [1/3]

static const ON_Xform ON_Xform::TranslationTransformation ( const ON_2dVector & delta )

static

Right column is (delta.x, delta.y, 0, 1).

◆ TranslationTransformation() [2/3]

static const ON_Xform ON_Xform::TranslationTransformation ( const ON_3dVector & delta )

static

Right column is (delta.x, delta.y, delta.z, 1).

◆ TranslationTransformation() [3/3]

static const ON_Xform ON_Xform::TranslationTransformation	(	double	dx,
		double	dy,
		double	dz
	)

static

Right column is (dx, dy, dz, 1).

◆ Transpose()

void ON_Xform::Transpose ( )

matrix operations

transposes 4x4 matrix

◆ WorldToCamera()

void ON_Xform::WorldToCamera	(	const ON_3dPoint &	,
		const ON_3dVector &	,
		const ON_3dVector &	,
		const ON_3dVector &
	)

standard viewing transformations

Member Data Documentation

◆ IdentityTransformation

const ON_Xform ON_Xform::IdentityTransformation

static

ON_Xform IdentityTransformation diagonal = (1,1,1,1)

◆ m_xform

double ON_Xform::m_xform[4][4]

[i][j] = row i, column j. I.e.,

           [0][0] [0][1] [0][2] [0][3]
           [1][0] [1][1] [1][2] [1][3]
           [2][0] [2][1] [2][2] [2][3]
           [3][0] [3][1] [3][2] [3][3]

◆ Nan

const ON_Xform ON_Xform::Nan

static

ON_Xform::Nan - every coefficient is ON_DBL_QNAN.

◆ Unset

const ON_Xform ON_Xform::Unset

static

ON_Xform::Unset - every coefficient is ON_UNSET_VALUE.

◆ Zero4x4

const ON_Xform ON_Xform::Zero4x4

static

ON_Xform::Zero4x4 - every coefficient is 0.0.

◆ ZeroTransformation

const ON_Xform ON_Xform::ZeroTransformation

static

ON_Xform ZeroTransformation diagonal = (0,0,0,1)

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Constructor & Destructor Documentation

◆ ON_Xform() [1/9]

◆ ~ON_Xform()

◆ ON_Xform() [2/9]

◆ ON_Xform() [3/9]

◆ ON_Xform() [4/9]

◆ ON_Xform() [5/9]

◆ ON_Xform() [6/9]

◆ ON_Xform() [7/9]

◆ ON_Xform() [8/9]

◆ ON_Xform() [9/9]

Member Function Documentation

◆ ActOnLeft()

◆ ActOnRight()

◆ Affineize()

◆ CameraToClip()

◆ CameraToWorld()

◆ ChangeBasis() [1/3]

◆ ChangeBasis() [2/3]

◆ ChangeBasis() [3/3]

◆ ClipFlag3d() [1/2]

◆ ClipFlag3d() [2/2]

◆ ClipFlag3dBox()

◆ ClipFlag4d() [1/2]

◆ ClipFlag4d() [2/2]

◆ ClipToCamera()

◆ ClipToScreen()

◆ Compare()

◆ CRC32()

◆ DecomposeAffine() [1/3]

◆ DecomposeAffine() [2/3]

◆ DecomposeAffine() [3/3]

◆ DecomposeRigid()

◆ DecomposeSimilarity()

◆ DecomposeSymmetric()

◆ DecomposeTextureMapping()

◆ Determinant()

◆ Diagonal()

◆ DiagonalTransformation() [1/3]

◆ DiagonalTransformation() [2/3]

◆ DiagonalTransformation() [3/3]

◆ GetEulerZYZ()

◆ GetKMLOrientationAnglesDegrees()

◆ GetKMLOrientationAnglesRadians()

◆ GetMappingXforms()

◆ GetQuaternion()

◆ GetSurfaceNormalXform()

◆ GetSurfaceNormalXformKeepLengthAndOrientation()

◆ GetYawPitchRoll()

◆ Hash()

◆ Identity()

◆ IntervalChange()

◆ Inverse()

◆ Invert()

◆ IsAffine()

◆ IsIdentity()

◆ IsLinear()

◆ IsNan()

◆ IsNotIdentity()

◆ IsRigid()

◆ IsRotation()

◆ IsSimilarity() [1/2]

◆ IsSimilarity() [2/2]

◆ IsTranslation()

◆ IsValid()

◆ IsValidAndNotZeroAndNotIdentity()

◆ IsZero()

◆ IsZero4x4() [1/2]

◆ IsZero4x4() [2/2]

◆ IsZeroTransformation() [1/2]

◆ IsZeroTransformation() [2/2]

◆ Linearize()

◆ Mirror()

◆ MirrorTransformation()

◆ operator!=()

◆ operator*() [1/6]