#include <opennurbs_xform.h>

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

	ON_Xform (const ON_Xform &)=default

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

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

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

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

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

	ON_Xform (const ON_Matrix &)

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

	~ON_Xform ()=default

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

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

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_Plane &plane0, const ON_Plane &plane1)

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_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)

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

double	Determinant (double *=nullptr) const

void	Diagonal (double d)

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

double	GetSurfaceNormalXform (ON_Xform &N_xform) 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	IsNan () const

bool	IsNotIdentity (double zero_tolerance=0.0) const

int	IsSimilarity () 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	IsZeroTransformation () const

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_3dPoint	operator* (const ON_3dPoint &) const

ON_4dPoint	operator* (const ON_4dPoint &) const

ON_2dVector	operator* (const ON_2dVector &) const

ON_3dVector	operator* (const ON_3dVector &) 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_Xform &)=default

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

bool	operator== (const ON_Xform &rhs) const

double *	operator[] (int)

const double *	operator[] (int) const

void	PlanarProjection (const ON_Plane &plane)

int	Rank (double *=nullptr) const

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

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

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

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_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_Plane &plane0, const ON_Plane &plane1)

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

void	Scale (const ON_3dVector &scale_vector)

void	Scale (ON_3dPoint fixed_point, double scale_factor)

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

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 (double d)

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

static const ON_Xform	DiagonalTransformation (const ON_3dVector &diagnoal)

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	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

◆ 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_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 - inital plane plane1 - final plane

Returns: 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().

◆ 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_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)

◆ 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: 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: 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: 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 bTeztZ

◆ 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.

◆ Determinant()

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

◆ Diagonal()

void ON_Xform::Diagonal ( double d )

◆ DiagonalTransformation() [1/3]

static const ON_Xform ON_Xform::DiagonalTransformation ( double d )

static

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

◆ DiagonalTransformation() [2/3]

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

static

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

◆ DiagonalTransformation() [3/3]

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

static

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

◆ 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 recalcalculate 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 invertable and P_xform and N_xform were calculated. False if "this" is not invertable, in which case the returned P_xform and N_xform are the identity.

◆ 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 tranform normal vectors. Parameters: N_xform - [out] Returns: The determinant of the transformation. If non-zero, "this" is invertable and N_xform can be calculated. False if "this" is not invertable, in which case the returned N_xform = this with the right hand column and bottom row zeroed out.

◆ Identity()

void ON_Xform::Identity ( )

standard transformations

diagonal is (1,1,1,1)

◆ 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 An affine transformation can be broken into a linear transformation and a translation. Example: A perspective transformation is not affine. Returns: True if this is an affine transformation.

◆ 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.

◆ 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.

◆ IsSimilarity()

int ON_Xform::IsSimilarity ( ) const

Description: A similarity transformation can be broken into a sequence of dialations, translations, rotations, and reflections. Returns: +1: This transformation is an orientation preserving similarity. -1: This transformation is an orientation reversing similarity. 0: This transformation is not a similarity.

◆ 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()

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

◆ IsZeroTransformation()

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

◆ 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.

◆ 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.

◆ operator*() [2/6]

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

◆ operator*() [3/6]

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

◆ operator*() [4/6]

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

◆ operator*() [5/6]

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

default

◆ operator=() [2/2]

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==()

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

◆ 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 transformaton 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	(	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() [2/6]

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() [3/6]

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.

◆ Rotation() [4/6]

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() [5/6]

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() [6/6]

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]

◆ Scale() [1/4]

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)

◆ Scale() [2/4]

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)

◆ Scale() [3/4]

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]

◆ Scale() [4/4]

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

◆ 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
	)

◆ 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

◆ Translation() [1/2]

void ON_Xform::Translation ( const ON_3dVector & delta )

◆ Translation() [2/2]

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

◆ 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()

◆ Determinant()

◆ Diagonal()

◆ DiagonalTransformation() [1/3]

◆ DiagonalTransformation() [2/3]

◆ DiagonalTransformation() [3/3]

◆ GetMappingXforms()

◆ GetSurfaceNormalXform()

◆ Identity()

◆ IntervalChange()

◆ Inverse()

◆ Invert()

◆ IsAffine()

◆ IsIdentity()

◆ IsNan()

◆ IsNotIdentity()

◆ IsSimilarity()

◆ IsTranslation()

◆ IsValid()

◆ IsValidAndNotZeroAndNotIdentity()

◆ IsZero()

◆ IsZero4x4()

◆ IsZeroTransformation()

◆ Mirror()

◆ operator!=()

◆ operator*() [1/6]

◆ operator*() [2/6]

◆ operator*() [3/6]

◆ operator*() [4/6]

◆ operator*() [5/6]

◆ operator*() [6/6]

◆ operator+()

◆ operator-()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ PlanarProjection()

◆ Rank()

◆ Rotation() [1/6]

◆ Rotation() [2/6]

◆ Rotation() [3/6]

◆ Rotation() [4/6]

◆ Rotation() [5/6]

◆ Rotation() [6/6]

◆ Scale() [1/4]

◆ Scale() [2/4]

◆ Scale() [3/4]

◆ Scale() [4/4]