ON_Xform Class Reference

#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])
	ON_Xform (const float[4][4])
	ON_Xform (const double *)
	ON_Xform (const float *)
	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
	Computes matrix * transpose([x,y,z,w]). More...
void	ActOnRight (double, double, double, double, double[4]) const
	Computes [x,y,z,w] * matrix. More...
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)
	Get a change of basis transformation. More...
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
	Computes 3d point clipping flags and returns an int with bits set to indicate if the point is outside of the clipping box. More...
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
	Well ordered dictionary compare that is nan aware. More...
double	Determinant (double *=nullptr) const
void	Diagonal (double d)
double	GetMappingXforms (ON_Xform &P_xform, ON_Xform &N_xform) const
	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. More...
double	GetSurfaceNormalXform (ON_Xform &N_xform) const
	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. More...
void	Identity ()
	standard transformations More...
bool	IntervalChange (int dir, ON_Interval old_interval, ON_Interval new_interval)
	Calculates the transformation that linearly maps old_interval to new_interval. More...
ON_Xform	Inverse (double *=nullptr) const
bool	Invert (double *=nullptr)
bool	IsAffine () const
	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. More...
bool	IsIdentity (double zero_tolerance=0.0) const
bool	IsNan () const
	Test the entries of the transformation matrix to see if they are valid number. More...
bool	IsNotIdentity (double zero_tolerance=0.0) const
int	IsSimilarity () const
	A similarity transformation can be broken into a sequence of dialations, translations, rotations, and reflections. More...
bool	IsTranslation (double zero_tolerance=0.0) const
bool	IsValid () const
	Test the entries of the transformation matrix to see if they are valid number. More...
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)
	Create mirror transformation matrix. More...
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)
	Get transformation that projects to a plane More...
int	Rank (double *=nullptr) const
void	Rotation (double sin_angle, double cos_angle, ON_3dVector rotation_axis, ON_3dPoint rotation_center)
	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. More...
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)
	Calculate the minimal transformation that rotates start_dir to end_dir while fixing rotation_center. More...
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)
	Create rotation transformation that maps plane0 to plane1. More...
void	Scale (double x_scale_factor, double y_scale_factor, double z_scale_factor)
	Create non-uniform scale transformation with the origin as a fixed point. More...
void	Scale (const ON_3dVector &scale_vector)
	Create non-uniform scale transformation with the origin as the fixed point. More...
void	Scale (ON_3dPoint fixed_point, double scale_factor)
	Create uniform scale transformation with a specified fixed point. More...
void	Scale (const ON_Plane &plane, double x_scale_factor, double y_scale_factor, double z_scale_factor)
	Create non-uniform scale transformation with a specified fixed point. More...
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)
	Create non-uniform scale transformation with a specified fixed point. More...
static const ON_Xform	ShearTransformation (const ON_Plane &plane, const ON_3dVector &x1, const ON_3dVector &y1, const ON_3dVector &z1)
	Create shear transformation. More...
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

ON_Xform() [5/9]

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

explicit

ON_Xform() [6/9]

ON_Xform::ON_Xform ( const double *  )

explicit

ON_Xform() [7/9]

ON_Xform::ON_Xform ( const float *  )

explicit

ON_Xform() [8/9]

ON_Xform::ON_Xform ( const ON_Matrix &  )

explicit

ON_Xform() [9/9]

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

Member Function Documentation

ActOnLeft()

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

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

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
	)

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
	)

Parameters

plane0	inital plane
plane1	final plane

Returns

table true success false vectors for initial frame are not a basis

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
	)

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

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

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

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

ClipFlag3dBox()

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

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

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

ClipToCamera()

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

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

ClipToScreen()

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

Compare()

int ON_Xform::Compare

(

const ON_Xform &

other

)

const

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

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

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
	)

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

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.

Returns

True if this is an affine transformation.

A perspective transformation is not affine.

IsIdentity()

bool ON_Xform::IsIdentity

(

double

zero_tolerance = 0.0

)

const

Returns

true if matrix is the identity transformation

    1 0 0 0
    0 1 0 0
    0 0 1 0
    0 0 0 1

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

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

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

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

    1 0 0 dx
    0 1 0 dy
    0 0 1 dz
    0 0 0 1

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

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
	)

Create mirror transformation matrix.

Parameters

point_on_mirror_plane	[in] point on mirror plane
normal_to_mirror_plane	[in] normal to mirror plane

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

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

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

)

Get transformation that projects to a plane

Parameters

plane

[in] plane to project to

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
	)

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

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
	)

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
	)

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
	)

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]

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

)

Create non-uniform scale transformation with the origin as the fixed point.

Parameters

fixed_point	[in]
scale_vector	[in]

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
	)

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
	)

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

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
	)

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

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

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]

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)