Similar< Shape > Class Template Reference

A shape transformed by a similarity transform (translation, rotation, and scale). More...

#include <geomc/shape/Similar.h>

Inheritance diagram for Similar< Shape >:

Public Types
using	elem_t = typename Shape::elem_t
using	point_t
	The type of a point in this object's space.
using	T = elem_t

Public Member Functions
	Similar ()
	Wrap a default-constructed shape with the identity transform.
	Similar (const Shape &shape)
	Wrap a shape with an identity transform.
	Similar (const Shape &shape, const Similarity< T, N > &xf)
	Wrap a shape with a similarity transform.
Rect< T, N >	bounds () const
	Compute the axis-aligned bounding box of the shape.
Vec< Shape::elem_t, N >	clip (Vec< Shape::elem_t, N > p) const
	Nearest point on the interior of the shape.
bool	contains (Vec< Shape::elem_t, N > p) const
	Shape-point overlap test.
bool	contains (typename Shape::point_t p) const
	Shape-point intersection test.
point_t	convex_support (point_t d) const
	Geometric convex support function.
Vec< T, N >	convex_support (Vec< T, N > d) const
Rect< T, 1 >	intersect (const Ray< T, N > &ray) const
	Ray-shape intersection.
bool	intersects (const Convex< Shape::elem_t, N, Shape > &other) const
	Convex shape overlap test.
template<typename S> requires requires (Similarity<T,N> xf, const Shape s, const S b) { s.intersects(b); { b / xf } -> std::same_as<S>; }
bool	intersects (const S &s) const
	Intersection with another shape. Available if the other shape can be transformed into our space while preserving its type.
template<typename S> requires requires (const Similar<Shape> s, const S b) { s.intersects(b); }
bool	intersects (const Similar< S > &s) const
	Intersecion with another similar shape. Available if our shape can intersect the other shape's base shape.
T	measure_boundary () const
	Measure the boundary (surface area) of the shape.
T	measure_interior () const
	Measure the interior (volume) of the shape.
Vec< T, N >	normal (Vec< T, N > p) const
	Direction away from the surface of the shape at point p.
	operator Transformed< Shape > () const
	Convert this shape to a Transformed shape.
bool	operator== (const Similar &other) const
Vec< T, N >	project (Vec< T, N > p) const
	Orthogonally project p to the surface of this shape.
T	sdf (Vec< T, N > p) const
	Signed distance function.
Similar< Rect< T, N > >	transformed_bounds () const

Static Public Member Functions
static constexpr bool	admits_cusps ()

Public Attributes
Shape	shape
	Un-transformed shape.
Similarity< T, N >	xf

Static Public Attributes
static constexpr index_t	N = Shape::N

Related Symbols
(Note that these are not member symbols.)
template<typename T, index_t N>
using	Box = Similar<Rect<T,N>>
	Convenience typedef for arbitrarily-oriented Rects.
template<typename Shape>
Similar< Shape >	operator* (const Similarity< typename Shape::elem_t, Shape::N > &xf, const Shape &shape)
	Transform the shape shape by wrapping it with a Similarity transform.
template<typename Shape>
Similar< Shape >	operator* (const Similarity< typename Shape::elem_t, Shape::N > &xf, const Similar< Shape > &s)
	Transform the shape s by xf.
template<typename Shape>
Similar< Shape > &	operator*= (Similar< Shape > &s, const Similarity< typename Shape::elem_t, Shape::N > &xf)
	In-place transform the shape s by xf.
template<typename Shape>
Similar< Shape >	operator/ (const Shape &s, const Similarity< typename Shape::elem_t, Shape::N > &xf)
	Transform the shape s by the inverse of xf.
template<typename Shape>
Similar< Shape >	operator/ (const Similar< Shape > &s, const Similarity< typename Shape::elem_t, Shape::N > &xf)
	Transform the shape s by the inverse of xf.
template<typename Shape>
Similar< Shape > &	operator/= (Similar< Shape > &s, const Similarity< typename Shape::elem_t, Shape::N > &xf)
	In-place transform the shape s by the inverse of xf.

Detailed Description

template<typename Shape>
class geom::Similar< Shape >

A shape transformed by a similarity transform (translation, rotation, and scale).

Similar transfrorms guarantee that shapes and relative distances are preserved. For arbitrarily-transformed shapes, see Transformed.

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.

Member Function Documentation

clip()

Vec< Shape::elem_t, N > clip ( Vec< Shape::elem_t, N > p ) const

inlineinherited

Nearest point on the interior of the shape.

If p is on the interior of the shape, return p unaltered; otherwise orthogonally project p to the shape's surface.

contains()

bool contains ( Vec< Shape::elem_t, N > p ) const

inlineinherited

Shape-point overlap test.

Return true if the point p is on the surface or interior of the shape, false otherwise.

convex_support() [1/2]

point_t convex_support ( point_t d ) const

inlineinherited

Geometric convex support function.

Returns the point on the surface of this convex shape that is furthest along direction d (i.e., has the highest dot product with d).

All shapes which implement this function automatically support geometrical intersection tests with any other Convex object.

Parameters

d	Direction along which to find a support plane.

Returns

A point on the surface of this convex shape.

convex_support() [2/2]

template<typename Shape>

Vec< T, N > convex_support ( Vec< T, N > d ) const

inline

Convex support function. Return the point on the surface of the shape which is farthest in the direction d.

intersects()

bool intersects ( const Convex< Shape::elem_t, N, Shape > & other ) const

inlineinherited

Convex shape overlap test.

Returns

True if and only if this convex shape overlaps other; false otherwise.

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

• geomc/shape/ShapeTypes.h
• geomc/shape/Similar.h