Half-edge class for navigating a DCEL mesh. More...

#include <EBGeometry_DCEL_Edge.hpp>

Public Types
using	Vec3 = Vec3T< T >
	Alias for vector type.

using	Vertex = VertexT< T >
	Alias for vertex type.

using	Edge = EdgeT< T >
	Alias for edge type.

using	Face = FaceT< T >
	Alias for face type.

using	Mesh = MeshT< T >
	Alias for mesh type.

Public Member Functions
	EdgeT () noexcept=default
	Default constructor. Sets all topology indices to the unset sentinel and vectors to zero vectors.

	EdgeT (const Edge &a_otherEdge)=default
	Copy constructor.

	EdgeT (Edge &&a_otherEdge)=default
	Move constructor.

	EdgeT (const uint32_t a_vertexIndex) noexcept
	Partial constructor. Calls the default constructor but sets the starting vertex.

	~EdgeT ()=default
	Destructor (does nothing)

Edge &	operator= (const Edge &a_otherEdge)=default
	Copy assignment operator.

Edge &	operator= (Edge &&a_otherEdge)=default
	Move assignment operator.

size_t	size () const noexcept
	Get the number of vertices spanned by a half-edge.

void	define (const uint32_t a_vertexIndex, const uint32_t a_pairEdgeIndex, const uint32_t a_nextEdgeIndex) noexcept
	Define function. Sets the starting vertex, pair/next edge indices.

void	reconcile (const Mesh &a_mesh) noexcept
	Reconcile internal logic.

void	flipNormal () noexcept
	Flip surface normal.

void	setVertex (const uint32_t a_vertexIndex) noexcept
	Set the index of the starting vertex.

void	setPairEdge (const uint32_t a_pairEdgeIndex) noexcept
	Set the index of the pair edge.

void	setNextEdge (const uint32_t a_nextEdgeIndex) noexcept
	Set the index of the next edge.

void	setFace (const uint32_t a_faceIndex) noexcept
	Set the index of this half-edge's face.

uint32_t	getVertexIndex () const noexcept
	Get the index of the starting vertex.

uint32_t	getPairEdgeIndex () const noexcept
	Get the index of the pair edge.

uint32_t	getNextEdgeIndex () const noexcept
	Get the index of the next edge.

uint32_t	getFaceIndex () const noexcept
	Get the index of this half-edge's face.

Vertex &	getVertex (Mesh &a_mesh) noexcept
	Get the starting vertex.

const Vertex &	getVertex (const Mesh &a_mesh) const noexcept
	Get the starting vertex (const overload).

Vertex &	getOtherVertex (Mesh &a_mesh) noexcept
	Get the end vertex.

const Vertex &	getOtherVertex (const Mesh &a_mesh) const noexcept
	Get the end vertex (const overload).

Edge &	getPairEdge (Mesh &a_mesh) noexcept
	Get the pair edge.

const Edge &	getPairEdge (const Mesh &a_mesh) const noexcept
	Get the pair edge (const overload).

Edge &	getNextEdge (Mesh &a_mesh) noexcept
	Get the next edge.

const Edge &	getNextEdge (const Mesh &a_mesh) const noexcept
	Get the next edge (const overload).

Vec3T< T >	computeNormal (const Mesh &a_mesh) const noexcept
	Compute the normal vector as the average of the face normals on both sides of this edge.

Vec3T< T > &	getNormal () noexcept
	Get modifiable normal vector.

const Vec3T< T > &	getNormal () const noexcept
	Get the stored normal vector.

Face &	getFace (Mesh &a_mesh) noexcept
	Get this half-edge's face.

const Face &	getFace (const Mesh &a_mesh) const noexcept
	Get this half-edge's face (const overload).

T	signedDistance (const Vec3 &a_x0, const Mesh &a_mesh) const noexcept
	Get the signed distance from a_x0 to this half-edge.

T	unsignedDistance2 (const Vec3 &a_x0, const Mesh &a_mesh) const noexcept
	Get the squared unsigned distance from a_x0 to this half-edge.

Protected Member Functions
T	projectPointToEdge (const Vec3 &a_x0, const Mesh &a_mesh) const noexcept
	Returns the parametric projection of a_x0 onto this edge.

Vec3T< T >	getX2X1 (const Mesh &a_mesh) const noexcept
	Get the vector pointing along this edge (from start to end vertex).

Protected Attributes
Vec3	m_normal = Vec3::zeros()
	Normal vector.

uint32_t	m_vertex = UINT32_MAX
	Index of the starting vertex.

uint32_t	m_pairEdge = UINT32_MAX
	Index of the pair edge. See m_vertex for the indexing convention.

uint32_t	m_nextEdge = UINT32_MAX
	Index of the next edge. See m_vertex for the indexing convention.

uint32_t	m_face = UINT32_MAX
	Index of the enclosing polygon face, into the owning mesh's face array, or UINT32_MAX if unset.

Detailed Description

template<class T>
class EBGeometry::DCEL::EdgeT< T >

Half-edge class for navigating a DCEL mesh.

Class which represents a half-edge in a doubly-connected edge list (DCEL).

Template Parameters

T	Floating-point precision type.

This class is used in DCEL functionality which stores polygonal surfaces in a mesh. The information contain in an EdgeT object contains the necessary object for logically circulating the inside of a polygon face. This means that a polygon face has a double-connected list of half-edges which circulate the interior of the face. The EdgeT object is such a half-edge; it represents the outgoing half-edge from a vertex, located such that it can be logically represented as a half edge on the "inside" of a polygon face. It stores the indices of the polygon face, vertex, and next half edge in the owning mesh's arrays. It also stores the index of the "pair" half edge, i.e. the corresponding half-edge on the other face that shares this edge. Since this class is used with DCEL functionality and signed distance fields, this class also has a signed distance function and thus a "normal vector".

Note: The normal vector is outgoing, i.e. a point x is "outside" if the dot product between n and (x - x0) is positive.; All topology indices below (m_vertex, m_pairEdge, m_nextEdge, m_face) are indices into the owning DCEL::MeshT's own vertex/edge/face arrays, resolved by passing that mesh to the accessors below. Using indices rather than pointers keeps EdgeT a plain, relocatable value: the owning mesh's arrays are the sole storage, and every cross-reference is a position within them, not an address – so an EdgeT is meaningful under a memcpy or a host-to-device mirror with no pointer patching.; Every member here resolves purely through plain values and an explicitly-supplied Mesh&, so the entire public and protected interface is annotated EBGEOMETRY_HOST_DEVICE.

Template Parameters

T	Floating-point precision.

Constructor & Destructor Documentation

◆ EdgeT() [1/3]

template<class T >

EBGeometry::DCEL::EdgeT< T >::EdgeT ( const Edge & a_otherEdge )

default

Copy constructor.

Defaulted memberwise copy of every member – the normal vector, and all four topology indices (vertex, pair edge, next edge, face). This is what lets EdgeT be trivially copyable: std::is_trivially_copyable requires the copy constructor to be the implicit/defaulted one, so a user-provided body – even one that does nothing but a plain memberwise copy – would disqualify it. operator=(const Edge&) has identical semantics.

Parameters

[in] a_otherEdge Other edge.

◆ EdgeT() [2/3]

template<class T >

EBGeometry::DCEL::EdgeT< T >::EdgeT ( Edge && a_otherEdge )

default

Move constructor.

Defaulted memberwise move; equivalent to the copy constructor since every member is a plain value.

Parameters

[in,out] a_otherEdge Other edge.

◆ EdgeT() [3/3]

template<class T >

EBGeometry::DCEL::EdgeT< T >::EdgeT ( const uint32_t a_vertexIndex )

noexcept

Partial constructor. Calls the default constructor but sets the starting vertex.

Parameters

[in] a_vertexIndex Index of the starting vertex in the owning mesh's vertex array.

Member Function Documentation

◆ computeNormal()

template<class T >

Vec3T< T > EBGeometry::DCEL::EdgeT< T >::computeNormal ( const Mesh & a_mesh ) const

inlinenoexcept

Compute the normal vector as the average of the face normals on both sides of this edge.

An edge with no pair edge (a hole) uses its own face's normal alone.

Parameters

[in] a_mesh Owning mesh, used to resolve the face/pair-edge indices.

Returns: Unit normal vector for this edge, or the zero vector if the two faces fold back onto each other (their normals cancel).

◆ define()

template<class T >

void EBGeometry::DCEL::EdgeT< T >::define	(	const uint32_t	a_vertexIndex,
		const uint32_t	a_pairEdgeIndex,
		const uint32_t	a_nextEdgeIndex
	)

inlinenoexcept

Define function. Sets the starting vertex, pair/next edge indices.

Parameters

[in]	a_vertexIndex	Index of the starting vertex in the owning mesh's vertex array.
[in]	a_pairEdgeIndex	Index of the pair half-edge in the owning mesh's edge array, or UINT32_MAX if unset.
[in]	a_nextEdgeIndex	Index of the next half-edge in the owning mesh's edge array, or UINT32_MAX if unset.

◆ getFace() [1/2]

template<class T >

const Face & EBGeometry::DCEL::EdgeT< T >::getFace ( const Mesh & a_mesh ) const

inlinenoexcept

Get this half-edge's face (const overload).

Parameters

[in] a_mesh Owning mesh, used to resolve the face index.

Returns: Const reference to the owning face. m_face must be set (see getFaceIndex()).

◆ getFace() [2/2]

template<class T >

Face & EBGeometry::DCEL::EdgeT< T >::getFace ( Mesh & a_mesh )

inlinenoexcept

Get this half-edge's face.

Parameters

[in] a_mesh Owning mesh, used to resolve the face index.

Returns: Reference to the owning face. m_face must be set (see getFaceIndex()).

◆ getFaceIndex()

template<class T >

uint32_t EBGeometry::DCEL::EdgeT< T >::getFaceIndex ( ) const

inlinenoexcept

Get the index of this half-edge's face.

Returns: Index of the face in the owning mesh's face array, or UINT32_MAX if unset.

◆ getNextEdge() [1/2]

template<class T >

const Edge & EBGeometry::DCEL::EdgeT< T >::getNextEdge ( const Mesh & a_mesh ) const

inlinenoexcept

Get the next edge (const overload).

Parameters

[in] a_mesh Owning mesh, used to resolve the next-edge index.

Returns: Const reference to the next edge. m_nextEdge must be set (see getNextEdgeIndex()).

◆ getNextEdge() [2/2]

template<class T >

Edge & EBGeometry::DCEL::EdgeT< T >::getNextEdge ( Mesh & a_mesh )

inlinenoexcept

Get the next edge.

Parameters

[in] a_mesh Owning mesh, used to resolve the next-edge index.

Returns: Reference to the next edge. m_nextEdge must be set (see getNextEdgeIndex()).

◆ getNextEdgeIndex()

template<class T >

uint32_t EBGeometry::DCEL::EdgeT< T >::getNextEdgeIndex ( ) const

inlinenoexcept

Get the index of the next edge.

Returns: Index of the next edge in the owning mesh's edge array, or UINT32_MAX if unset.

◆ getNormal() [1/2]

template<class T >

const Vec3T< T > & EBGeometry::DCEL::EdgeT< T >::getNormal ( ) const

inlinenoexcept

Get the stored normal vector.

Returns: Const reference to m_normal.

◆ getNormal() [2/2]

template<class T >

Vec3T< T > & EBGeometry::DCEL::EdgeT< T >::getNormal ( )

inlinenoexcept

Get modifiable normal vector.

Returns: Reference to m_normal.

◆ getOtherVertex() [1/2]

template<class T >

const Vertex & EBGeometry::DCEL::EdgeT< T >::getOtherVertex ( const Mesh & a_mesh ) const

inlinenoexcept

Get the end vertex (const overload).

Parameters

[in] a_mesh Owning mesh, used to resolve the next-edge and vertex indices.

Returns: Const reference to the next half-edge's starting vertex. m_nextEdge must be set.

◆ getOtherVertex() [2/2]

template<class T >

Vertex & EBGeometry::DCEL::EdgeT< T >::getOtherVertex ( Mesh & a_mesh )

inlinenoexcept

Get the end vertex.

Parameters

[in] a_mesh Owning mesh, used to resolve the next-edge and vertex indices.

Returns: Reference to the next half-edge's starting vertex. m_nextEdge must be set.

◆ getPairEdge() [1/2]

template<class T >

const Edge & EBGeometry::DCEL::EdgeT< T >::getPairEdge ( const Mesh & a_mesh ) const

inlinenoexcept

Get the pair edge (const overload).

Parameters

[in] a_mesh Owning mesh, used to resolve the pair-edge index.

Returns: Const reference to the pair edge. m_pairEdge must be set (see getPairEdgeIndex()).

◆ getPairEdge() [2/2]

template<class T >

Edge & EBGeometry::DCEL::EdgeT< T >::getPairEdge ( Mesh & a_mesh )

inlinenoexcept

Get the pair edge.

Parameters

[in] a_mesh Owning mesh, used to resolve the pair-edge index.

Returns: Reference to the pair edge. m_pairEdge must be set (see getPairEdgeIndex()).

◆ getPairEdgeIndex()

template<class T >

uint32_t EBGeometry::DCEL::EdgeT< T >::getPairEdgeIndex ( ) const

inlinenoexcept

Get the index of the pair edge.

Returns: Index of the pair edge in the owning mesh's edge array, or UINT32_MAX if unset.

◆ getVertex() [1/2]

template<class T >

const Vertex & EBGeometry::DCEL::EdgeT< T >::getVertex ( const Mesh & a_mesh ) const

inlinenoexcept

Get the starting vertex (const overload).

Parameters

[in] a_mesh Owning mesh, used to resolve the vertex index.

Returns: Const reference to the starting vertex. m_vertex must be set (see getVertexIndex()).

◆ getVertex() [2/2]

template<class T >

Vertex & EBGeometry::DCEL::EdgeT< T >::getVertex ( Mesh & a_mesh )

inlinenoexcept

Get the starting vertex.

Parameters

[in] a_mesh Owning mesh, used to resolve the vertex index.

Returns: Reference to the starting vertex. m_vertex must be set (see getVertexIndex()).

◆ getVertexIndex()

template<class T >

uint32_t EBGeometry::DCEL::EdgeT< T >::getVertexIndex ( ) const

inlinenoexcept

Get the index of the starting vertex.

Returns: Index of the starting vertex in the owning mesh's vertex array, or UINT32_MAX if unset.

◆ getX2X1()

template<class T >

Vec3T< T > EBGeometry::DCEL::EdgeT< T >::getX2X1 ( const Mesh & a_mesh ) const

inlineprotectednoexcept

Get the vector pointing along this edge (from start to end vertex).

Parameters

[in] a_mesh Owning mesh, used to resolve the vertex indices.

Returns: x2 - x1, where x1 = getVertex(a_mesh).getPosition() and x2 = getOtherVertex(a_mesh).getPosition().

◆ operator=() [1/2]

template<class T >

Edge & EBGeometry::DCEL::EdgeT< T >::operator= ( const Edge & a_otherEdge )

default

Copy assignment operator.

Defaulted memberwise copy; see the copy constructor's documentation.

Parameters

[in] a_otherEdge Other edge.

Returns: Reference to (*this).

◆ operator=() [2/2]

template<class T >

Edge & EBGeometry::DCEL::EdgeT< T >::operator= ( Edge && a_otherEdge )

default

Move assignment operator.

Defaulted memberwise move; equivalent to copy assignment since every member is a plain value (see the copy constructor for why it must stay defaulted).

Parameters

[in,out] a_otherEdge Other edge.

Returns: Reference to (*this).

◆ projectPointToEdge()

template<class T >

T EBGeometry::DCEL::EdgeT< T >::projectPointToEdge	(	const Vec3 &	a_x0,
		const Mesh &	a_mesh
	)		const

inlineprotectednoexcept

Returns the parametric projection of a_x0 onto this edge.

Parametrizes the edge as x(t) = x1 + (x2-x1)*t and computes t such that x(t) is the closest point to a_x0. Returns t in (-inf, +inf); the point is on the segment when t in [0,1].

Parameters

[in]	a_x0	Query point.
[in]	a_mesh	Owning mesh, used to resolve the vertex indices.

Returns: Projection parameter t.

◆ reconcile()

template<class T >

void EBGeometry::DCEL::EdgeT< T >::reconcile ( const Mesh & a_mesh )

inlinenoexcept

Reconcile internal logic.

Computes the normal vector.

Parameters

[in] a_mesh Owning mesh, used to resolve the face/pair-edge indices.

◆ setFace()

template<class T >

void EBGeometry::DCEL::EdgeT< T >::setFace ( const uint32_t a_faceIndex )

inlinenoexcept

Set the index of this half-edge's face.

Parameters

[in] a_faceIndex Index of the face in the owning mesh's face array, or UINT32_MAX to mark it unset.

◆ setNextEdge()

template<class T >

void EBGeometry::DCEL::EdgeT< T >::setNextEdge ( const uint32_t a_nextEdgeIndex )

inlinenoexcept

Set the index of the next edge.

Parameters

[in] a_nextEdgeIndex Index of the next edge in the owning mesh's edge array, or UINT32_MAX to mark it unset.

◆ setPairEdge()

template<class T >

void EBGeometry::DCEL::EdgeT< T >::setPairEdge ( const uint32_t a_pairEdgeIndex )

inlinenoexcept

Set the index of the pair edge.

Parameters

[in] a_pairEdgeIndex Index of the pair edge in the owning mesh's edge array, or UINT32_MAX to mark it unset.

◆ setVertex()

template<class T >

void EBGeometry::DCEL::EdgeT< T >::setVertex ( const uint32_t a_vertexIndex )

inlinenoexcept

Set the index of the starting vertex.

Parameters

[in] a_vertexIndex Index of the starting vertex in the owning mesh's vertex array.

◆ signedDistance()

template<class T >

T EBGeometry::DCEL::EdgeT< T >::signedDistance	(	const Vec3 &	a_x0,
		const Mesh &	a_mesh
	)		const

inlinenoexcept

Get the signed distance from a_x0 to this half-edge.

Checks whether a_x0 projects onto the edge segment or past one of the end vertices. If it projects to a vertex, the signed distance to that vertex is returned. Otherwise the sign is determined from the edge normal.

Parameters

[in]	a_x0	Query point.
[in]	a_mesh	Owning mesh, used to resolve the vertex indices.

Returns: Signed distance; positive on the normal side of the edge (or of the closest end vertex).

◆ size()

template<class T >

size_t EBGeometry::DCEL::EdgeT< T >::size ( ) const

inlinenoexcept

Get the number of vertices spanned by a half-edge.

Returns: Always 2 (the starting and ending vertex); not the object's size in bytes.

◆ unsignedDistance2()

template<class T >

T EBGeometry::DCEL::EdgeT< T >::unsignedDistance2	(	const Vec3 &	a_x0,
		const Mesh &	a_mesh
	)		const

inlinenoexcept

Get the squared unsigned distance from a_x0 to this half-edge.

Clamps the projection parameter to [0,1] so the closest point is always on the segment, then returns the squared distance. Faster than signedDistance().

Parameters

[in]	a_x0	Query point.
[in]	a_mesh	Owning mesh, used to resolve the vertex indices.

Returns: Squared Euclidean distance to the closest point on the edge.

Member Data Documentation

◆ m_vertex

template<class T >

uint32_t EBGeometry::DCEL::EdgeT< T >::m_vertex = UINT32_MAX

protected

Index of the starting vertex.

Index into the owning DCEL::MeshT's vertex array, or UINT32_MAX if unset.

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

Source/EBGeometry_DCEL.hpp
Source/EBGeometry_DCEL_Edge.hpp

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ EdgeT() [1/3]

◆ EdgeT() [2/3]

◆ EdgeT() [3/3]

Member Function Documentation

◆ computeNormal()

◆ define()

◆ getFace() [1/2]

◆ getFace() [2/2]

◆ getFaceIndex()

◆ getNextEdge() [1/2]

◆ getNextEdge() [2/2]

◆ getNextEdgeIndex()

◆ getNormal() [1/2]

◆ getNormal() [2/2]

◆ getOtherVertex() [1/2]

◆ getOtherVertex() [2/2]

◆ getPairEdge() [1/2]

◆ getPairEdge() [2/2]

◆ getPairEdgeIndex()

◆ getVertex() [1/2]

◆ getVertex() [2/2]

◆ getVertexIndex()

◆ getX2X1()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ projectPointToEdge()

◆ reconcile()

◆ setFace()

◆ setNextEdge()

◆ setPairEdge()

◆ setVertex()

◆ signedDistance()

◆ size()

◆ unsignedDistance2()

Member Data Documentation

◆ m_vertex