A convex polytope. More...

#include <convex.h>

Inheritance diagram for fcl::Convex< S_ >:

Public Types
using	S = S_

Public Types inherited from fcl::ShapeBase< S_ >
using	S = S_

Public Member Functions
Vector3< S >	computeCOM () const override

void	computeLocalAABB () override
	Computes AABB ~~in the geometry's canonical frame.~~ More...

Matrix3< S >	computeMomentofInertia () const override

S	computeVolume () const override

	Convex (const Convex &other)
	Copy constructor. More...

	Convex (const std::shared_ptr< const std::vector< Vector3< S >>> &vertices, int num_faces, const std::shared_ptr< const std::vector< int >> &faces, bool throw_if_invalid=false)
	Constructor. More...

const Vector3< S > &	findExtremeVertex (const Vector3< S > &v_C) const
	Reports a vertex in this convex polytope that lies farthest in the given direction v_C. The direction vector must be expressed in the same frame C as the vertices of `this` Convex polytope. More...

std::vector< Vector3< S > >	getBoundVertices (const Transform3< S > &tf) const
	Gets the vertices of some convex shape which can bound this shape in a specific configuration. More...

int	getFaceCount () const
	Gets the total number of faces in the convex mesh. More...

const std::vector< int > &	getFaces () const
	Gets the representation of the faces of the convex hull. More...

const Vector3< S > &	getInteriorPoint () const
	A point guaranteed to be on the interior of the convex polytope, used for collision. More...

NODE_TYPE	getNodeType () const override
	Gets node type: a convex polytope. More...

const std::vector< Vector3< S > > &	getVertices () const
	Gets the vertex positions in the geometry's frame G. More...

std::string	representation (int precision=20) const
	Create a string that should be sufficient to recreate this shape. This is akin to the repr() implementation in python. More...

	~Convex ()=default

Public Member Functions inherited from fcl::ShapeBase< S_ >
OBJECT_TYPE	getObjectType () const
	Get object type: a geometric shape. More...

	ShapeBase ()

Public Member Functions inherited from fcl::CollisionGeometry< S_ >
	CollisionGeometry ()

virtual Vector3< S_ >	computeCOM () const
	compute center of mass More...

virtual Matrix3< S_ >	computeMomentofInertia () const
	compute the inertia matrix, related to the origin More...

virtual Matrix3< S_ >	computeMomentofInertiaRelatedToCOM () const
	compute the inertia matrix, related to the com More...

virtual S_	computeVolume () const
	compute the volume More...

virtual NODE_TYPE	getNodeType () const
	get the node type More...

virtual OBJECT_TYPE	getObjectType () const
	get the type of the object More...

void *	getUserData () const
	get user data in geometry More...

bool	isFree () const
	whether the object is completely free More...

bool	isOccupied () const
	whether the object is completely occupied More...

bool	isUncertain () const
	whether the object has some uncertainty More...

void	setUserData (void *data)
	set user data in geometry More...

virtual	~CollisionGeometry ()

Private Member Functions
void	FindVertexNeighbors ()

void	ValidateMesh (bool throw_on_error)

void	ValidateTopology (bool throw_on_error)

Private Attributes
const std::shared_ptr< const std::vector< int > >	faces_

bool	find_extreme_via_neighbors_ {false}

Vector3< S >	interior_point_

std::vector< int >	neighbors_

const int	num_faces_

const bool	throw_if_invalid_ {}

const std::shared_ptr< const std::vector< Vector3< S > > >	vertices_

Static Private Attributes
static constexpr int	kMinVertCountForEdgeWalking = 32

Friends
class	ConvexTester

std::ostream &	operator<< (std::ostream &out, const Convex &convex)

Additional Inherited Members
Public Attributes inherited from fcl::CollisionGeometry< S_ >
Vector3< S_ >	aabb_center
	AABB center in local coordinate. More...

AABB< S_ >	aabb_local
	AABB in local coordinate, used for tight AABB when only translation transform. More...

S_	aabb_radius
	AABB radius. More...

S_	cost_density
	collision cost for unit volume More...

S_	threshold_free
	threshold for free (<= is free) More...

S_	threshold_occupied
	threshold for occupied ( >= is occupied) More...

void *	user_data
	pointer to user defined data specific to this object More...

Detailed Description

template<typename S_>
class fcl::Convex< S_ >

A convex polytope.

The Convex class represents a subset of general meshes: convex meshes. The class represents its underlying mesh quite simply: an ordered list of vertices, V = [v₀, v₁, ..., vₙ₋₁], and an ordered list of faces, F = [f₀, f₁, ..., fₘ₋₁], built on those vertices (via vertex indices).

A mesh is only compatible with Convex if it satisfies the following properties:

Each face, fᵢ, must be planar and completely lies on a supporting plane πᵢ. The ordered sets F = [f₀, f₁, ..., fₙ₋₁] and Π = [π₀, π₁, ..., πₙ₋₁] are defined such that face fᵢ has supporting plane πᵢ.
A face fᵢ is defined by an ordered list of vertex indices (e.g., fᵢ = [iᵢ₀, iᵢ₁, ..., iᵢₖ₋₁] (for a face with k vertices and k edges). The ordering of the vertex indices must visit the face's vertices in a counter-clockwise order when viewed from outside the mesh and the vertices must all lie on the face's supporting plane.
Define functions πᵢ(x) which report the signed distance from point x to plane πᵢ. To be convex, it must be true that π(v) ≤ 0, ∀ π ∈ Π ∧ v ∈ V.

If those requirements are satisfied, for a given convex region, the mesh with the smallest number of faces may have non-triangular faces. In fact, they could be polygons with an arbitrary number of edges/vertices. The Convex class supports compact representation. But it also supports representations that decompose a large n-gon into a set of smaller polygons or triangles. In this case, each of the triangles supporting planes would be the same and the requirements listed above would still be satisfied.

Template Parameters

S_	The scalar type; must be a valid Eigen scalar.

Definition at line 84 of file convex.h.

Member Typedef Documentation

◆ S

template<typename S_ >

using fcl::Convex< S_ >::S = S_

Definition at line 88 of file convex.h.

Constructor & Destructor Documentation

◆ Convex() [1/2]

template<typename S >

fcl::Convex< S >::Convex	(	const std::shared_ptr< const std::vector< Vector3< S >>> &	vertices,
		int	num_faces,
		const std::shared_ptr< const std::vector< int >> &	faces,
		bool	throw_if_invalid = `false`
	)

Constructor.

Note: : The Convex geometry assumes that the input data vertices and faces do not change through the life of the object.

Warning: : The Convex class only partially validates the input; it generally trusts that the inputs truly represent a coherent convex polytope. For those aspects that are validated, the constructor will throw for failed tests if throw_if_invalid is set to true.

Parameters

vertices	The positions of the polytope vertices.
num_faces	The number of faces defined in `faces`.
faces	Encoding of the polytope faces. Must encode `num_faces` number of faces. See member documentation for details on encoding.
throw_if_invalid	If `true`, failed attempts to validate the mesh will throw an exception.

Definition at line 60 of file convex-inl.h.

◆ Convex() [2/2]

template<typename S >

fcl::Convex< S >::Convex ( const Convex< S_ > & other )

default

Copy constructor.

◆ ~Convex()

template<typename S_ >

fcl::Convex< S_ >::~Convex ( )

default

Member Function Documentation

◆ computeCOM()

template<typename S >

Vector3< S > fcl::Convex< S >::computeCOM

override

Definition at line 166 of file convex-inl.h.

◆ computeLocalAABB()

template<typename S >

void fcl::Convex< S >::computeLocalAABB

overridevirtual

Computes AABB ~~in the geometry's canonical frame.~~

Implements fcl::CollisionGeometry< S_ >.

Definition at line 86 of file convex-inl.h.

◆ computeMomentofInertia()

template<typename S >

Matrix3< S > fcl::Convex< S >::computeMomentofInertia

override

Definition at line 111 of file convex-inl.h.

◆ computeVolume()

template<typename S >

S fcl::Convex< S >::computeVolume

override

Definition at line 205 of file convex-inl.h.

◆ findExtremeVertex()

template<typename S >

const Vector3< S > & fcl::Convex< S >::findExtremeVertex ( const Vector3< S > & v_C ) const

Reports a vertex in this convex polytope that lies farthest in the given direction v_C. The direction vector must be expressed in the same frame C as the vertices of this Convex polytope.

Return values

p_CE	the position vector from Frame C's origin to the extreme vertex E. It is guaranteed that v_C⋅p_CE ≥ v_C⋅p_CF for all F ≠ E in the Convex polytope's set of vertices.

Definition at line 266 of file convex-inl.h.

◆ FindVertexNeighbors()

template<typename S >

void fcl::Convex< S >::FindVertexNeighbors

private

Definition at line 440 of file convex-inl.h.

◆ getBoundVertices()

template<typename S >

std::vector< Vector3< S > > fcl::Convex< S >::getBoundVertices ( const Transform3< S > & tf ) const

Gets the vertices of some convex shape which can bound this shape in a specific configuration.

Definition at line 252 of file convex-inl.h.

◆ getFaceCount()

template<typename S_ >

int fcl::Convex< S_ >::getFaceCount ( ) const

inline

Gets the total number of faces in the convex mesh.

Definition at line 129 of file convex.h.

◆ getFaces()

template<typename S_ >

const std::vector<int>& fcl::Convex< S_ >::getFaces ( ) const

inline

Gets the representation of the faces of the convex hull.

The array is the concatenation of an integer-based representations of each face. A single face is encoded as a sub-array of ints where the first int is the number n of vertices in the face, and the following n values are ordered indices into vertices which visit the vertex values in a counter-clockwise order (viewed from the outside).

For a well-formed face f consisting of indices [i₀, i₁, ..., iₘ₋₁], it should be the case that:

eⱼ × eⱼ₊₁ · n̂ₚ = |eⱼ × eⱼ₊₁|, ∀ 0 ≤ j < m, j ∈ ℤ, where n̂ₚ is the normal for plane π on which face f lies. eⱼ = vertices[iⱼ] - vertices[iⱼ₋₁] is the edge vector of face f defined by adjacent vertex indices at jᵗʰ vertex (wrapping around such that j - 1 = m - 1 for j = 0).

Satisfying this condition implies the following:

vertices are not coincident and
the indices of the face correspond to a proper counter-clockwise ordering.

Definition at line 152 of file convex.h.

◆ getInteriorPoint()

template<typename S_ >

const Vector3<S>& fcl::Convex< S_ >::getInteriorPoint ( ) const

inline

A point guaranteed to be on the interior of the convex polytope, used for collision.

Definition at line 156 of file convex.h.

◆ getNodeType()

template<typename S >

NODE_TYPE fcl::Convex< S >::getNodeType

override

Gets node type: a convex polytope.

Definition at line 100 of file convex-inl.h.

◆ getVertices()

template<typename S_ >

const std::vector<Vector3<S> >& fcl::Convex< S_ >::getVertices ( ) const

inline

Gets the vertex positions in the geometry's frame G.

Definition at line 126 of file convex.h.

◆ representation()

template<typename S >

std::string fcl::Convex< S >::representation ( int precision = 20 ) const

Create a string that should be sufficient to recreate this shape. This is akin to the repr() implementation in python.

Parameters

precision The requested digits of precision for the numerical measures (same semantics as std::setprecision()).

Returns: The string representation of this instance.

Definition at line 318 of file convex-inl.h.

◆ ValidateMesh()

template<typename S >

void fcl::Convex< S >::ValidateMesh ( bool throw_on_error )

private

Definition at line 352 of file convex-inl.h.

◆ ValidateTopology()

template<typename S >

void fcl::Convex< S >::ValidateTopology ( bool throw_on_error )

private

Definition at line 360 of file convex-inl.h.

Friends And Related Function Documentation

◆ ConvexTester

template<typename S_ >

friend class ConvexTester

friend

Definition at line 195 of file convex.h.

◆ operator<<

template<typename S_ >

std::ostream& operator<<	(	std::ostream &	out,
		const Convex< S_ > &	convex
	)

friend

Definition at line 187 of file convex.h.

Member Data Documentation

◆ faces_

template<typename S_ >

const std::shared_ptr<const std::vector<int> > fcl::Convex< S_ >::faces_

private

Definition at line 235 of file convex.h.

◆ find_extreme_via_neighbors_

template<typename S_ >

bool fcl::Convex< S_ >::find_extreme_via_neighbors_ {false}

private

Definition at line 267 of file convex.h.

◆ interior_point_

template<typename S_ >

Vector3<S> fcl::Convex< S_ >::interior_point_

private

Definition at line 238 of file convex.h.

◆ kMinVertCountForEdgeWalking

template<typename S_ >

constexpr int fcl::Convex< S_ >::kMinVertCountForEdgeWalking = 32

staticconstexprprivate

Definition at line 272 of file convex.h.

◆ neighbors_

template<typename S_ >

std::vector<int> fcl::Convex< S_ >::neighbors_

private

Definition at line 263 of file convex.h.

◆ num_faces_

template<typename S_ >

const int fcl::Convex< S_ >::num_faces_

private

Definition at line 234 of file convex.h.

◆ throw_if_invalid_

template<typename S_ >

const bool fcl::Convex< S_ >::throw_if_invalid_ {}

private

Definition at line 237 of file convex.h.

◆ vertices_

template<typename S_ >

const std::shared_ptr<const std::vector<Vector3<S> > > fcl::Convex< S_ >::vertices_

private

Definition at line 233 of file convex.h.

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

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Friends

Additional Inherited Members

Detailed Description

template<typename S_> class fcl::Convex< S_ >

Member Typedef Documentation

◆ S

Constructor & Destructor Documentation

◆ Convex() [1/2]

◆ Convex() [2/2]

◆ ~Convex()

Member Function Documentation

◆ computeCOM()

◆ computeLocalAABB()

◆ computeMomentofInertia()

◆ computeVolume()

◆ findExtremeVertex()

◆ FindVertexNeighbors()

◆ getBoundVertices()

◆ getFaceCount()

◆ getFaces()

◆ getInteriorPoint()

◆ getNodeType()

◆ getVertices()

◆ representation()

◆ ValidateMesh()

◆ ValidateTopology()

Friends And Related Function Documentation

◆ ConvexTester

◆ operator<<

Member Data Documentation

◆ faces_

◆ find_extreme_via_neighbors_

◆ interior_point_

◆ kMinVertCountForEdgeWalking

◆ neighbors_

◆ num_faces_

◆ throw_if_invalid_

◆ vertices_

template<typename S_>
class fcl::Convex< S_ >