Shape

Shape-related functions and classes. More...

Modules
	Traits
	Metadata about shape classes.

Classes
class	Cylinder< T, N >
	An N-dimensional cylinder, given by its radius and endpoints. More...
class	Dilated< Shape >
	A wrapper shape which dilates the extents of another Shape. More...
class	Extrusion< Shape >
	An axis-aligned extrusion of an arbitrary N-1 dimensional Convex shape. More...
class	Frustum< Shape >
	An N-dimensional frustum (truncated pyramid) with an arbitrary Convex shape as its base, and its (possibly excluded) point at the origin. More...
class	GridIterator< T, N, Order >
	Iterator over the integer points in an N-dimensional grid. More...
class	KDTree< T, N, Object, NodeData >
	A hierarchical spatial index. More...
class	Oriented< Shape >
	A wrapper shape which orients another arbitrary shape with an AffineTransform. More...
class	Oriented< Rect< T, N > >
	Partial specialization of Oriented for Rects. More...
class	Plane< T, N >
	A geometric plane or hyperplane. More...
class	Rect< T, N >
	An N-dimensional axis-aligned interval. More...
class	Bounded< T, _N, Derived >
	Base class describing shapes with finite extents in N dimensions. More...
class	Convex< T, N, Derived >
	Base class describing convex shapes in N-dimensional space. More...
class	RayIntersectable< T, N, Derived >
	Base class describing N-dimensional shapes which can be intersection-tested with a Ray. More...
class	SdfEvaluable< T, N, Derived >
	Base class describing N-dimensional shapes which implement a signed distance function. More...
class	Projectable< T, N, Derived >
	Base class describing N-dimensional shapes which implement the ability to project an arbitrary point to the nearest point on their surface. More...
class	AnyConvex< T, N >
	Helper class which virtualizes the static polymorphism of Convex shapes. More...
class	AnyConvexImpl< Shape >
	Implementation of AnyConvex for a specific Shape. More...
class	Sphere< T, N >
	A N-dimensional circle, sphere, or hypersphere. More...
class	Simplex< T, N >
	A simplex in N dimensions (e.g. a tetrahedron, triangle, line, point). More...
class	SphericalSector< T, N >
	A N-dimensional circle, sphere, or hypersphere. More...

Macros
#define	MAX_KDTREE_ARITY   16

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

Enumerations
enum class	KDAxisChoice { AXIS_LONGEST , AXIS_HIGHEST_VARIANCE , AXIS_CYCLICAL }
	Strategy for choosing an axis along which to split a group of objects in a spatial index. More...
enum class	KDPivotChoice { PIVOT_MEAN , PIVOT_MEDIAN }
	Strategy for choosing the pivot value when splitting a group of objects in a spatial index. More...
enum class	KDInsertionChoice { INSERT_SMALLEST_VOLUME_INCREASE , INSERT_SHORTEST_DISTANCE }
	Strategy for insertion of an object into an existing tree. More...
enum	ArrayOrder { ARRAYORDER_FIRST_DIM_CONSECUTIVE , ARRAYORDER_LAST_DIM_CONSECUTIVE }
	Array traversal order, specified in terms of which axes to increment first. More...

Functions
template<typename T , index_t N>
bool	gjk_intersect (const AnyConvex< T, N > &shape_a, const AnyConvex< T, N > &shape_b, Vec< T, N > *overlap_axis=NULL)
template<typename T , index_t N>
bool	minimal_separation_axis (const AnyConvex< T, N > &shape_a, const AnyConvex< T, N > &shape_b, Vec< T, N > *overlap_axis, double fractional_tolerance=0.001, index_t iteration_limit=-1, bool emit_debug=false)
template<typename Shape >
AnyConvexImpl< Shape >	as_any_convex (const Shape &s)
	Wrap s in a virtual class which implements the Convex concept.
template<typename Shape >
Dilated< Shape >	dilate (const Shape &s, typename Shape::elem_t dilation)
	Dilate the shape s by the amount dilation.
template<typename Shape >
Dilated< Shape >	dilate (const Dilated< Shape > &s, typename Shape::elem_t dilation)
	Dilate the shape s by the amount dilation.
template<typename T , index_t N>
Plane< T, N >	dilate (Plane< T, N > p, T dilation)
	Dilate the Plane p by the amount dilation. More...
template<typename T , index_t N>
Sphere< T, N >	dilate (const Sphere< T, N > &s, T dilation)
	Dilate the Sphere s by the amount dilation. More...
template<typename Shape >
Extrusion< Shape >	extrude (const Shape &s, typename Shape::elem_t h0, typename Shape::elem_t h1)
	Convenience function to extrude the shape s between heights h0 and h1 by wrapping s in the Extrusion template.
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 Shape >
Oriented< Shape >	operator* (const AffineTransform< typename Shape::elem_t, Shape::N > &xf, const Shape &s)
	Transform the shape s by wrapping it in an Oriented class.
template<typename Shape >
Oriented< Shape >	operator* (const AffineTransform< typename Shape::elem_t, Shape::N > &xf, const Oriented< Shape > &s)
	Transform the oriented shape s by xf.
template<typename Shape >
Oriented< Shape > &	operator*= (Oriented< Shape > &s, const AffineTransform< typename Shape::elem_t, Shape::N > &xf)
	In-place transform the oriented shape s by xf.
template<typename Shape >
Oriented< Shape >	operator/ (const Shape &s, const AffineTransform< typename Shape::elem_t, Shape::N > &xf)
	Transform the shape s by the inverse of xf.
template<typename Shape >
Oriented< Shape >	operator/ (const Oriented< Shape > &s, const AffineTransform< typename Shape::elem_t, Shape::N > &xf)
	Transform the oriented shape s by the inverse of xf.
template<typename Shape >
Oriented< Shape > &	operator/= (Oriented< Shape > &s, const AffineTransform< typename Shape::elem_t, Shape::N > &xf)
	In-place transform the oriented shape s by the inverse of xf.

Detailed Description

Shape-related functions and classes.

Enumeration Type Documentation

ArrayOrder

enum ArrayOrder

Array traversal order, specified in terms of which axes to increment first.

Enumerator
ARRAYORDER_FIRST_DIM_CONSECUTIVE	Array traversal by incrementing the first coordinate in the innermost loop. For matrices, whose coordinates are ordered (row, col), this represens column-major (i.e. "fortran") order. If coordinates are (x, y, ...), then this is row-major order.
ARRAYORDER_LAST_DIM_CONSECUTIVE	Array traversal by incrementing the last coordinate in the innermost loop. For matrices, whose coordinates are ordered (row, col), this represents row-major (i.e. "C") order. If coordinates are (x, y, ...), then this is column-major order.

KDAxisChoice

enum class KDAxisChoice

strong

Strategy for choosing an axis along which to split a group of objects in a spatial index.

Enumerator
AXIS_LONGEST	Divide a node along its longest axis.
AXIS_HIGHEST_VARIANCE	Divide a node along the axis with the highest position variance.
AXIS_CYCLICAL	Divide each node along an axis that cycles with tree depth, starting with the x (first) axis at the root node.

KDInsertionChoice

enum class KDInsertionChoice

strong

Strategy for insertion of an object into an existing tree.

Enumerator
INSERT_SMALLEST_VOLUME_INCREASE	Insert objects into the node that will experience the smallest volume increase as a result of the addition.
INSERT_SHORTEST_DISTANCE	Insert objects into the node which is closest.

KDPivotChoice

enum class KDPivotChoice

strong

Strategy for choosing the pivot value when splitting a group of objects in a spatial index.

Enumerator
PIVOT_MEAN	Split a node at the population average.
PIVOT_MEDIAN	Split a node at the population median.

Function Documentation

dilate() [1/2]

Sphere< T, N > dilate ( const Sphere< T, N > &  s, T  dilation  )

related

Dilate the Sphere s by the amount dilation.

(This just adds the amount dilation to the Sphere's radius).

dilate() [2/2]

Plane< T, N > dilate ( Plane< T, N >  p, T  dilation  )

related

Dilate the Plane p by the amount dilation.

(This just moves the plane dilation units along its normal).

gjk_intersect()

bool geom::gjk_intersect	(	const AnyConvex< T, N > &	shape_a,
		const AnyConvex< T, N > &	shape_b,
		Vec< T, N > *	overlap_axis = NULL
	)

Use the Gilbert-Johnson-Keerthi algorithm to determine if two convex shapes overlap, and return an axis of overlap.

Parameters

shape_a	A convex shape.
shape_b	A convex shape.
overlap_axis	An initial axis along which to test for overlap; upon completion this will be populated with an axis (not necessarily minimal) of overlap or separation. Pass null to choose an arbitrary initial axis.

Returns

true if and only if shape_a and shape_b overlap.

minimal_separation_axis()

bool geom::minimal_separation_axis	(	const AnyConvex< T, N > &	shape_a,
		const AnyConvex< T, N > &	shape_b,
		Vec< T, N > *	overlap_axis,
		double	fractional_tolerance = 0.001,
		index_t	iteration_limit = -1,
		bool	emit_debug = false
	)

Use the Expanding Polytope Algorithm to find a minimum translation vector that would bring shape B into contact with A. If A and B are not interpenetrating the separation axis is undefined.

Parameters

shape_a	A convex shape.
shape_b	A convex shape.
overlap_axis	An initial test axis, and return variable for the separation vector.
fractional_tolerance	Convergence condition: When the magnitude of the difference between iterations is less than this fraction of the total separation, terminate the algorithm.
iteration_limit	Hard limit on number of convergence iterations. Pass -1 (default) to impose no hard limit.

Returns

true if and only if the two shapes overlap.