EBGeometry::Affine3T< T > Struct Template Reference

An affine map of 3D space, x -> A x + b, with A stored by rows. More...

#include <EBGeometry_Affine.hpp>

Public Member Functions
Vec3T< T >	operator() (const Vec3T< T > &a_point) const noexcept
	Apply the map.
Affine3T	then (const Affine3T &a_next) const noexcept
	The map that applies this one and then a_next.
bool	isAxisAligned () const noexcept
	Whether every row of A has at most one non-zero entry, so that the map sends axis-aligned boxes to axis-aligned boxes exactly.
BoundingVolumes::AABBT< T >	transform (const BoundingVolumes::AABBT< T > &a_box) const noexcept
	A box enclosing the image of a box under the map.

Static Public Member Functions
static Affine3T	identity () noexcept
	The identity map.
static Affine3T	translation (const Vec3T< T > &a_shift) noexcept
	A translation.
static Affine3T	rotation (const T a_degrees, const size_t a_axis) noexcept
	A rotation about a coordinate axis, counterclockwise seen from the positive end of the axis.
static Affine3T	rotation (const T a_degrees, const Vec3T< T > &a_axis) noexcept
	A rotation about an arbitrary axis through the origin, counterclockwise seen from the positive end of the axis (Rodrigues' formula).
static Affine3T	scaling (const T a_factor) noexcept
	A uniform scaling.
static Affine3T	reflection (const size_t a_axis) noexcept
	A reflection in a coordinate plane through the origin.

Public Attributes
Vec3T< T >	m_row0
	First row of A.
Vec3T< T >	m_row1
	Second row of A.
Vec3T< T >	m_row2
	Third row of A.
Vec3T< T >	m_shift
	The shift b.

Detailed Description

template<class T>
struct EBGeometry::Affine3T< T >

An affine map of 3D space, x -> A x + b, with A stored by rows.

A plain, trivially copyable value type. The factory functions build the maps the transforms need; then() composes two maps. Value-initialized (Affine3T<T>{}), it is the zero map, not the identity: use identity().

Template Parameters

T	Floating-point precision.

Member Function Documentation

identity()

template<class T >

static Affine3T EBGeometry::Affine3T< T >::identity ( )

inlinestaticnoexcept

The identity map.

Returns

x -> x.

isAxisAligned()

template<class T >

bool EBGeometry::Affine3T< T >::isAxisAligned ( ) const

inlinenoexcept

Whether every row of A has at most one non-zero entry, so that the map sends axis-aligned boxes to axis-aligned boxes exactly.

Returns

True for translations, scalings, reflections and quarter-turn rotations.

operator()()

template<class T >

Vec3T< T > EBGeometry::Affine3T< T >::operator() ( const Vec3T< T > &  a_point ) const

inlinenoexcept

Apply the map.

Parameters

[in]

a_point

Point.

Returns

A a_point + b.

reflection()

template<class T >

static Affine3T EBGeometry::Affine3T< T >::reflection ( const size_t  a_axis )

inlinestaticnoexcept

A reflection in a coordinate plane through the origin.

Parameters

[in]

a_axis

Axis normal to the plane (0, 1 or 2); that coordinate changes sign.

Returns

x -> x with component a_axis negated.

rotation() [1/2]

template<class T >

static Affine3T EBGeometry::Affine3T< T >::rotation ( const T  a_degrees, const size_t  a_axis  )

inlinestaticnoexcept

A rotation about a coordinate axis, counterclockwise seen from the positive end of the axis.

Parameters

[in]	a_degrees	Angle in degrees.
[in]	a_axis	Coordinate axis (0, 1 or 2).

Returns

x -> R x.

rotation() [2/2]

template<class T >

static Affine3T EBGeometry::Affine3T< T >::rotation ( const T  a_degrees, const Vec3T< T > &  a_axis  )

inlinestaticnoexcept

A rotation about an arbitrary axis through the origin, counterclockwise seen from the positive end of the axis (Rodrigues' formula).

Parameters

[in]	a_degrees	Angle in degrees.
[in]	a_axis	Axis direction; need not be normalized, must not be zero.

Returns

x -> R x.

scaling()

template<class T >

static Affine3T EBGeometry::Affine3T< T >::scaling ( const T  a_factor )

inlinestaticnoexcept

A uniform scaling.

Parameters

[in]

a_factor

Scale factor.

Returns

x -> a_factor x.

then()

template<class T >

Affine3T EBGeometry::Affine3T< T >::then ( const Affine3T< T > &  a_next ) const

inlinenoexcept

The map that applies this one and then a_next.

Parameters

[in]

a_next

Map to apply second.

Returns

x -> a_next(this(x)).

transform()

template<class T >

BoundingVolumes::AABBT< T > EBGeometry::Affine3T< T >::transform ( const BoundingVolumes::AABBT< T > &  a_box ) const

inlinenoexcept

A box enclosing the image of a box under the map.

Exact for an axis-aligned map, which also keeps an unbounded box unbounded only along the axes it maps an unbounded axis to. For any other map, a bounded box's image is enclosed by the box around its eight transformed corners, and an unbounded box gives an unbounded box. Coordinates saturate at plus or minus Math::Limits<T>::max(). An empty box stays empty.

Parameters

[in]

a_box

Box.

Returns

Box enclosing the image.

translation()

template<class T >

static Affine3T EBGeometry::Affine3T< T >::translation ( const Vec3T< T > &  a_shift )

inlinestaticnoexcept

A translation.

Parameters

[in]

a_shift

Shift.

Returns

x -> x + a_shift.

---

The documentation for this struct was generated from the following file:

• Source/EBGeometry_Affine.hpp