Isometry< T, N > Class Template Reference

A rigid rotation and translation. More...

#include <geomc/linalg/Isometry.h>

Inheritance diagram for Isometry< T, N >:

Public Types
using	elem_t
	The coordinate type of this object.
using	point_t
	The type of a point in this object's space.

Public Member Functions
	Isometry (const Rotation< T, N > &rx)
	Isometry (const Rotation< T, N > &rx, const Vec< T, N > &tx)
	Isometry (const Vec< T, N > &tx)
Vec< T, N >	apply_direction (const Vec< T, N > v) const
	Transform a direction vector.
Vec< T, N >	apply_inverse_direction (const Vec< T, N > v) const
	Inverse transform a direction vector.
Isometry< T, N >	inverse () const
	Compute the inverse of the isometry.
	operator AffineTransform< T, N > () const
	Cast to an affine transform.
template<index_t M> requires (M > N)
	operator Isometry< T, M > () const
	Extend the dimensionality of this isometry.
template<typename U, index_t M> requires (M > N)
	operator Isometry< U, M > () const
	Extend the dimensionality of this isometry and change the coordinate type.
template<typename U>
	operator Isometry< U, N > () const
	Cast the underlying coordinate type.
Isometry< T, N >	operator* (const Isometry< T, N > &other) const
	Compose two isometric transforms.
Vec< T, N >	operator* (const Vec< T, N > &p) const
	Transform a point.
Isometry< T, N > &	operator*= (const Isometry< T, N > &other)
	Compose in-place.
Isometry< T, N >	operator+= (const Vec< T, N > &v)
	Apply a translation.
Isometry< T, N >	operator/ (const Isometry< T, N > &other) const
	Compose with the inverse of an isometry.
Isometry< T, N > &	operator/= (const Isometry< T, N > &other)
	In-place apply inverse.

Public Attributes
Rotation< T, N >	rx
	Rotation component.
Vec< T, N >	tx
	Translation component.

Static Public Attributes
static constexpr index_t	N
	The dimension of this object.

Related Symbols
(Note that these are not member symbols.)
template<typename T, index_t N>
Isometry< T, N >	mix (T s, const Isometry< T, N > &a, const Isometry< T, N > &b)
	Continuously interpolate two isometries.
template<typename T, index_t N>
Capsule< T, N >	operator* (const Isometry< T, N > &xf, const Capsule< T, N > &c)
	Transform a capsule by an isometry.
template<typename T, index_t N>
Cylinder< T, N >	operator* (const Isometry< T, N > &xf, const Cylinder< T, N > &c)
	Transform a cylinder by an isometry.
template<typename T, index_t N, typename Shape>
Dilated< Shape >	operator* (const Isometry< T, N > &xf, const Dilated< Shape > &s)
	Transform a dilated shape by an isometry.
template<typename T, index_t N>
Simplex< T, N >	operator* (const Isometry< T, N > &xf, const Simplex< T, N > &s)
	Transform a simplex by an isometry.
template<typename T, index_t N>
Sphere< T, N >	operator* (const Isometry< T, N > &xf, const Sphere< T, N > &s)
	Transform a sphere by an isometry.
template<typename T, index_t N>
Isometry< T, N >	operator* (const Isometry< T, N > &xf, T s)
	Scale the magnitude of an isometry.
template<typename T, index_t N>
Isometry< T, N >	operator* (T s, const Isometry< T, N > &xf)
	Scale the magnitude of an isometry. A scale of 0 produces an identity transform. Applying a scale of 1 to an isometry results in no change.
template<typename T, index_t N>
Isometry< T, N >	operator+ (const Isometry< T, N > &i, const Vec< T, N > &v)
	Apply a translation to an isometry.
template<typename T, index_t N>
Isometry< T, N >	operator+ (const Vec< T, N > &v, const Isometry< T, N > &i)
	Apply a translation to an isometry.
template<typename T, index_t N>
Capsule< T, N >	operator/ (const Capsule< T, N > &c, const Isometry< T, N > &xf)
	Inverse-transform a capsule by an isometry.
template<typename T, index_t N>
Cylinder< T, N >	operator/ (const Cylinder< T, N > &c, const Isometry< T, N > &xf)
	Inverse-transform a cylinder by an isometry.
template<typename T, index_t N, typename Shape>
Dilated< Shape >	operator/ (const Dilated< Shape > &s, const Isometry< T, N > &xf)
	Inverse-transform a dilated shape by an isometry.
template<typename T, index_t N>
Simplex< T, N >	operator/ (const Simplex< T, N > &s, const Isometry< T, N > &xf)
	Inverse-transform a simplex by an isometry.
template<typename T, index_t N>
Sphere< T, N >	operator/ (const Sphere< T, N > &s, const Isometry< T, N > &xf)
	Inverse-transform a sphere by an isometry.
template<typename T, index_t N>
Vec< T, N >	operator/ (const Vec< T, N > &v, const Isometry< T, N > &i)
	Transform a point.

Detailed Description

template<typename T, index_t N>
class geom::Isometry< T, N >

A rigid rotation and translation.

Isometric transfroms do not have any skew or scales; they preserve shapes, angles, and distances.

Isometries meet the Transform concept. For transforms which include a scaling, see Similarity. For nonuniform scaling or skew transforms, see AffineTransform.

Isometries compose like transforms, with multiplication on the left:

Isometry<T,N> i1, i2;
Isometry<T,N> i3 = i2 * i1;  // isometry which applies i1, then i2
Vec<T,N> v = i3 * i1 * v0;   // apply i1 to v0, then i3 to the result
Sphere<T,N> s = i1 * sphere; // apply i1 to a sphere

Isometries can be inverted with the / operator:

Isometry<T,N> i1, i2;
Isometry<T,N> i3 = i2 / i1; // isometry which takes i1 to i2
Vec<T,N> v = v0 / i3;       // apply the inverse of i3 to v0

Compose with rotations and translations:

Isometry<T,3> i;
Rotation<T,3> r;
Isoemtry<T,3> i2 = r * i; // i2 is i with r post-applied
Isometry<T,3> i3 = i + Vec<T,3>(1,2,3); // i3 is i translated by (1,2,3)

Member Typedef Documentation

point_t

using point_t

inherited

The type of a point in this object's space.

An N-vector of T if N > 1, otherwise a T.

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

• geomc/linalg/Isometry.h
• geomc/shape/Capsule.h
• geomc/shape/Cylinder.h
• geomc/shape/Dilated.h
• geomc/shape/Simplex.h
• geomc/shape/Sphere.h