This class implements convex polygons. More...

#include "Polygon.hpp"

Public Types
enum	SideT { Empty =0, On =1, Front =2, FrontAndOn =3, Back =4, BackAndOn =5, Both =6, BothAndOn =7, InIdentical =8, InMirrored =9 }
	Describes on which side of a plane the polygon is. More...

Public Member Functions
bool	IsValid (const double RoundEpsilon, const double MinVertexDist) const
	This methods returns whether a polygon is valid wrt. More...

Plane3T< T >	GetEdgePlane (unsigned long VertexNr, const T Epsilon) const
	Returns the plane that contains the polygon edge defined by (VertexNr, VertexNr+1), that is orthogonal to the polygons plane and whose normal vector points towards the polygon center. More...

Polygon3T< T >	GetMirror () const
	Returns a mirrored copy of this polygon, with reversed plane and reversed order. More...

T	GetArea () const
	Determines the spatial area (Flächeninhalt) of this polygon. More...

bool	HasVertex (const Vector3T< T > &A, const T Epsilon) const
	Determines whether this polygon has a vertex A, within Epsilon tolerance of the existing vertices. More...

SideT	WhatSide (const Plane3T< T > &P, const T HalfPlaneThickness) const
	Determines on what side of plane P this polygon is. More...

SideT	WhatSideSimple (const Plane3T< T > &P, const T HalfPlaneThickness) const
	Like WhatSide(), but it integrates the "...AndOn" answers with the non-"AndOn" answers. More...

bool	Overlaps (const Polygon3T< T > &OtherPoly, bool ReportTouchesAsOverlaps, const T EdgeThickness) const
	Determines whether this polygon overlaps OtherPoly (in the same plane). More...

bool	Encloses (const Polygon3T< T > &OtherPoly, bool MayTouchEdges, const T EdgeThickness) const
	Determines whether this polygon entirely encloses OtherPoly (in the same or mirrored plane). More...

ArrayT< Polygon3T< T > >	GetSplits (const Plane3T< T > &SplitPlane, const T HalfPlaneThickness) const
	Splits the polygon along the passed plane. More...

void	GetChoppedUpAlong (const Polygon3T< T > &Poly, const T EdgeThickness, ArrayT< Polygon3T< T > > &NewPolys) const
	Cuts this polygon along the edges of Poly. More...

void	FillTJunctions (const Polygon3T< T > &Poly, const T EdgeThickness)
	If poly builds t-junctions at this polygon, the according vertives are added to this polygon. More...

Static Public Member Functions
static Polygon3T< T >	Merge (const Polygon3T< T > &Poly1, const Polygon3T< T > &Poly2, const T EdgeThickness)
	Merge Poly1 and Poly2 under the following prerequisites: More...

static void	Complete (ArrayT< Polygon3T< T > > &Polys, const T HalfPlaneThickness, const Vector3T< T > &BoundingSphereCenter=Vector3T< T >(0, 0, 0), const T BoundingSphereRadius=10.0 1000.0 1000.0)
	Given a brush (here: array of polygons), from which only the planes are known. More...

Public Attributes
ArrayT< Vector3T< T > >	Vertices
	Vertices of this polygon. More...

Plane3T< T >	Plane
	Plane of this polygon. More...

Detailed Description

template<class T>
class Polygon3T< T >

This class implements convex polygons.

Properties / invariants of polygons:

Polygons are always convex.
Polygons are always on the "front" side of their plane.
The vertices of a polygon are always ordered in clockwise (CW) order, as seen from the front half-space (against the normal vectors direction) of the polygons plane.
A polygon has at least three vertices and its plane is not degenerate, or it is the "null" polygon.
There are no coincident vertices, that is, V[n]!=V[n+1] for all n.

Member Enumeration Documentation

template<class T>

enum Polygon3T::SideT

Describes on which side of a plane the polygon is.

Enumerator
Empty	The polygon is empty (it has no vertices).
On	The polygon has vertices in the plane. Note that this value alone is never returned by WhatSide().
Front	The polygon has vertices on the front-side of the plane.
FrontAndOn	The polygon has vertices on the front-side of and in the plane.
Back	The polygon has vertices on the back-side of the plane.
BackAndOn	The polygon has vertices on the back-side of and in the plane.
Both	The polygon has vertices on both sides of the plane.
BothAndOn	The polygon has vertices on both sides of and in the plane.
InIdentical	The polygon is in the plane.
InMirrored	The polygon is in the mirrored version of the plane (opposite normal vectors).

Member Function Documentation

template<class T>

void Polygon3T< T >::Complete	(	ArrayT< Polygon3T< T > > &	Polys,
		const T	HalfPlaneThickness,
		const Vector3T< T > &	BoundingSphereCenter = `Vector3T<T>(0, 0, 0)`,
		const T	BoundingSphereRadius = `10.01000.01000.0`
	)

static

Given a brush (here: array of polygons), from which only the planes are known.

WARNING: All normal vectors of the polygons must point to the outside! Find the vertices of all polygons and sort them in clockwise direction. WARNING: Degenerated inputs are also possible, e.g. the planes from a cube with one side missing. Those cases can't be caught here as errors because this functionality is necessary for portal creation. In this case polygons with fewer than 3 vertices are returned and an explicit validity check is necessary! It is also possible that the input planes of a polygon for example specify a triangle where one edge is shorter than GeometryEpsilon. In this case the vertices would be combined and a polygon with only 2 vertices would be the result! Further example for similar degenerated cases are also possible. Consequence: Check the returned polygon sets ALWAYS for validity, e.g. Polys[...].Vertices.Size()>=3 !

Parameters

Polys	Polygons to complete
HalfPlaneThickness	DOCTODO
BoundingSphereCenter	DOCTODO
BoundingSphereRadius	DOCTODO

template<class T>

bool Polygon3T< T >::Encloses	(	const Polygon3T< T > &	OtherPoly,
		bool	MayTouchEdges,
		const T	EdgeThickness
	)		const

Determines whether this polygon entirely encloses OtherPoly (in the same or mirrored plane).

Parameters

OtherPoly	The polygon for which is determined whether it is enclosed by this polygon.
MayTouchEdges	If true, OtherPoly may touch the edges of this polygon within EdgeThickness tolerance and is still being considered enclosed. If false, OtherPoly must truly be inside this polygon, and it must not touch its edges.
EdgeThickness	describes both the "thickness" of the edges of this polygon and the minimum length of the edges of this polygon and OtherPoly.

Returns: true if this polygon encloses OtherPoly, false otherwise. All edge lengths of this and OtherPoly should be longer than 2*EdgeThinkness, or else the result will be undefined.

Exceptions

InvalidOperationE if an edge of this polygon is shorter than EdgeThickness.

template<class T>

void Polygon3T< T >::FillTJunctions	(	const Polygon3T< T > &	Poly,
		const T	EdgeThickness
	)

If poly builds t-junctions at this polygon, the according vertives are added to this polygon.

WARNING: The resulting polygon will, in general, be INVALID (several vertices per edge).

Parameters

Poly	Polygon that is checked for t-junctions with this polygon.
EdgeThickness	DOCTODO

template<class T >

T Polygon3T< T >::GetArea ( ) const

Determines the spatial area (Flächeninhalt) of this polygon.

template<class T>

void Polygon3T< T >::GetChoppedUpAlong	(	const Polygon3T< T > &	Poly,
		const T	EdgeThickness,
		ArrayT< Polygon3T< T > > &	NewPolys
	)		const

Cuts this polygon along the edges of Poly.

Prerequisite: this->Overlaps(Poly)! The last polygon in NewPolys is the overlapping one (*), the front entries lie outside the polygon. (If this polygon is contained in Poly (even then this->Overlaps(Poly) is true), NewPolys contains only a copy of this polygon.) This also works without this prerequisite, but (*) is no longer true! WARNING: This function uses GetSplits() and therfore has the same troubles as this method!

Parameters

Poly	Polygon to cut this polygon with.
EdgeThickness	DOCTODO
NewPolys	The resulting polygons.

template<class T>

Plane3T<T> Polygon3T< T >::GetEdgePlane	(	unsigned long	VertexNr,
		const T	Epsilon
	)		const

inline

Returns the plane that contains the polygon edge defined by (VertexNr, VertexNr+1), that is orthogonal to the polygons plane and whose normal vector points towards the polygon center.

Parameters

VertexNr	The edge defined by (VertexNr, VertexNr+1) for which a plane should be created.
Epsilon	Maximum error value.

Exceptions

DivisionByZeroE if the edge is shorter than accounted for by Epsilon.

template<class T >

Polygon3T< T > Polygon3T< T >::GetMirror ( ) const

Returns a mirrored copy of this polygon, with reversed plane and reversed order.

(If this polygon was valid, the mirrored polygon is valid, too.)

template<class T>

ArrayT< Polygon3T< T > > Polygon3T< T >::GetSplits	(	const Plane3T< T > &	SplitPlane,
		const T	HalfPlaneThickness
	)		const

Splits the polygon along the passed plane.

WARNING: This function can return invalid polygons from a valid polygon! This happens for example if the polygon is a sharp wedge whose top is cut of. If the wedge was sharp enough, vertices may be created at the cut surface that concur with each other! Therefore the resulting polygons should ALWAYS be checked for validity by IsValid()!

Parameters

SplitPlane	The plane to split the polygon with.
HalfPlaneThickness	DOCTODO

Returns: The resulting polygons.

template<class T>

bool Polygon3T< T >::HasVertex	(	const Vector3T< T > &	A,
		const T	Epsilon
	)		const

Determines whether this polygon has a vertex A, within Epsilon tolerance of the existing vertices.

template<class T >

bool Polygon3T< T >::IsValid	(	const double	RoundEpsilon,
		const double	MinVertexDist
	)		const

This methods returns whether a polygon is valid wrt.

the above stipulated properties/terms.

Parameters

RoundEpsilon	The epsilon tolerance that is acceptable for rounding errors.
MinVertexDist	The minimum distance that vertices must be apart. The MinVertexDist value should be a good deal larger than the RoundEpsilon value, because very subtle problems can easily arise whenever the "structural object size" is as small as the maximally permitted rounding error!

Returns: true if the polygon is valid, false otherwise.

template<class T>

Polygon3T< T > Polygon3T< T >::Merge	(	const Polygon3T< T > &	Poly1,
		const Polygon3T< T > &	Poly2,
		const T	EdgeThickness
	)

static

Merge Poly1 and Poly2 under the following prerequisites:

Poly1 and Poly2 have at least 3 vertices (non-degenerate).
Both polygons lie in the same plane with the same orientation.
Poly1 and Poly2 have one common, but opposed edge.
The new polygon is (at the welded joint) also konvex.
Parameters

Poly1 First polygon to merge.

Poly2 Second polygon to merge.

EdgeThickness DOCTODO

Exceptions

InvalidOperationE if Poly1 and Poly2 could not be merged.

template<class T>

bool Polygon3T< T >::Overlaps	(	const Polygon3T< T > &	OtherPoly,
		bool	ReportTouchesAsOverlaps,
		const T	EdgeThickness
	)		const

Determines whether this polygon overlaps OtherPoly (in the same plane).

Parameters

OtherPoly	The polygon for which is determined whether it is overlapped by this polygon.
ReportTouchesAsOverlaps	If true, an overlap is reported even if it has zero area, that is, even if the two polygons merely "touch" within the thickness of the edges. If false, an overlap is only reported if it has a positive, non-zero area.
EdgeThickness	describes both the "thickness" of the edges within which small gaps (i.e. non-overlaps) are tolerated, and the minimum length of the edges of this polygon and OtherPoly.

Exceptions

InvalidOperationE if an edge of this polygon or OtherPoly is shorter than EdgeThickness.

Returns: true if there is an overlap, false otherwise.

template<class T>

Polygon3T< T >::SideT Polygon3T< T >::WhatSide	(	const Plane3T< T > &	P,
		const T	HalfPlaneThickness
	)		const

Determines on what side of plane P this polygon is.

Parameters

P	The plane to check with.
HalfPlaneThickness	DOCTODO

Returns: one of the values of SideT. Note however that SideT::On is never returned in favour of either SideT::InIdentical or SideT::InMirrored. If this polygon has edges that are shorter than the plane thickness (==2*HalfPlaneThickness) and SideT::InIdentical or SideT::InMirrored is returned, the result is inreliable and should not be trusted. (The polygon should then be considered as invalid and be discarded.)

template<class T>

Polygon3T< T >::SideT Polygon3T< T >::WhatSideSimple	(	const Plane3T< T > &	P,
		const T	HalfPlaneThickness
	)		const

Like WhatSide(), but it integrates the "...AndOn" answers with the non-"AndOn" answers.

That is, instead of FrontAndOn only Front is returned, instead of BackAndOn Back, and instead of BothAndOn Both is returned.

Parameters

P	The plane to check with.
HalfPlaneThickness	DOCTODO

See Also: WhatSide()

Member Data Documentation

template<class T>

Plane3T<T> Polygon3T< T >::Plane

Plane of this polygon.

template<class T>

ArrayT< Vector3T<T> > Polygon3T< T >::Vertices

Vertices of this polygon.

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

Libs/Math3D/Polygon.hpp
Libs/Math3D/Polygon.cpp

Poly1	First polygon to merge.
Poly2	Second polygon to merge.
EdgeThickness	DOCTODO

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

template<class T> class Polygon3T< T >

Member Enumeration Documentation

Member Function Documentation

Member Data Documentation

template<class T>
class Polygon3T< T >