An N-dimensional frustum (truncated pyramid) with an arbitrary Convex shape as its base, and its (possibly excluded) point at the origin. More...

#include <geomc/shape/Frustum.h>

Inheritance diagram for Frustum< Shape >:

Public Types
typedef PointType< T, Shape::N >::point_t	base_point_t
	Point type of the base shape.

using	elem_t
	The coordinate type of this object.

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

typedef Shape::elem_t	T
	The coordinate type of this Shape.

Public Member Functions
	Frustum ()
	Construct a pyramid with its tip at the origin and a default-constructed cross-sectional base at h=1.

	Frustum (const Shape &base, const Rect< T, 1 > &h)
	Construct a new Frustum having `base` as a cross section, and spanning the height range `h`.

	Frustum (const Shape &base, T h0, T h1)
	Construct a new Frustum having `base` as a cross section, and spanning heights between `h0` and `h1`.

Rect< T, N >	bounds () const

Rect< T, 1 >	clipped_height () const
	Return the height range of this Frustum after it has been clipped by the origin.

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

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.

bool	operator== (const Frustum &other) const

Static Public Member Functions
static constexpr bool	admits_cusps ()

Public Attributes
Shape	base
	Cross-section of this frustum at the `h=1` plane.

Rect< T, 1 >	height
	Height range spanned by this frustum.

Static Public Attributes
static constexpr size_t	N = Shape::N + 1
	The dimension of this Shape.

Related Symbols
(Note that these are not member symbols.)
template<typename T>
using	Cone = Frustum<Circle<T>>
	Convenience typedef for a 3D cone with its tip at the origin.

template<typename Shape>
Frustum< Shape >	frustum (const Shape &s, typename Shape::elem_t h0, typename Shape::elem_t h1)
	Convenience function to raise the shape `s` into a frustum between heights `h0` and `h1`, by wrapping `s` in the `Frustum` template.

template<typename T, index_t N>
using	ViewFrustum = Transformed< Frustum< Rect<T,N-1> > >
	Convenience typedef for oriented, rectangular, N-dimensional Frustums.

Detailed Description

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

An N-dimensional frustum (truncated pyramid) with an arbitrary Convex shape as its base, and its (possibly excluded) point at the origin.

The first N-1 dimensions have cross-sections which are Shapes. The last dimension is the "height" of the frustum. The base Shape is specified lying on the h = 1 plane. (Note that below the origin, the base shape will be flipped due to the change of sign).

If the height range spans height = 0, then the height extending below the origin is excluded from the shape. Use clipped_height() to obtain the height range actually spanned by the shape. (A frustum spanning the origin would not be convex).

Oriented, Rect-based Frustums are very commonly needed to represent viewing frustums; for these consider using ViewFrustum, which is a templated type alias for Transformed<Frustum<Rect>>.

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

◆ contains()

template<typename Shape>

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

inline

Frustum-point intersection test.

Parameters

p A point.

Returns: true if p is on or inside this frustum; false otherwise.

◆ convex_support()

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.

◆ 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.

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

geomc/shape/Frustum.h

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes