mc::domains::PolyTope< dim > Class Template Reference

Convex polytope (convex polyhedron) integration domain. More...

#include <polytope.hpp>

Inheritance diagram for mc::domains::PolyTope< dim >:

Collaboration diagram for mc::domains::PolyTope< dim >:

Public Member Functions
	PolyTope (const std::vector< geom::Point< dim > > &vertices, const std::vector< std::array< double, dim > > &norms, const std::vector< double > &offs)
	Construct a polytope from vertices and facet constraints.
geom::Bounds< dim >	getBounds () const override
	Get the axis-aligned bounding box containing the polytope.
double	getBoxVolume () const override
	Get the volume of the axis-aligned bounding box.
bool	isInside (const geom::Point< dim > &p) const override
	Test if a point is inside or on the boundary of the polytope.
Public Member Functions inherited from mc::domains::IntegrationDomain< dim >
virtual	~IntegrationDomain ()=default
	Virtual destructor for proper cleanup of derived classes.

Detailed Description

template<size_t dim>
class mc::domains::PolyTope< dim >

Convex polytope (convex polyhedron) integration domain.

Template Parameters

dim	The dimensionality of the space.

A polytope is the intersection of half-spaces defined by linear inequalities: normal_i · point + offset_i ≤ 0 for all facets i

where normal_i is an inward-pointing unit normal and offset_i is the constant term. This representation supports arbitrary convex polytopes with any number of facets.

Note

For efficiency, ensure normals are normalized and offsets are accurate.

Typically generated using Qhull (Qt Qx Fn flags).

Definition at line 34 of file polytope.hpp.

Constructor & Destructor Documentation

PolyTope()

template<size_t dim>

mc::domains::PolyTope< dim >::PolyTope	(	const std::vector< geom::Point< dim > > &	vertices,
		const std::vector< std::array< double, dim > > &	norms,
		const std::vector< double > &	offs
	)

Construct a polytope from vertices and facet constraints.

Parameters

vertices	Vector of vertices (corners) of the polytope. Used only for computing the bounding box.
norms	Vector of inward-pointing normal vectors; one per facet. Each normal is an array of dim coefficients.
offs	Vector of offset values (constant terms); one per facet.

Exceptions

std::runtime_error

if norms and offs have different sizes, or if vertices is empty.

Note

norms.size() must equal offs.size() (number of facets).

Member Function Documentation

getBounds()

template<size_t dim>

geom::Bounds< dim > mc::domains::PolyTope< dim >::getBounds ( ) const

overridevirtual

Get the axis-aligned bounding box containing the polytope.

Returns

Bounds<dim> with min/max coordinates in each dimension, computed from the vertex set.

Implements mc::domains::IntegrationDomain< dim >.

getBoxVolume()

template<size_t dim>

double mc::domains::PolyTope< dim >::getBoxVolume ( ) const

overridevirtual

Get the volume of the axis-aligned bounding box.

Returns

Product of side lengths: ∏(max_i - min_i)

Used for Monte Carlo weight normalization in sampling.

Implements mc::domains::IntegrationDomain< dim >.

isInside()

template<size_t dim>

bool mc::domains::PolyTope< dim >::isInside ( const geom::Point< dim > &  p ) const

overridevirtual

Test if a point is inside or on the boundary of the polytope.

Parameters

p	The point to test.

Returns

true if normal_i · p + offset_i ≤ (tol) for all facets i; false otherwise (point violates at least one constraint).

Note

Applies a small numerical tolerance (1e-12) for robustness.

Implements mc::domains::IntegrationDomain< dim >.

---

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

• src/montecarlo/domains/polytope.hpp