a linear 3D transformation More...

#include <transformation_3d.h>

Inheritance diagram for lass::prim::Transformation3D< T >:

Public Member Functions
	Transformation3D ()
	construct an identity transformation.

	Transformation3D (const TPoint &origin, const TVector &baseX, const TVector &baseY, const TVector &baseZ)
	construct an matrix from an origin and three base vectors

template<typename InputIterator>
	Transformation3D (InputIterator first, InputIterator last)
	construct a transformation from a 4x4 tranformation matrix.

const TSelf	inverse () const
	return the inverse transformation.

const TValue *	matrix () const
	Return pointer to row major matrix representation of transformation.

const TValue *	inverseMatrix () const
	Return pointer to row major matrix representation of inverse transformation.

Static Public Member Functions
static const TSelf	identity ()
	make a 3D identity transformation

static const TSelf	translation (const TVector &offset)
	make a 3D transformation representing a translation

static const TSelf	scaler (TParam scale)
	make a 3D transformation representing a uniform scaling

static const TSelf	scaler (const TVector &scale)
	make a 3D transformation representing a scaling with different factors per axis

static const TSelf	rotation (XYZ axis, TParam radians)
	make a 3D transformation representing a rotation around a primary axis

static const TSelf	rotation (const TVector &axis, TParam radians)
	make a 3D transformation representing a rotation around an arbitrary axis

Related Symbols
(Note that these are not member symbols.)
template<typename T, class MMP>
Aabb2D< T, MMP >	transform (const Aabb2D< T, MMP > &subject, const Transformation2D< T > &transformation)
	apply transformation to axis aligned bounding box

template<typename T, class MMP>
Aabb3D< T, MMP >	transform (const Aabb3D< T, MMP > &subject, const Transformation3D< T > &transformation)
	apply transformation to axis aligned bounding box

template<typename T>
ColorRGBA	transform (const ColorRGBA &subject, const Transformation3D< T > &transformation)
	apply transformation to axis aligned bounding box

template<typename T, class NP>
Plane3D< T, Cartesian, NP >	transform (const Plane3D< T, Cartesian, NP > &plane, const Transformation3D< T > &transformation)
	apply transformation to cartesian plane

template<typename T, class NP>
Plane3D< T, Parametric, NP >	transform (const Plane3D< T, Parametric, NP > &plane, const Transformation3D< T > &transformation)
	apply transformation to parametric plane

template<typename T, class NP>
Plane3D< T, Combined, NP >	transform (const Plane3D< T, Combined, NP > &plane, const Transformation3D< T > &transformation)
	apply transformation to combined plane

template<typename T, class NP, class PP>
Ray3D< T, NP, PP >	transform (const Ray3D< T, NP, PP > &subject, const Transformation3D< T > &transformation)
	apply transformation to ray

template<typename T, class NP, class PP>
Ray3D< T, NP, PP >	transform (const Ray3D< T, NP, PP > &subject, const Transformation3D< T > &transformation, T &tRay)
	apply transformation to ray, and rescale a parameter to represent same point

template<typename T>
Transformation3D< T >	concatenate (const Transformation3D< T > &first, const Transformation3D< T > &second)
	concatenate two transformations first and second in one.

template<typename T>
Vector3D< T >	transform (const Vector3D< T > &subject, const Transformation3D< T > &transformation)
	apply transformation to a vector

template<typename T>
Point3D< T >	transform (const Point3D< T > &subject, const Transformation3D< T > &transformation)
	apply transformation to a point

template<typename T>
Vector3D< T >	normalTransform (const Vector3D< T > &subject, const Transformation3D< T > &transformation)
	apply transformation to a normal vector.

template<typename T>
std::pair< Vector3D< T >, T >	normalTransform (const std::pair< Vector3D< T >, T > &subject, const Transformation3D< T > &transformation)
	apply transformation to a 4D normal vector.

Detailed Description

template<typename T>
class lass::prim::Transformation3D< T >

a linear 3D transformation

Author: Bram de Greve [BdG]

Definition at line 108 of file transformation_3d.h.

Constructor & Destructor Documentation

◆ Transformation3D() [1/3]

template<typename T>

lass::prim::Transformation3D< T >::Transformation3D ( )

construct an identity transformation.

An identity transformation transforms every point to itself.

Definition at line 62 of file transformation_3d.inl.

Referenced by identity(), rotation(), rotation(), scaler(), scaler(), and translation().

◆ Transformation3D() [2/3]

template<typename T>

lass::prim::Transformation3D< T >::Transformation3D	(	const TPoint &	origin,
		const TVector &	baseX,
		const TVector &	baseY,
		const TVector &	baseZ )

construct an matrix from an origin and three base vectors

TVector3D<T> i, j, k;
TPoint3D<T> o, p;
// ...
 
Transformation3D<T> transformation(o, i, j, k);
LASS_ASSERT(transform(p, transformation) == (o + i * p.x + j * p.y + k * p.z));

Definition at line 82 of file transformation_3d.inl.

◆ Transformation3D() [3/3]

template<typename T>

template<typename InputIterator>

lass::prim::Transformation3D< T >::Transformation3D	(	InputIterator	first,
		InputIterator	last )

construct a transformation from a 4x4 tranformation matrix.

The elements of the 4x4 matrix will represented in a row major way by an iterator range [first, last) of 16 elements.

Definition at line 102 of file transformation_3d.inl.

Member Function Documentation

◆ inverse()

template<typename T>

const Transformation3D< T > lass::prim::Transformation3D< T >::inverse ( ) const

return the inverse transformation.

The inverse is calculated on the first call, and then cached for later use. For the transformation, we've use the C version of Cramer's rule as described in the Intel (R) article "Streaming SIMD Extensions -Inverse of 4x4 Matrix" which can be found here: http://www.intel.com/design/pentiumiii/sml/245043.htm

Definition at line 135 of file transformation_3d.inl.

Referenced by rotation(), scaler(), scaler(), and translation().

◆ matrix()

template<typename T>

const Transformation3D< T >::TValue * lass::prim::Transformation3D< T >::matrix ( ) const

inline

Return pointer to row major matrix representation of transformation.

This is for immediate use only, like std::basic_string::data().

Definition at line 149 of file transformation_3d.inl.

Referenced by lass::prim::Transformation3D::concatenate(), lass::prim::Transformation3D::transform(), lass::prim::Transformation3D::transform(), and lass::prim::Transformation3D::transform().

◆ inverseMatrix()

template<typename T>

const Transformation3D< T >::TValue * lass::prim::Transformation3D< T >::inverseMatrix ( ) const

inline

Return pointer to row major matrix representation of inverse transformation.

This is for immediate use only, like std::basic_string::data().

Definition at line 162 of file transformation_3d.inl.

Referenced by lass::prim::Transformation3D::normalTransform(), and lass::prim::Transformation3D::normalTransform().

Friends And Related Symbol Documentation

◆ transform()

template<typename T, class NP, class PP>

Ray3D< T, NP, PP > transform	(	const Ray3D< T, NP, PP > &	subject,
		const Transformation3D< T > &	transformation,
		T &	tRay )

apply transformation to ray, and rescale a parameter to represent same point

Parameters

tRay

INPUT & OUTPUT
if direction gets renormalized, then a point on ray is no longer represented by same parameter. Adjust parameter tRay to fix this.
If you fill in 1 as tRay, you can use the result to rescale multiple parameters by multiplying it.
transform(ray, transf).point(t') == transform(ray.point(t), transf)

Definition at line 111 of file ray_3d_transformation_3d.h.

◆ concatenate()

template<typename T>

Transformation3D< T > concatenate	(	const Transformation3D< T > &	first,
		const Transformation3D< T > &	second )

concatenate two transformations first and second in one.

The result is one transformation that performs the same actions as first performing first and then second. Hence, the following lines of code are equivalent (ignoring numerical imprecions):

y = transform(x, concatenate(first, second));

y = transform(transform(x, first), second);

lass::prim::Transformation3D::concatenate

Transformation3D< T > concatenate(const Transformation3D< T > &first, const Transformation3D< T > &second)

concatenate two transformations first and second in one.

Definition transformation_3d.inl:555

Definition at line 555 of file transformation_3d.inl.

◆ normalTransform() [1/2]

template<typename T>

Vector3D< T > normalTransform	(	const Vector3D< T > &	subject,
		const Transformation3D< T > &	transformation )

apply transformation to a normal vector.

Vectors that represent a normal vector should transform differentely than ordinary vectors. Use this transformation function for normals.

Definition at line 615 of file transformation_3d.inl.

◆ normalTransform() [2/2]

template<typename T>

std::pair< Vector3D< T >, T > normalTransform	(	const std::pair< Vector3D< T >, T > &	subject,
		const Transformation3D< T > &	transformation )

apply transformation to a 4D normal vector.

Vectors that represent a normal vector should transform differentely than ordinary vectors. Use this transformation function for normals.

Cartesian planes have a 4D normal vector that must be transformed in 3D. Use this function to do it:

// ax + by + cz + d == 0

normalTransform(std::make_pair(Vector3D<float>(a, b, c), d), transformation);

lass::prim::Transformation3D::normalTransform

Vector3D< T > normalTransform(const Vector3D< T > &subject, const Transformation3D< T > &transformation)

apply transformation to a normal vector.

Definition transformation_3d.inl:615

lass::prim::Vector3D

3D Vector

Definition vector_3d.h:73

Definition at line 640 of file transformation_3d.inl.

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

Public Member Functions

Static Public Member Functions

Related Symbols

Detailed Description

Constructor & Destructor Documentation

◆ Transformation3D() [1/3]

◆ Transformation3D() [2/3]

◆ Transformation3D() [3/3]

Member Function Documentation

◆ inverse()

◆ matrix()

◆ inverseMatrix()

Friends And Related Symbol Documentation

◆ transform()

◆ concatenate()

◆ normalTransform() [1/2]

◆ normalTransform() [2/2]