A very simple 2D polygon :) More...

#include <triangle_2d.h>

Inheritance diagram for lass::prim::Triangle2D< T >:

Public Member Functions
	Triangle2D ()
	constructs an empty triangle.

	Triangle2D (const TPoint &iA, const TPoint &iB, const TPoint &iC)
	Constructs a triangle through three points in positive sequence.

const TPoint &	operator[] (size_t iIndexOfVertex) const
	return vertex of polygon by its index, not wrapped, no bounds check.

TPoint &	operator[] (size_t iIndexOfVertex)
	return vertex of polygon by its index, not wrapped, no bounds check.

const TPoint &	at (int iIndexOfVertex) const
	return vertex of polygon by its index, but wrap around the bounds.

TPoint &	at (int iIndexOfVertex)
	return vertex of polygon by its index, but wrap around the bounds.

const TLineSegment	edge (int iIndexOfTailVertex) const
	return the edge of the polygon between vertices at(iIndex) and at(iIndex + 1).

const TVector	vector (int iIndexOfTailVertex) const
	return the vector between vertices at(iIndex) and at(iIndex + 1)\

bool	isEmpty () const
	return true if polygon has no vertices

int	size () const
	return number of vertices

const TValue	signedArea () const
	return signed polygon area.

const TValue	area () const
	return area of the polygons surface.

const TValue	perimeter () const
	return sum of the lengths of all edges

const TPointH	vertexCentroid () const
	return the barycenter of all vertices.

const TPointH	surfaceCentroid () const
	return the barycenter of all vertices.

bool	isSimple () const
	return true if polygon is simple, false if not.

bool	isConvex () const
	return true if polygon is convex, false if not.

Orientation	orientation () const
	return orientation of polygon.

bool	isReflex (int iIndexOfVertex) const
	return true if inner angle of vertex is reflex (is > 180 degrees).

bool	contains (const TPoint &iP) const
	return true when a point is inside or on the edge of a triangle.

void	flip ()
	flip orientation of polygon.

Related Symbols
(Note that these are not member symbols.)
template<typename T>
Aabb2D< T >	aabb (const Triangle2D< T > &triangle)
	determine axis aligned bounding box of a 2D triangle

template<typename T, class NP, class PP>
Result	intersect (const Triangle2D< T > &triangle, const Ray2D< T, NP, PP > &ray, T &t, const T &tMin=T())
	Find the intersection of a ray and a triangle by their parameter t on the ray.

template<typename T>
T	partialVoronoiArea (const Triangle2D< T > iT, int vertexIndex)
	Returns the surface of the partial Voronoi cell constructed around vertex vertexIndex (say vertex a in triangle abc).

Detailed Description

template<typename T>
class lass::prim::Triangle2D< T >

A very simple 2D polygon :)

Author: Bram de Greve [BdG]

Definition at line 64 of file triangle_2d.h.

Constructor & Destructor Documentation

◆ Triangle2D()

template<typename T>

lass::prim::Triangle2D< T >::Triangle2D ( )

constructs an empty triangle.

all vertices are (0, 0) and thus equal.

Definition at line 61 of file triangle_2d.inl.

Member Function Documentation

◆ operator[]() [1/2]

template<typename T>

const Triangle2D< T >::TPoint & lass::prim::Triangle2D< T >::operator[] ( size_t vertexIndex ) const

return vertex of polygon by its index, not wrapped, no bounds check.

Definition at line 82 of file triangle_2d.inl.

◆ operator[]() [2/2]

template<typename T>

Triangle2D< T >::TPoint & lass::prim::Triangle2D< T >::operator[] ( size_t vertexIndex )

return vertex of polygon by its index, not wrapped, no bounds check.

Definition at line 93 of file triangle_2d.inl.

◆ at() [1/2]

template<typename T>

const Triangle2D< T >::TPoint & lass::prim::Triangle2D< T >::at ( int vertexIndex ) const

return vertex of polygon by its index, but wrap around the bounds.

this->at(-1) will return the same vertex as this->at(this->size() - 1);

Exceptions

an	exception is thrown if polygon is empty

Definition at line 104 of file triangle_2d.inl.

Referenced by edge(), lass::prim::Triangle2D< U >::partialVoronoiArea(), and vector().

◆ at() [2/2]

template<typename T>

Triangle2D< T >::TPoint & lass::prim::Triangle2D< T >::at ( int vertexIndex )

return vertex of polygon by its index, but wrap around the bounds.

this->at(-1) will return the same vertex as this->at(this->size() - 1);

Exceptions

an	exception is thrown if polygon is empty

Definition at line 116 of file triangle_2d.inl.

◆ edge()

template<typename T>

const Triangle2D< T >::TLineSegment lass::prim::Triangle2D< T >::edge ( int tailVertexIndex ) const

return the edge of the polygon between vertices at(iIndex) and at(iIndex + 1).

Exceptions

an	exception is thrown if polygon has less than two vertices

Definition at line 128 of file triangle_2d.inl.

References at().

◆ vector()

template<typename T>

const Triangle2D< T >::TVector lass::prim::Triangle2D< T >::vector ( int tailVertexIndex ) const

return the vector between vertices at(iIndex) and at(iIndex + 1)\

Definition at line 138 of file triangle_2d.inl.

References at().

◆ isEmpty()

template<typename T>

bool lass::prim::Triangle2D< T >::isEmpty ( ) const

return true if polygon has no vertices

Triangle specific:: if all vertices are equal, we assume the triangle is empty

Definition at line 150 of file triangle_2d.inl.

◆ size()

template<typename T>

int lass::prim::Triangle2D< T >::size ( ) const

return number of vertices

Definition at line 160 of file triangle_2d.inl.

◆ signedArea()

template<typename T>

const Triangle2D< T >::TValue lass::prim::Triangle2D< T >::signedArea ( ) const

return signed polygon area.

The area of a convex polygon is defined to be positive if the points are arranged in a counterclockwise order, and negative if they are in clockwise order., Eric W. Weisstein. "Polygon Area." From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/PolygonArea.html

Algorithm:: comp.graphics.algorithms Frequently Asked Questions: Subject 2.01: "How do I find the area of a polygon?" http://www.faqs.org/faqs/graphics/algorithms-faq/

https://www.johndcook.com/blog/2018/09/26/polygon-area/

Warning: polygon must be simple accoring degenerate policy.

Definition at line 170 of file triangle_2d.inl.

Referenced by area(), and orientation().

◆ area()

template<typename T>

const Triangle2D< T >::TValue lass::prim::Triangle2D< T >::area ( ) const

return area of the polygons surface.

The area of a surface is the amount of material needed to "cover" it completely, Eric W. Weisstein. "Area." From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/Area.html

Warning: polygon must be simple accoring DegeneratePolicy.

Definition at line 181 of file triangle_2d.inl.

References lass::num::abs(), and signedArea().

Referenced by orientation(), and lass::prim::Triangle2D< U >::partialVoronoiArea().

◆ perimeter()

template<typename T>

const Triangle2D< T >::TValue lass::prim::Triangle2D< T >::perimeter ( ) const

return sum of the lengths of all edges

Definition at line 191 of file triangle_2d.inl.

◆ vertexCentroid()

template<typename T>

const Triangle2D< T >::TPointH lass::prim::Triangle2D< T >::vertexCentroid ( ) const

return the barycenter of all vertices.

The vertex centroid is the homogenous sum of all vertices.

Warning: for non-convex polygons, it's NOT guaranteed that this center is inside the polygon.

Definition at line 204 of file triangle_2d.inl.

Referenced by surfaceCentroid().

◆ surfaceCentroid()

template<typename T>

const Triangle2D< T >::TPointH lass::prim::Triangle2D< T >::surfaceCentroid ( ) const

inline

return the barycenter of all vertices.

The vertex centroid is the homogenous sum of all vertices.

Warning: for non-convex polygons, it's NOT guaranteed that this center is inside the polygon.

Definition at line 216 of file triangle_2d.inl.

References vertexCentroid().

◆ isSimple()

template<typename T>

bool lass::prim::Triangle2D< T >::isSimple ( ) const

return true if polygon is simple, false if not.

A polygon P is said to be simple (or Jordan) if the only points of the plane belonging to two polygon edges of P are the polygon vertices of P. Such a polygon has a well defined interior and exterior. Simple polygons are topologically equivalent to a disk., Eric W. Weisstein. "Simple Polygon." From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/SimplePolygon.html

A polygon with less than four vertices is always simple.

Warning: this is a brute force test. we simple test for all edges if they are not intersecting Hence, this is O(n^2).

Triangle specific:: A triangle always is simple

Definition at line 228 of file triangle_2d.inl.

◆ isConvex()

template<typename T>

bool lass::prim::Triangle2D< T >::isConvex ( ) const

return true if polygon is convex, false if not.

A planar polygon is convex if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is convex, while an indented pentagon is not. A planar polygon that is not convex is said to be a concave polygon, Eric W. Weisstein. "Convex Polygon." From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/ConvexPolygon.html

A simple polygon is convex if all the cross products of adjacent edges will be the same sign (we ignore zero cross products of colinear edges, only + or - are taken in account), a concave polygon will have a mixture of cross product signs.

A polygon with less than three vertices is always convex. A polygon with all coincident. vertices is considered convex if DegeneratePolicy allows this.

Warning: polygon must be simple and should not have coincident vertices, according DegeneratePolicy.

Triangle specific:: A triangle always is convex

Definition at line 240 of file triangle_2d.inl.

◆ orientation()

template<typename T>

Orientation lass::prim::Triangle2D< T >::orientation ( ) const

return orientation of polygon.

Warning: polygon must be simple accoring DegeneratePolicy.

Definition at line 250 of file triangle_2d.inl.

References area(), lass::prim::oClockWise, lass::prim::oCounterClockWise, lass::prim::oInvalid, and signedArea().

◆ isReflex()

template<typename T>

bool lass::prim::Triangle2D< T >::isReflex ( int iIndexOfVertex ) const

return true if inner angle of vertex is reflex (is > 180 degrees).

Reflect Angle: An angle more than 180�, Eric W. Weisstein. "Reflex Angle." From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/ReflexAngle.html

test if signedArea() and perdDot(...) have different sign. if one of them is zero, it will return false by default.

Warning: polygon must be simple accoring DegeneratePolicy.

Triangle specific:: triangles never have reflex vertices, so always returns false.

Definition at line 274 of file triangle_2d.inl.

Friends And Related Symbol Documentation

◆ aabb()

template<typename T>

Aabb2D< T > aabb ( const Triangle2D< T > & triangle )

determine axis aligned bounding box of a 2D triangle

See also: lass::prim::Aabb2D

Definition at line 60 of file aabb_2d_triangle_2d.h.

◆ intersect()

template<typename T, class NP, class PP>

Result intersect	(	const Triangle2D< T > &	triangle,
		const Ray2D< T, NP, PP > &	ray,
		T &	t,
		const T &	tMin = T() )

Find the intersection of a ray and a triangle by their parameter t on the ray.

A maximum of two possible intersections with t > 0.

Parameters

triangle	[in] the triangle
ray	[in] the ray
t	[out] the parameter of the intersection point > tMin.
tMin	[in] the minimum t that may be returned as valid intersection.

Returns

rNone no intersections with t > tMin found t is not assigned.
rOne a intersection with t > tMin is found t is assigned.

Definition at line 72 of file ray_2d_triangle_2d.h.

◆ partialVoronoiArea()

template<typename T>

T partialVoronoiArea	(	const Triangle2D< T >	iT,
		int	vertexIndex )

Returns the surface of the partial Voronoi cell constructed around vertex vertexIndex (say vertex a in triangle abc).

Then the surface is determined by the quad built by a, the two midpoints on ab and ac and the intersection of the two perpendicular bisectors.

Definition at line 468 of file triangle_2d.inl.

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

Public Member Functions

Related Symbols

Detailed Description

Constructor & Destructor Documentation

◆ Triangle2D()

Member Function Documentation

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ at() [1/2]

◆ at() [2/2]

◆ edge()

◆ vector()

◆ isEmpty()

◆ size()

◆ signedArea()

◆ area()

◆ perimeter()

◆ vertexCentroid()

◆ surfaceCentroid()

◆ isSimple()

◆ isConvex()

◆ orientation()

◆ isReflex()

Friends And Related Symbol Documentation

◆ aabb()

◆ intersect()

◆ partialVoronoiArea()