KTope Class Reference

Convex polytopes with fixed normals, also referred to as k-topes. More...

#include <ktope.h>

Public Member Functions
	KTope ()
	Empty.
	KTope (const Vector &)
	Creates a single vertex k-tope. More...
	KTope (const Box &)
	Creates a cubic k-tope. More...
KTope &	operator+= (const Vector &)
	Adds a vertex to the k-tope structure. More...
Vector	Normal (int) const
	Returns the i-th normal of the k-tope.
bool	Intersect (const Ray &, double &, double &) const
	Compute the intersection between a k-tope and a ray parametrized by its origin and direction vectors. Sorted intersection depths are returned if intersection occurs. More...
bool	Inside (const Vector &) const
	Check if a point is inside the KTope. More...
bool	Intersect (const KTope &) const
	Check if two k-topes intersect. More...
KTope	operator+ (const KTope &) const
	Computes the Minkowski sum of two k-topes structures. More...
KTope	Scale (const double &) const
	Scale a k-tope. More...

Protected Attributes
double	c [18] = { 0.0 }
	Array of constants defining the planes.

Detailed Description

Convex polytopes with fixed normals, also referred to as k-topes.

This version implements a 18-polytope, which performs the fastest for a variety of applications. Refer to Klosowki, Efficient collision detection using bounding volumes hierarchies of k-dops, IEEE Transactions on Visualisation and Computer Graphics, 4(1), 1998.

The class stores the offset corresponding to the fixed normal directions.

This class implements some useful functions, such as the intersection between a k-tope and a ray.

Constructor & Destructor Documentation

KTope() [1/2]

KTope::KTope ( const Vector &  v )

explicit

Creates a single vertex k-tope.

Parameters

v

Point.

KTope() [2/2]

KTope::KTope ( const Box &  box )

explicit

Creates a cubic k-tope.

Parameters

box

The box.

Member Function Documentation

Inside()

bool KTope::Inside

(

const Vector &

p

)

const

Check if a point is inside the KTope.

Parameters

p

Point.

Intersect() [1/2]

bool KTope::Intersect

(

const KTope &

k

)

const

Check if two k-topes intersect.

Parameters

k	Argument k-tope.

Intersect() [2/2]

bool KTope::Intersect	(	const Ray &	ray,
		double &	tmin,
		double &	tmax
	)		const

Compute the intersection between a k-tope and a ray parametrized by its origin and direction vectors. Sorted intersection depths are returned if intersection occurs.

Parameters

ray	The ray.
tmin,tmax	Intersection depths.

operator+()

KTope KTope::operator+

(

const KTope &

b

)

const

Computes the Minkowski sum of two k-topes structures.

Parameters

b	Argument k-topes.

operator+=()

KTope & KTope::operator+=

(

const Vector &

p

)

Adds a vertex to the k-tope structure.

This function does not modify the k-tope if the point lies inside the k-tope, otherwise plane coefficients are updated accordingly.

Parameters

p

Point.

Scale()

KTope KTope::Scale

(

const double &

a

)

const

Scale a k-tope.

Parameters

a

Real.