Class for Transform objects. More...

#include <Transform.h>

Public Member Functions
	Transform ()
	Default Transform constructor. More...

	Transform (const Transform &transform)
	Transform copy constructor. More...

	~Transform ()
	Transform destructor. More...

Transform &	operator= (const Transform &transform)
	Transform assignment operator. More...

Point	apply (const Point &point) const
	Apply a transformation to a Point. More...

Direction	apply (const Direction &direction) const
	Apply a transformation to a Direction. More...

Normal	apply (const Normal &normal) const
	Apply a transformation to a Normal. More...

Ray	apply (const Ray &ray) const
	Apply a transformation to a Ray. More...

Point	applyInverse (const Point &point) const
	Apply an inverse transformation to a Point. More...

Direction	applyInverse (const Direction &direction) const
	Apply an inverse transformation to a Direction. More...

Normal	applyInverse (const Normal &normal) const
	Apply an inverse transformation to a Normal. More...

Ray	applyInverse (const Ray &ray) const
	Apply an inverse transformation to a Ray. More...

void	rotateX (double rx)
	Apply a rotation about the X-axis. More...

void	rotateY (double ry)
	Apply a rotation about the Y-axis. More...

void	rotateZ (double rz)
	Apply a rotation about the Z-axis. More...

void	scale (double s)
	Apply a uniform scaling in all directions. More...

void	scale (double sx, double sy, double sz)
	Apply a non-uniform scaling along the axes. More...

void	translate (double tx, double ty, double tz)
	Shift along the X-, Y-, and Z-axes. More...

void	translate (const Direction &direction)
	Shift along a Direction Vector. More...

Private Attributes
Matrix	T_
	The 4x4 homogeneous transformation matrix. More...

Matrix	Tinv_
	The 4x4 inverse transformation matrix. More...

Detailed Description

Class for Transform objects.

A Transform is essentially a 4x4 matrix which is applied to a Vector represented in homogeneous form. How the Transform is applied, however, depends on what the Vector represents. This is accounted for by having separate subclasses of Vector for Point, Normal, and Direction representations. The Transform can then be applied to any of these in the correct way.

A Transform is computed through a series of basic transformations, such as scaling or translation. As these are applied, an inverse transformation matrix is also computed, by applying geometrical reasoning to generate matrix inverses.

Constructor & Destructor Documentation

◆ Transform() [1/2]

Transform::Transform ( )

Default Transform constructor.

Creates a Transform with an identity transformation matrix.

◆ Transform() [2/2]

Transform::Transform ( const Transform & transform )

Transform copy constructor.

Creates a Transform with an identity transformation matrix.

Parameters

transform The Transform to copy to this.

◆ ~Transform()

Transform::~Transform ( )

Transform destructor.

Member Function Documentation

◆ apply() [1/4]

Direction Transform::apply ( const Direction & direction ) const

Apply a transformation to a Direction.

A Direction is transformed by applying the transformation matrix to a homogeneous vector with a 0 in the last co-ordinate. This prevents translations from being applied to Direction vectors.

Parameters

direction The Direction to Transform.

Returns: The transformed Direction.

◆ apply() [2/4]

Normal Transform::apply ( const Normal & normal ) const

Apply a transformation to a Normal.

A Normal is transformed by applying the transposed inverse transformation matrix. As with ordinary Direction vectors, the homgeneous form is created with a 0 in the last co-ordinate to prevent translations from being applied. For discussion on why the normal transforms with the transposed inverse, see the lecture notes or Abnormal Normals by Eric Haines.

Parameters

normal The Normal to Transform.

Returns: The transformed Normal.

◆ apply() [3/4]

Point Transform::apply ( const Point & point ) const

Apply a transformation to a Point.

A Point is transformed by applying the transformation matrix to a homogeneous vector with a 1 in the last co-ordinate.

Parameters

point The Point to Transform.

Returns: The transformed Point.

◆ apply() [4/4]

Ray Transform::apply ( const Ray & ray ) const

Apply a transformation to a Ray.

A Ray is a Point and a Direction, and both need to be transformed appropriately.

Parameters

ray	The Ray to Transform.

Returns: The transformed Ray.

◆ applyInverse() [1/4]

Direction Transform::applyInverse ( const Direction & direction ) const

Apply an inverse transformation to a Direction.

Parameters

direction The Direction to Transform.

Returns: The transformed Direction.

See also: Transform::apply(const Direction&) const

◆ applyInverse() [2/4]

Normal Transform::applyInverse ( const Normal & normal ) const

Apply an inverse transformation to a Normal.

Parameters

normal The Normal to Transform.

Returns: The transformed Normal.

See also: Transform::apply(const Normal&) const

◆ applyInverse() [3/4]

Point Transform::applyInverse ( const Point & point ) const

Apply an inverse transformation to a Point.

Parameters

point The Point to Transform.

Returns: The transformed Point.

See also: Transform::apply(const Point&) const

◆ applyInverse() [4/4]

Ray Transform::applyInverse ( const Ray & ray ) const

Apply an inverse transformation to a Ray.

Parameters

ray	The Ray to Transform.

Returns: The transformed Ray.

See also: Transform::apply(const Ray&) const

◆ operator=()

Transform & Transform::operator= ( const Transform & transform )

Transform assignment operator.

Parameters

transform The Transform to assign to this.

Returns: A reference to this to allow for chaining of assignment.

◆ rotateX()

void Transform::rotateX ( double rx )

Apply a rotation about the X-axis.

Rotate by some angle (in degrees) about the X-axis. Following the right-handed co-ordinate convention, this is a rotation from the positive Y-axis towards the positive Z-axis.

Parameters

rx	The rotation in degrees.

◆ rotateY()

void Transform::rotateY ( double ry )

Apply a rotation about the Y-axis.

Rotate by some angle (in degrees) about the Y-axis. Following the right-handed co-ordinate convention, this is a rotation from the positive Z-axis towards the positive X-axis.

Parameters

ry	The rotation in degrees.

◆ rotateZ()

void Transform::rotateZ ( double rz )

Apply a rotation about the Z-axis.

Rotate by some angle (in degrees) about the Z-axis. Following the right-handed co-ordinate convention, this is a rotation from the positive X-axis towards the positive Y-axis.

Parameters

rz	The rotation in degrees.

◆ scale() [1/2]

void Transform::scale ( double s )

Apply a uniform scaling in all directions.

Scale by some constant factor in all directions. If the scaling factor is greater than 1 it represents a magnification. Scaling factors less than 1 represent a reduction. Negative scaling factors are valid but cause a reflection as well as a scaling.

Parameters

s	The scaling factor to apply.

◆ scale() [2/2]

void Transform::scale	(	double	sx,
		double	sy,
		double	sz
	)

Apply a non-uniform scaling along the axes.

Scale by different factors in the X-, Y-, and Z-directions. If a scaling factor is greater than 1 it represents a magnification. Scaling factors less than 1 represent a reduction. Negative scaling factors are valid but cause a reflection as well as a scaling.

Parameters

sx	The scaling factor to apply in the X-direction.
sy	The scaling factor to apply in the Y-direction.
sz	The scaling factor to apply in the Z-direction.

◆ translate() [1/2]

void Transform::translate ( const Direction & direction )

Shift along a Direction Vector.

Parameters

direction The Direction to move along.

◆ translate() [2/2]

void Transform::translate	(	double	tx,
		double	ty,
		double	tz
	)

Shift along the X-, Y-, and Z-axes.

Shift by some distance along each of the X-, Y-, and Z- axes.

Parameters

tx	The distance to move in the X-direction.
ty	The distance to move in the Y-direction.
tz	The distance to move in the Z-direction.

Member Data Documentation

◆ T_

Matrix Transform::T_

private

The 4x4 homogeneous transformation matrix.

◆ Tinv_

Matrix Transform::Tinv_

private

The 4x4 inverse transformation matrix.

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

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Transform() [1/2]

◆ Transform() [2/2]

◆ ~Transform()

Member Function Documentation

◆ apply() [1/4]

◆ apply() [2/4]

◆ apply() [3/4]

◆ apply() [4/4]

◆ applyInverse() [1/4]

◆ applyInverse() [2/4]

◆ applyInverse() [3/4]

◆ applyInverse() [4/4]

◆ operator=()

◆ rotateX()

◆ rotateY()

◆ rotateZ()

◆ scale() [1/2]

◆ scale() [2/2]

◆ translate() [1/2]

◆ translate() [2/2]

Member Data Documentation

◆ T_

◆ Tinv_