stator::geometry Namespace Reference

Geometric types and algorithms for calculating properties (e.g., intersection, volume).

Namespaces
	detail

Classes
class	AABox
	An axis-aligned box/block (including its interior volume). More...
class	Ball
	An n-ball (an n-sphere including its interior volume). More...
class	HalfSpace
	A planar half-space (a plane and the volume on one side of the plane). More...
class	InverseBall
	An inverse n-ball (an n-sphere including its exterior volume). More...
class	Plane
	An infinite flat surface of fixed thickness. More...
class	Point
	A point. More...

Functions
template<typename Scalar , size_t D>
Scalar	area (const Point< Scalar, D > &sphere)
template<typename Scalar , size_t D>
Scalar	area (const AABox< Scalar, D > &bb)
	Calculate the surface area of an Axis-Aligned Box. More...
template<typename Scalar , size_t D>
Scalar	area (const Ball< Scalar, D > &sphere)
	Calculate the surface area of a n-ball. More...
template<typename Obj >
auto	area (const Obj &)
	Compute a Hausdorf measure of the boundary/boundaries of an object. More...
template<class Scalar , size_t D, class DeltaRijFunc >
auto	indicator (const Ball< Scalar, D > &bi, const Point< Scalar, D > &bj, const DeltaRijFunc &deltarij) -> STATOR_AUTORETURN_BYVALUE(pow< 2 >(try_simplify(deltarij+bi.center() - bj.center())) - pow< 2 >(bi.radius()))
	Ball-Point indicator function. More...
template<class Scalar , size_t D, class DeltaRijFunc >
auto	indicator (const Point< Scalar, D > &bi, const Ball< Scalar, D > &bj, const DeltaRijFunc &deltarij) -> STATOR_AUTORETURN_BYVALUE(indicator(bj, bi, -deltarij))
	Point-Ball indicator function. More...
template<class Scalar , size_t D, class DeltaRijFunc >
auto	indicator (const Ball< Scalar, D > &bi, const Ball< Scalar, D > &bj, const DeltaRijFunc &deltarij) -> STATOR_AUTORETURN_BYVALUE(pow< 2 >(try_simplify(deltarij+bi.center() - bj.center())) - pow< 2 >(bi.radius()+bj.radius()))
	Ball-Ball indicator function. More...
template<class Scalar , size_t D, class DeltaRijFunc >
auto	indicator (const Ball< Scalar, D > &bi, const HalfSpace< Scalar, D > &bj, const DeltaRijFunc &deltarij) -> STATOR_AUTORETURN_BYVALUE(try_simplify(dot(bj.normal(), deltarij+bi.center() - bj.center()) - bi.radius()))
	Ball-HalfSpace indicator function. More...
template<class Scalar , size_t D, class DeltaRijFunc >
auto	indicator (const HalfSpace< Scalar, D > &bi, const Ball< Scalar, D > &bj, const DeltaRijFunc &deltarij) -> STATOR_AUTORETURN_BYVALUE(indicator(bj, bi, -deltarij))
	HalfSpace-Ball indicator function. More...
bool	intersects (const Object1 &, const Object2 &)
	Determine if two objects are intersecting. More...
template<typename Scalar , size_t D>
Scalar	volume (const AABox< Scalar, D > &bb)
	Calculate the volume of an Axis-Aligned Box. More...
template<typename Scalar , size_t D>
constexpr Scalar	volume (const Point< Scalar, D > &ball)
template<typename Scalar , size_t D>
Scalar	volume (const Ball< Scalar, D > &ball)
	Calculate the volume of a n-ball. More...
template<typename Obj >
auto	volume (const Obj &)
	Compute a Hausdorf measure of the interior of an object. More...

Function Documentation

area() [1/4]

template<typename Scalar , size_t D>

Scalar stator::geometry::area

(

const Point< Scalar, D > &

sphere

)

Definition at line 61 of file point.hpp.

area() [2/4]

template<typename Scalar , size_t D>

Scalar stator::geometry::area

(

const AABox< Scalar, D > &

bb

)

Definition at line 64 of file box.hpp.

area() [3/4]

template<typename Scalar , size_t D>

Scalar stator::geometry::area

(

const Ball< Scalar, D > &

sphere

)

Definition at line 127 of file sphere.hpp.

area() [4/4]

template<typename Obj >

auto stator::geometry::area

(

const Obj &

)

The measure returned depends on the dimensionality object. For example, a Sphere will return its surface area whereas a circle will return its perimeter.

indicator() [1/5]

template<class Scalar , size_t D, class DeltaRijFunc >

auto stator::geometry::indicator	(	const Ball< Scalar, D > &	bi,
		const Point< Scalar, D > &	bj,
		const DeltaRijFunc &	deltarij
	)		-> STATOR_AUTORETURN_BYVALUE(pow< 2 >(try_simplify(deltarij+bi.center() - bj.center())) - pow< 2 >(bi.radius()))

indicator() [2/5]

template<class Scalar , size_t D, class DeltaRijFunc >

auto stator::geometry::indicator	(	const Point< Scalar, D > &	bi,
		const Ball< Scalar, D > &	bj,
		const DeltaRijFunc &	deltarij
	)		-> STATOR_AUTORETURN_BYVALUE(indicator(bj, bi, -deltarij))

indicator() [3/5]

template<class Scalar , size_t D, class DeltaRijFunc >

auto stator::geometry::indicator	(	const Ball< Scalar, D > &	bi,
		const Ball< Scalar, D > &	bj,
		const DeltaRijFunc &	deltarij
	)		-> STATOR_AUTORETURN_BYVALUE(pow< 2 >(try_simplify(deltarij+bi.center() - bj.center())) - pow< 2 >(bi.radius()+bj.radius()))

indicator() [4/5]

template<class Scalar , size_t D, class DeltaRijFunc >

auto stator::geometry::indicator	(	const Ball< Scalar, D > &	bi,
		const HalfSpace< Scalar, D > &	bj,
		const DeltaRijFunc &	deltarij
	)		-> STATOR_AUTORETURN_BYVALUE(try_simplify(dot(bj.normal(), deltarij+bi.center() - bj.center()) - bi.radius()))

indicator() [5/5]

template<class Scalar , size_t D, class DeltaRijFunc >

auto stator::geometry::indicator	(	const HalfSpace< Scalar, D > &	bi,
		const Ball< Scalar, D > &	bj,
		const DeltaRijFunc &	deltarij
	)		-> STATOR_AUTORETURN_BYVALUE(indicator(bj, bi, -deltarij))

intersects()

bool stator::geometry::intersects	(	const Object1 &	,
		const Object2 &
	)

volume() [1/4]

template<typename Scalar , size_t D>

Scalar stator::geometry::volume

(

const AABox< Scalar, D > &

bb

)

Definition at line 54 of file box.hpp.

volume() [2/4]

template<typename Scalar , size_t D>

constexpr Scalar stator::geometry::volume

(

const Point< Scalar, D > &

ball

)

Definition at line 58 of file point.hpp.

volume() [3/4]

template<typename Scalar , size_t D>

Scalar stator::geometry::volume

(

const Ball< Scalar, D > &

ball

)

Definition at line 121 of file sphere.hpp.

volume() [4/4]

template<typename Obj >

auto stator::geometry::volume

(

const Obj &

)

The measure returned depends on the dimensionality of the object, a circle will return its area but a sphere will return its volume