Simplex< T, N > Class Template Reference

A simplex in N dimensions (e.g. a tetrahedron, triangle, line, point). More...

#include <geomc/shape/Simplex.h>

Inheritance diagram for Simplex< T, N >:

Public Types
typedef PointType< T, N >::point_t	point_t
typedef T	elem_t
	The coordinate type of this shape.

Public Member Functions
	Simplex ()
	Construct an empty simplex, with no vertices.
	Simplex (const Vec< T, N > *verts, index_t n)
	Construct an n-cornered simplex with vertices at verts.
Vec< T, N > &	operator[] (index_t i)
	Get the ith vertex in this simplex.
Vec< T, N >	operator[] (index_t i) const
	Get the ith vertex in this simplex.
bool	operator== (const Simplex< T, N > &other) const
	Simplex equality check. More...
bool	operator!= (const Simplex< T, N > &other) const
	Simplex inequality check.
Simplex< T, N >	operator| (const Vec< T, N > &p) const
	Return a copy of this simplex with an additional vertex at p. More...
Simplex< T, N > &	operator|= (const Vec< T, N > &p)
	Extend this simplex to include p by adding p as a vertex. More...
Simplex< T, N > &	operator*= (const AffineTransform< T, N > &xf)
	Apply a transformation to the points of this Simplex.
Simplex< T, N > &	operator/= (const AffineTransform< T, N > &xf)
	Apply an inverse transformation to the points of this Simplex.
Rect< T, 1 >	intersect (const Ray< T, N > &r) const
	Ray-shape intersection. More...
bool	projection_contains (const Vec< T, N > &p, Vec< T, N > *params=nullptr) const
	Project the point to the simplex along its orthogonal basis (if there is one) and test for containment. More...
T	volume () const
	Compute the volume of the simplex. More...
bool	contains (const Vec< T, N > &p) const
	Simplex-point intersection test. More...
T	sdf (Vec< T, N > p) const
	Return the signed distance to the surface of the shape.
Simplex< T, N >	exclude (index_t i) const
	Create a new sub-simplex by excluding the ith vertex in this simplex.
Vec< T, N >	project (const Vec< T, N > &p, Simplex< T, N > *onto=nullptr) const
	Project p to the nearest point on the simplex. More...
Rect< T, N >	bounds () const
Vec< T, N >	convex_support (Vec< T, N > d) const
bool	intersects (const Convex< T, N, Shape > &other) const
	Convex shape overlap test. More...
bool	contains (Vec< T, N > p) const
	Shape-point overlap test. More...

Public Attributes
Vec< T, N >	pts [N+1]
	Vertices of this simplex.
index_t	n
	Number of vertices in this simplex.

Static Public Attributes
static constexpr size_t	N = _N
	The dimension of this shape.

Detailed Description

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

A simplex in N dimensions (e.g. a tetrahedron, triangle, line, point).

The simplex may contain up to N + 1 points, in which case it encloses a volume, if it is not degenerate. If it contains fewer points, then it spans a subspace of the space in which it is embedded.

Member Function Documentation

contains() [1/2]

bool contains ( const Vec< T, N > &  p ) const

inline

Simplex-point intersection test.

If this simplex has fewer than N + 1 vertices, this simplex is not a volume, and this function returns false.

If the simplex is degenerate (two or more coincident points), then it is also considered empty and this function returns false.

Parameters

p

A point.

Returns

true if p is on or inside this simplex; false otherwise.

contains() [2/2]

bool contains ( Vec< 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.

intersect()

Rect< T, 1 > intersect ( const Ray< T, N > &  r ) const

inline

Ray-shape intersection.

Return the interval over which the ray intersects the simplex.

If the simplex is N-1 dimensional (i.e., planar, like a triangle in 3D), then an intersecting interval will have both of its limits equal to the single value of s for which the ray o + s*v intersects the simplex.

Simplexes with fewer than N-1 dimensions cannot be intersected, and the interval will always be empty.

intersects()

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

inlineinherited

Convex shape overlap test.

Returns

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

operator==()

bool operator== ( const Simplex< T, N > &  other ) const

inline

Simplex equality check.

Simplexes are equal if they have identical vertices in identical order.

operator|()

Simplex< T, N > operator| ( const Vec< T, N > &  p ) const

inline

Return a copy of this simplex with an additional vertex at p.

If this simplex already has N + 1 points, a copy of this simplex is returned.

operator|=()

Simplex< T, N > & operator|= ( const Vec< T, N > &  p )

inline

Extend this simplex to include p by adding p as a vertex.

If this Simplex already has N+1 vertices, then this operator has no effect.

project()

Vec< T, N > project ( const Vec< T, N > &  p, Simplex< T, N > *  onto = nullptr  ) const

inline

Project p to the nearest point on the simplex.

The point is unchanged if p is already inside the simplex.

Parameters

p	The point to project onto the surface of this simplex.
onto	Optional output parameter to receive the sub-simplex onto which p was projected. It is permissible for onto to alias this.

Returns

The location of p's projection.

projection_contains()

bool projection_contains ( const Vec< T, N > &  p, Vec< T, N > *  params = nullptr  ) const

inline

Project the point to the simplex along its orthogonal basis (if there is one) and test for containment.

Parameters

p	A point.
params	Optional return variable; return the n - 1 surface parameters of this simplex representing the projection of p onto the space spanned by this simplex.

Returns

true if p is on or inside this simplex after projection; false otherwise.

volume()

T volume ( ) const

inline

Compute the volume of the simplex.

If the simplex is not a full volume (i.e., the number of vertices is less than N+1), then its volume is zero.

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

• geomc/shape/ShapeTypes.h
• geomc/shape/Simplex.h