The building blocks of a geometric model, a HalfEdge consists of a reference to a start and end point, and links to the counter-clockwise Next, Previous, and Oppostie HalfEdges. More...

Inheritance diagram for PolyLink.HalfEdge:

Public Member Functions
HalfEdge[]	DetourToVertex (PointRef p)
	Create a pair of Half-Edges following this one, which go from this's End to p, and back again More...

Dictionary< HalfEdge, HalfEdge >	LinkNext (HalfEdge he)
	Links a HalfEdge to this one and saves references to possibly unlinked HalfEdges More...

void	MergeAcross ()
	Removes this HalfEdge and joins two neighboring facets More...

override string	ToString ()

	HalfEdge (PointRef start, PointRef end)

void	Unfold (IEnumerable< PointRef > stowaways=null, IEnumerable< HalfEdge > stowawayHalfEdges=null)
	Moves the entire Facet so that it is coplanar with the neighbor opposite this HalfEdge. More...

void	TransformFacet (Expr matrix)
	Transforms every HalfEdge in the facet by a matrix. More...

void	UselessTransform ()
	Transforms the facet by translating it {0,0,0}. In other words, doesn't move the facet at all. More...

void	Anchor (IEnumerable< PointRef > stowaways)
	Moves the facet so that this HalfEdge's start point is at the origin, the EndPoint is in the direction {1,0,0}, and the whole facet is in the xy plane. More...

void	Transform (Expr transform, bool includeStart=true, bool includeEnd=true)
	Transforms just this HalfEdge. More...

void	NegativeTranslate (Vector v)
	Translates this HalfEdge in the opposite direction as the vector v. More...

Expr	Label (int i)
	Returns a Mathematica graphics primitive for an inset label above this HalfEdge. More...

void	MoveStartPoint (Expr p)

IEnumerable< HalfEdge >	BreadthFirstGrab (bool includeTorn=false)
	Creates a list of all connected half-edges in Breadth-First order, starting from here. More...

void	CascadingUnfold (Polyhedron p)
	Unfolds along a halfedge and moves whole sections of the polyhedron with it. More...

IEnumerable< PointRef >	BreadthFirstPoints ()

IEnumerable< HalfEdge >	BreadthFirstGrabAll ()

Public Member Functions inherited from PolyLink.MathLinked
	MathLinked ()

Protected Attributes
PointRef	_start

PointRef	_end

HalfEdge	_opposite

HalfEdge	_next

HalfEdge	_prev

Properties
Facet	Facet `[get, set]`
	Reference to the Facet that owns this HalfEdge. More...

string	Tag `[get]`
	A string used to identify this HalfEdge. Not used in code, but useful for debugging. More...

EndPointPacket	EndPointPacket `[get]`
	Exports the EndpointPacket for this HalfEdge More...

EndPointPacket	OppositesEndPointPacket `[get]`
	Exports the OppositeEndpointPacket for this HalfEdge More...

PointRef	Start `[get, set]`
	Reference to the start point of this HalfEdge. More...

PointRef	End `[get, set]`
	Reference to the end point of this HalfEdge. More...

HalfEdge	Opposite `[get, set]`
	The HalfEdge which represnts the same edge but bounds a neighboring facet More...

HalfEdge	Next `[get]`
	The next HalfEdge going counterclockwise More...

HalfEdge	Prev `[get]`
	The previous Halfedge More...

IEnumerable< HalfEdge >	HEsFromHere `[get]`
	Enumerates the halfedges around the facet that this binds More...

IEnumerable< HalfEdge >	HEsFromHereReversed `[get]`
	Enumerates the halfedges around the facet that this binds, but in reverse order. More...

Expr	AsVectorExpr `[get]`
	Gives the displacement vector from Start to End More...

Vector	AsVector `[get]`
	Gives the displacement vector from Start to End, as a Vector object. More...

Plane	Plane `[get]`
	Gives the plane containing this HalfEdge More...

Expr	DotOpposite `[get]`
	Dots this halfedge's facet with the facet's neighbor along this halfedge. More...

bool	OppIsNull `[get]`
	Returns true iff opposite is null More...

bool	DontCycle `[get, set]`
	Designates that this HalfEdge should break the cycle if the CycleBoutEndPoint property is called. Useful for if a HalfEdge is a working copy that references a real HalfEdge. More...

IEnumerable< HalfEdge >	CycleAboutEndPoint `[get]`
	Enumerates all HalfEdges which have End as their end point More...

Expr	DotNext `[get]`
	Turns the dot product of this and next More...

Expr	AngleToNext `[get]`
	Angle between this and next More...

Expr	SumAngles `[get]`
	Sum of all angles around this vertex More...

Expr	Curvature `[get]`
	Curvature of this vertex More...

Expr	Highlight `[get]`
	A graphics primitive that indicates this HalfEdge with a Thick Red Arrow. More...

static HalfEdge	LittleLine `[get]`
	For testing More...

static HalfEdge	Facetable `[get]`
	For testing More...

Expr	NormalGraphics `[get]`
	Graphics Primitive to visualize the Normal of this HalfEdge. More...

bool	Torn `[get]`
	Returns true iff this HalfEdge's opposite is not made of the same point reference as this. More...

Expr	Graphics `[get]`
	Give a graphical representation of the link between this HalfEdge and its opposite. More...

HalfEdge	FacetCloneWithOriginalOpposites `[get]`
	Clones all the HalfEdges in this HalfEdge's facet, then gives each HalfEdge a link to the (original) opposite. More...

HalfEdge	FacetRingClone `[get]`
	Clones all the HalfEdges in this HalfEdge's facet More...

HalfEdge	ShallowClone `[get]`
	Creates a "Shallow Clone" of this HalfEdge, using the original Start, End, Next, and Prev. Opposite is set to null. More...

Expr	Midpoint `[get]`
	Gives the midpoint between Start and End. More...

Facet	ForceNewFacet `[get]`

IEnumerable< PointRef >	StartPointsFromHere `[get]`

Properties inherited from PolyLink.MathLinked
IKernelDispatch	ML `[get, set]`

Detailed Description

The building blocks of a geometric model, a HalfEdge consists of a reference to a start and end point, and links to the counter-clockwise Next, Previous, and Oppostie HalfEdges.

Definition at line 14 of file HalfEdge.cs.

Constructor & Destructor Documentation

PolyLink.HalfEdge.HalfEdge	(	PointRef	start,
		PointRef	end
	)

Definition at line 365 of file HalfEdge.cs.

Member Function Documentation

void PolyLink.HalfEdge.Anchor ( IEnumerable< PointRef > stowaways )

Moves the facet so that this HalfEdge's start point is at the origin, the EndPoint is in the direction {1,0,0}, and the whole facet is in the xy plane.

Definition at line 492 of file HalfEdge.cs.

IEnumerable<HalfEdge> PolyLink.HalfEdge.BreadthFirstGrab ( bool includeTorn = false )

Creates a list of all connected half-edges in Breadth-First order, starting from here.

Parameters

includeTorn

Returns

Definition at line 690 of file HalfEdge.cs.

IEnumerable<HalfEdge> PolyLink.HalfEdge.BreadthFirstGrabAll ( )

Definition at line 759 of file HalfEdge.cs.

IEnumerable<PointRef> PolyLink.HalfEdge.BreadthFirstPoints ( )

Definition at line 754 of file HalfEdge.cs.

void PolyLink.HalfEdge.CascadingUnfold ( Polyhedron p )

Unfolds along a halfedge and moves whole sections of the polyhedron with it.

Parameters

p

Definition at line 730 of file HalfEdge.cs.

HalfEdge [] PolyLink.HalfEdge.DetourToVertex ( PointRef p )

Create a pair of Half-Edges following this one, which go from this's End to p, and back again

Parameters

p

Definition at line 181 of file HalfEdge.cs.

Expr PolyLink.HalfEdge.Label ( int i )

Returns a Mathematica graphics primitive for an inset label above this HalfEdge.

Parameters

i	The number for the label

Returns

Definition at line 665 of file HalfEdge.cs.

Dictionary<HalfEdge, HalfEdge> PolyLink.HalfEdge.LinkNext ( HalfEdge he )

Links a HalfEdge to this one and saves references to possibly unlinked HalfEdges

Parameters

he	HalfEdge which will become the new next

Returns: Small Dictionary. Value[this] is the old Next of this. Value[he] is the old Prev of he.

Definition at line 212 of file HalfEdge.cs.

void PolyLink.HalfEdge.MergeAcross ( )

Removes this HalfEdge and joins two neighboring facets

Definition at line 233 of file HalfEdge.cs.

void PolyLink.HalfEdge.MoveStartPoint ( Expr p )

Definition at line 672 of file HalfEdge.cs.

void PolyLink.HalfEdge.NegativeTranslate ( Vector v )

Translates this HalfEdge in the opposite direction as the vector v.

Parameters

v

Definition at line 584 of file HalfEdge.cs.

override string PolyLink.HalfEdge.ToString ( )

Definition at line 245 of file HalfEdge.cs.

void PolyLink.HalfEdge.Transform	(	Expr	transform,
		bool	includeStart = `true`,
		bool	includeEnd = `true`
	)

Transforms just this HalfEdge.

Parameters

transform A transform matrix by which to transform the start and end points of this HalfEdge.

Definition at line 550 of file HalfEdge.cs.

void PolyLink.HalfEdge.TransformFacet ( Expr matrix )

Transforms every HalfEdge in the facet by a matrix.

Parameters

matrix matrix to transform this facet

Definition at line 465 of file HalfEdge.cs.

void PolyLink.HalfEdge.Unfold	(	IEnumerable< PointRef >	stowaways = `null`,
		IEnumerable< HalfEdge >	stowawayHalfEdges = `null`
	)

Moves the entire Facet so that it is coplanar with the neighbor opposite this HalfEdge.

Definition at line 388 of file HalfEdge.cs.

void PolyLink.HalfEdge.UselessTransform ( )

Transforms the facet by translating it {0,0,0}. In other words, doesn't move the facet at all.

Definition at line 482 of file HalfEdge.cs.

Member Data Documentation

PointRef PolyLink.HalfEdge._end

protected

Definition at line 71 of file HalfEdge.cs.

HalfEdge PolyLink.HalfEdge._next

protected

Definition at line 87 of file HalfEdge.cs.

HalfEdge PolyLink.HalfEdge._opposite

protected

Definition at line 73 of file HalfEdge.cs.

HalfEdge PolyLink.HalfEdge._prev

protected

Definition at line 88 of file HalfEdge.cs.

PointRef PolyLink.HalfEdge._start

protected

Definition at line 70 of file HalfEdge.cs.

Property Documentation

Expr PolyLink.HalfEdge.AngleToNext

get

Angle between this and next

Definition at line 290 of file HalfEdge.cs.

Vector PolyLink.HalfEdge.AsVector

get

Gives the displacement vector from Start to End, as a Vector object.

Definition at line 152 of file HalfEdge.cs.

Expr PolyLink.HalfEdge.AsVectorExpr

get

Gives the displacement vector from Start to End

Definition at line 144 of file HalfEdge.cs.

Expr PolyLink.HalfEdge.Curvature

get

Curvature of this vertex

Definition at line 313 of file HalfEdge.cs.

IEnumerable<HalfEdge> PolyLink.HalfEdge.CycleAboutEndPoint

get

Enumerates all HalfEdges which have End as their end point

Definition at line 260 of file HalfEdge.cs.

bool PolyLink.HalfEdge.DontCycle

getset

Designates that this HalfEdge should break the cycle if the CycleBoutEndPoint property is called. Useful for if a HalfEdge is a working copy that references a real HalfEdge.

Definition at line 254 of file HalfEdge.cs.

Expr PolyLink.HalfEdge.DotNext

get

Turns the dot product of this and next

Definition at line 282 of file HalfEdge.cs.

Expr PolyLink.HalfEdge.DotOpposite

get

Dots this halfedge's facet with the facet's neighbor along this halfedge.

Definition at line 173 of file HalfEdge.cs.

PointRef PolyLink.HalfEdge.End

getset

Reference to the end point of this HalfEdge.

Definition at line 65 of file HalfEdge.cs.

EndPointPacket PolyLink.HalfEdge.EndPointPacket

get

Exports the EndpointPacket for this HalfEdge

Definition at line 34 of file HalfEdge.cs.

Facet PolyLink.HalfEdge.Facet

getset

Reference to the Facet that owns this HalfEdge.

Definition at line 20 of file HalfEdge.cs.

HalfEdge PolyLink.HalfEdge.Facetable

staticget

For testing

Definition at line 343 of file HalfEdge.cs.

HalfEdge PolyLink.HalfEdge.FacetCloneWithOriginalOpposites

get

Clones all the HalfEdges in this HalfEdge's facet, then gives each HalfEdge a link to the (original) opposite.

Definition at line 594 of file HalfEdge.cs.

HalfEdge PolyLink.HalfEdge.FacetRingClone

get

Clones all the HalfEdges in this HalfEdge's facet

Definition at line 613 of file HalfEdge.cs.

Facet PolyLink.HalfEdge.ForceNewFacet

get

Definition at line 678 of file HalfEdge.cs.

Expr PolyLink.HalfEdge.Graphics

get

Give a graphical representation of the link between this HalfEdge and its opposite.

Definition at line 569 of file HalfEdge.cs.

IEnumerable<HalfEdge> PolyLink.HalfEdge.HEsFromHere

get

Enumerates the halfedges around the facet that this binds

Definition at line 110 of file HalfEdge.cs.

IEnumerable<HalfEdge> PolyLink.HalfEdge.HEsFromHereReversed

get

Enumerates the halfedges around the facet that this binds, but in reverse order.

Definition at line 127 of file HalfEdge.cs.

Expr PolyLink.HalfEdge.Highlight

get

A graphics primitive that indicates this HalfEdge with a Thick Red Arrow.

Definition at line 321 of file HalfEdge.cs.

HalfEdge PolyLink.HalfEdge.LittleLine

staticget

For testing

Definition at line 335 of file HalfEdge.cs.

Expr PolyLink.HalfEdge.Midpoint

get

Gives the midpoint between Start and End.

Definition at line 655 of file HalfEdge.cs.

HalfEdge PolyLink.HalfEdge.Next

get

The next HalfEdge going counterclockwise

Definition at line 94 of file HalfEdge.cs.

Expr PolyLink.HalfEdge.NormalGraphics

get

Graphics Primitive to visualize the Normal of this HalfEdge.

Definition at line 360 of file HalfEdge.cs.

bool PolyLink.HalfEdge.OppIsNull

get

Returns true iff opposite is null

Definition at line 226 of file HalfEdge.cs.

HalfEdge PolyLink.HalfEdge.Opposite

getset

The HalfEdge which represnts the same edge but bounds a neighboring facet

Definition at line 79 of file HalfEdge.cs.

EndPointPacket PolyLink.HalfEdge.OppositesEndPointPacket

get

Exports the OppositeEndpointPacket for this HalfEdge

Definition at line 45 of file HalfEdge.cs.

Plane PolyLink.HalfEdge.Plane

get

Gives the plane containing this HalfEdge

Definition at line 160 of file HalfEdge.cs.

HalfEdge PolyLink.HalfEdge.Prev

get

The previous Halfedge

Definition at line 102 of file HalfEdge.cs.

HalfEdge PolyLink.HalfEdge.ShallowClone

getprotected

Creates a "Shallow Clone" of this HalfEdge, using the original Start, End, Next, and Prev. Opposite is set to null.

Definition at line 637 of file HalfEdge.cs.

PointRef PolyLink.HalfEdge.Start

getset

Reference to the start point of this HalfEdge.

Definition at line 56 of file HalfEdge.cs.

IEnumerable<PointRef> PolyLink.HalfEdge.StartPointsFromHere

get

Definition at line 722 of file HalfEdge.cs.

Expr PolyLink.HalfEdge.SumAngles

get

Sum of all angles around this vertex

Definition at line 302 of file HalfEdge.cs.

string PolyLink.HalfEdge.Tag

get

A string used to identify this HalfEdge. Not used in code, but useful for debugging.

Definition at line 26 of file HalfEdge.cs.

bool PolyLink.HalfEdge.Torn

get

Returns true iff this HalfEdge's opposite is not made of the same point reference as this.

Definition at line 376 of file HalfEdge.cs.

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

E:/DropBox/Dropbox/2013 REU/MathPolys/MathPolyLib/HalfEdge.cs

Public Member Functions

Protected Attributes

Properties

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

Property Documentation