A triangle primitive used to calculate face normals and swept volumes. Uses referred points. More...

#include <triangle.H>

Inheritance diagram for triangle< Point, PointRef >:

Classes
struct	dummyOp
	Dummy. More...
struct	sumAreaOp
	Sum resulting areas. More...
struct	storeOp
	Store resulting tris. More...

Public Types
enum	proxType { NONE = 0 , POINT , EDGE }
	Proximity classifications. More...
typedef Point	point_type
	The point type.
typedef FixedList< triPoints, 27 >	triIntersectionList
	Storage type for triangles originating from intersecting triangle with another triangle.

Public Member Functions
	triangle (const Point &p0, const Point &p1, const Point &p2)
	Construct from three points.
	triangle (const FixedList< Point, 3 > &pts)
	Construct from three points.
	triangle (const UList< Point > &points, const FixedList< label, 3 > &indices)
	Construct from three points out of the list of points.
	triangle (const UList< Point > &points, const label p0, const label p1, const label p2)
	Construct from three points out of the list of points.
	triangle (Istream &is)
	Construct from Istream.
const Point &	a () const noexcept
	The first vertex.
const Point &	b () const noexcept
	The second vertex.
const Point &	c () const noexcept
	The third vertex.
Point	centre () const
	Return centre (centroid).
vector	areaNormal () const
	The area normal - with magnitude equal to area of triangle.
vector	unitNormal () const
	Return unit normal.
	FOAM_DEPRECATED_FOR (2018-12, "areaNormal() or unitNormal()") vector normal() const
	Legacy name for areaNormal().
scalar	mag () const
	The magnitude of the triangle area.
scalar	magSqr () const
	The magnitude squared of the triangle area.
Pair< Point >	box () const
	The enclosing (bounding) box for the triangle.
Point	vecA () const
	Edge vector opposite point a(): from b() to c().
Point	vecB () const
	Edge vector opposite point b(): from c() to a().
Point	vecC () const
	Edge vector opposite point c(): from a() to b().
Point	circumCentre () const
	Return circum-centre.
scalar	circumRadius () const
	Return circum-radius.
scalar	quality () const
	Return quality: Ratio of triangle and circum-circle.
scalar	sweptVol (const triangle &t) const
	Return swept-volume.
tensor	inertia (PointRef refPt=Zero, scalar density=1.0) const
	Return the inertia tensor, with optional reference.
Point	randomPoint (Random &rndGen) const
	Return a random point on the triangle from a uniform distribution.
Point	barycentricToPoint (const barycentric2D &bary) const
	Calculate the point from the given barycentric coordinates.
barycentric2D	pointToBarycentric (const point &pt) const
	Calculate the barycentric coordinates from the given point.
scalar	pointToBarycentric (const point &pt, barycentric2D &bary) const
	Calculate the barycentric coordinates from the given point.
bool	intersects (const point &origin, const vector &normal) const
	Fast intersection detection with a plane.
bool	intersects (const point &origin, const vector::components axis) const
	Fast intersection detection with an axis plane.
pointHit	ray (const point &p, const vector &q, const intersection::algorithm=intersection::FULL_RAY, const intersection::direction dir=intersection::VECTOR) const
	Return point intersection with a ray.
pointHit	intersection (const point &p, const vector &q, const intersection::algorithm alg, const scalar tol=0.0) const
	Fast intersection with a ray.
pointHit	nearestPointClassify (const point &p, label &nearType, label &nearLabel) const
	Find the nearest point to p on the triangle and classify it:
pointHit	nearestPoint (const point &p) const
	Return nearest point to p on triangle.
bool	classify (const point &p, label &nearType, label &nearLabel) const
	Classify nearest point to p in triangle plane.
pointHit	nearestPoint (const linePointRef &edge, pointHit &edgePoint) const
	Return nearest point to line on triangle. Returns hit if.
int	sign (const point &p, const scalar tol=SMALL) const
	The sign for which side of the face plane the point is on.
template<class AboveOp, class BelowOp>
void	sliceWithPlane (const plane &pln, AboveOp &aboveOp, BelowOp &belowOp) const
	Decompose triangle into triangles above and below plane.
template<class InsideOp, class OutsideOp>
void	triangleOverlap (const vector &n, const triangle< Point, PointRef > &tri, InsideOp &insideOp, OutsideOp &outsideOp) const
	Decompose triangle into triangles inside and outside.

Static Public Member Functions
static Point	centre (const Point &p0, const Point &p1, const Point &p2)
	The centre (centroid) of three points.
static vector	areaNormal (const Point &p0, const Point &p1, const Point &p2)
	The area normal for a triangle defined by three points (right-hand rule). Magnitude equal to area of the triangle.
static vector	unitNormal (const Point &p0, const Point &p1, const Point &p2)
	The unit normal for a triangle defined by three points (right-hand rule).
static Pair< Point >	box (const Point &p0, const Point &p1, const Point &p2)
	The enclosing (bounding) box for three points.

Friends
Istream &	operator>> (Istream &, triangle &)
Ostream &	operator (Ostream &, const triangle &)

Detailed Description

template<class Point, class PointRef>
class Foam::triangle< Point, PointRef >

A triangle primitive used to calculate face normals and swept volumes. Uses referred points.

Source files

Definition at line 233 of file triangle.H.

Member Typedef Documentation

◆ point_type

template<class Point, class PointRef>

typedef Point point_type

The point type.

Definition at line 242 of file triangle.H.

◆ triIntersectionList

template<class Point, class PointRef>

typedef FixedList<triPoints, 27> triIntersectionList

Storage type for triangles originating from intersecting triangle with another triangle.

Definition at line 248 of file triangle.H.

Member Enumeration Documentation

◆ proxType

template<class Point, class PointRef>

enum proxType

Proximity classifications.

Enumerator
NONE	Unknown proximity.
POINT	Close to point.
EDGE	Close to edge.

Definition at line 253 of file triangle.H.

Constructor & Destructor Documentation

◆ triangle() [1/5]

template<class Point, class PointRef>

triangle	(	const Point &	p0,
		const Point &	p1,
		const Point &	p2 )

inline

Construct from three points.

Definition at line 80 of file triangleI.H.

References p0.

Referenced by triangle< Point, PointRef >::sumAreaOp::operator()(), sweptVol(), and triangleOverlap().

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◆ triangle() [2/5]

template<class Point, class PointRef>

triangle ( const FixedList< Point, 3 > & pts )

inline

Construct from three points.

Definition at line 94 of file triangleI.H.

References pts.

◆ triangle() [3/5]

template<class Point, class PointRef>

triangle	(	const UList< Point > &	points,
		const FixedList< label, 3 > &	indices )

inline

Construct from three points out of the list of points.

The indices could be from triFace etc.

Definition at line 106 of file triangleI.H.

References points.

◆ triangle() [4/5]

template<class Point, class PointRef>

triangle	(	const UList< Point > &	points,
		const label	p0,
		const label	p1,
		const label	p2 )

inline

Construct from three points out of the list of points.

Definition at line 119 of file triangleI.H.

References p0, and points.

◆ triangle() [5/5]

template<class Point, class PointRef>

triangle ( Istream & is )

inlineexplicit

Construct from Istream.

Definition at line 134 of file triangleI.H.

Member Function Documentation

◆ a()

template<class Point, class PointRef>

const Point & a ( ) const

inlinenoexcept

The first vertex.

Definition at line 398 of file triangle.H.

Referenced by triSurfaceTools::calcInterpolationWeights(), circumRadius(), inertia(), triangleFuncs::intersectBb(), offsetSurface::operator()(), and triangleOverlap().

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◆ b()

template<class Point, class PointRef>

const Point & b ( ) const

inlinenoexcept

The second vertex.

Definition at line 403 of file triangle.H.

Referenced by triSurfaceTools::calcInterpolationWeights(), triangleFuncs::intersectBb(), offsetSurface::operator()(), and triangleOverlap().

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◆ c()

template<class Point, class PointRef>

const Point & c ( ) const

inlinenoexcept

The third vertex.

Definition at line 408 of file triangle.H.

Referenced by triSurfaceTools::calcInterpolationWeights(), circumCentre(), triangleFuncs::intersectBb(), offsetSurface::operator()(), quality(), and triangleOverlap().

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◆ centre() [1/2]

template<class Point, class PointRef>

Point centre	(	const Point &	p0,
		const Point &	p1,
		const Point &	p2 )

inlinestatic

The centre (centroid) of three points.

Definition at line 143 of file triangleI.H.

References p0.

Referenced by circumCentre(), primitiveMeshTools::makeFaceCentresAndAreas(), stabilisedFvGeometryScheme::makeFaceCentresAndAreas(), momentOfInertia::massPropertiesShell(), nearestPointClassify(), polyMesh::pointInCell(), wallBoundedStreamLine::pushIn(), and primitiveMeshTools::updateFaceCentresAndAreas().

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◆ areaNormal() [1/2]

template<class Point, class PointRef>

Foam::vector areaNormal	(	const Point &	p0,
		const Point &	p1,
		const Point &	p2 )

inlinestatic

The area normal for a triangle defined by three points (right-hand rule). Magnitude equal to area of the triangle.

Definition at line 168 of file triangleI.H.

References p0.

Referenced by mag(), magSqr(), primitiveMeshTools::makeFaceCentresAndAreas(), stabilisedFvGeometryScheme::makeFaceCentresAndAreas(), tetrahedron< Point, PointRef >::nearestPoint(), polyMesh::pointInCell(), ray(), advancingFrontAMI::triangulatePatch(), unitNormal(), and primitiveMeshTools::updateFaceCentresAndAreas().

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◆ unitNormal() [1/2]

template<class Point, class PointRef>

Foam::vector unitNormal	(	const Point &	p0,
		const Point &	p1,
		const Point &	p2 )

inlinestatic

The unit normal for a triangle defined by three points (right-hand rule).

Definition at line 193 of file triangleI.H.

References areaNormal(), n, and p0.

Referenced by tetrahedron< Point, PointRef >::inside(), and sign().

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◆ box() [1/2]

template<class Point, class PointRef>

Foam::Pair< Point > box	(	const Point &	p0,
		const Point &	p1,
		const Point &	p2 )

inlinestatic

The enclosing (bounding) box for three points.

Definition at line 220 of file triangleI.H.

References Foam::max(), Foam::min(), and p0.

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◆ centre() [2/2]

template<class Point, class PointRef>

Point centre ( ) const

inline

Return centre (centroid).

Definition at line 155 of file triangleI.H.

◆ areaNormal() [2/2]

template<class Point, class PointRef>

Foam::vector areaNormal ( ) const

inline

The area normal - with magnitude equal to area of triangle.

Definition at line 180 of file triangleI.H.

Referenced by triangle< point, const point & >::FOAM_DEPRECATED_FOR(), tetrahedron< Point, PointRef >::Sa(), tetrahedron< Point, PointRef >::Sb(), tetrahedron< Point, PointRef >::Sc(), and tetrahedron< Point, PointRef >::Sd().

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◆ unitNormal() [2/2]

template<class Point, class PointRef>

Foam::vector unitNormal ( ) const

inline

Return unit normal.

Definition at line 207 of file triangleI.H.

References unitNormal().

Referenced by unitNormal().

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◆ FOAM_DEPRECATED_FOR()

template<class Point, class PointRef>

FOAM_DEPRECATED_FOR	(	2018-	12,
		"areaNormal() or unitNormal()"	) const

inline

Legacy name for areaNormal().

Deprecated: (2018-06) Deprecated for new use

Definition at line 478 of file triangle.H.

◆ mag()

template<class Point, class PointRef>

Foam::scalar mag ( ) const

inline

The magnitude of the triangle area.

Definition at line 309 of file triangleI.H.

References areaNormal().

Referenced by polyMeshGeometry::checkFaceFlatness(), FreeStream< CloudType >::inflow(), momentOfInertia::massPropertiesShell(), and advancingFrontAMI::triangulatePatch().

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◆ magSqr()

template<class Point, class PointRef>

Foam::scalar magSqr ( ) const

inline

The magnitude squared of the triangle area.

Definition at line 322 of file triangleI.H.

References areaNormal().

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◆ box() [2/2]

template<class Point, class PointRef>

Foam::Pair< Point > box ( ) const

inline

The enclosing (bounding) box for the triangle.

Definition at line 236 of file triangleI.H.

References box().

Referenced by box().

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◆ vecA()

template<class Point, class PointRef>

Point vecA ( ) const

inline

Edge vector opposite point a(): from b() to c().

Definition at line 249 of file triangleI.H.

◆ vecB()

template<class Point, class PointRef>

Point vecB ( ) const

inline

Edge vector opposite point b(): from c() to a().

Definition at line 255 of file triangleI.H.

◆ vecC()

template<class Point, class PointRef>

Point vecC ( ) const

inline

Edge vector opposite point c(): from a() to b().

Definition at line 261 of file triangleI.H.

◆ circumCentre()

template<class Point, class PointRef>

Point circumCentre ( ) const

inline

Return circum-centre.

Definition at line 329 of file triangleI.H.

References c(), centre(), and Foam::mag().

Referenced by Foam::edgeMeshTools::featureProximity().

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◆ circumRadius()

template<class Point, class PointRef>

Foam::scalar circumRadius ( ) const

inline

Return circum-radius.

Definition at line 356 of file triangleI.H.

References a(), Foam::clamp(), Foam::mag(), and Foam::sqrt().

Referenced by Foam::edgeMeshTools::featureProximity(), and quality().

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◆ quality()

template<class Point, class PointRef>

Foam::scalar quality ( ) const

inline

Return quality: Ratio of triangle and circum-circle.

area, scaled so that an equilateral triangle has a quality of 1

Definition at line 377 of file triangleI.H.

References c(), circumRadius(), Foam::mag(), Foam::sqr(), and Foam::sqrt().

Referenced by searchableSurfaces::checkQuality().

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◆ sweptVol()

template<class Point, class PointRef>

Foam::scalar sweptVol ( const triangle< Point, PointRef > & t ) const

inline

Return swept-volume.

Definition at line 392 of file triangleI.H.

References triangle().

Referenced by face::sweptVol().

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◆ inertia()

template<class Point, class PointRef>

Foam::tensor inertia	(	PointRef	refPt = Zero,
		scalar	density = 1.0 ) const

inline

Return the inertia tensor, with optional reference.

point and density specification

Definition at line 411 of file triangleI.H.

References a(), Foam::I, Foam::mag(), and VectorSpace< Form, Cmpt, Mrows *Ncols >::one.

Referenced by face::inertia(), and momentOfInertia::massPropertiesShell().

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◆ randomPoint()

template<class Point, class PointRef>

Point randomPoint ( Random & rndGen ) const

inline

Return a random point on the triangle from a uniform distribution.

Definition at line 448 of file triangleI.H.

References Foam::barycentric2D01(), barycentricToPoint(), and rndGen.

Referenced by FreeStream< CloudType >::inflow().

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◆ barycentricToPoint()

template<class Point, class PointRef>

Point barycentricToPoint ( const barycentric2D & bary ) const

inline

Calculate the point from the given barycentric coordinates.

Definition at line 455 of file triangleI.H.

Referenced by randomPoint().

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◆ pointToBarycentric() [1/2]

template<class Point, class PointRef>

Foam::barycentric2D pointToBarycentric ( const point & pt ) const

inline

Calculate the barycentric coordinates from the given point.

Definition at line 465 of file triangleI.H.

References pointToBarycentric().

Referenced by cellPointWeight::findTriangle(), distributedTriSurfaceMesh::getNormal(), offsetSurface::operator()(), and pointToBarycentric().

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◆ pointToBarycentric() [2/2]

template<class Point, class PointRef>

Foam::scalar pointToBarycentric	(	const point &	pt,
		barycentric2D &	bary ) const

inline

Calculate the barycentric coordinates from the given point.

Returns the determinant.

Definition at line 477 of file triangleI.H.

References Foam::mag().

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◆ intersects() [1/2]

template<class Point, class PointRef>

bool intersects	(	const point &	origin,
		const vector &	normal ) const

inline

Fast intersection detection with a plane.

Definition at line 516 of file triangleI.H.

◆ intersects() [2/2]

template<class Point, class PointRef>

bool intersects	(	const point &	origin,
		const vector::components	axis ) const

inline

Fast intersection detection with an axis plane.

Parameters

origin	Origin of the plane
axis	Normal of the plane (vector::X, vector::Y, vector::Z)

Definition at line 536 of file triangleI.H.

◆ ray()

template<class Point, class PointRef>

Foam::pointHit ray	(	const point &	p,
		const vector &	q,
		const intersection::algorithm	alg = intersection::FULL_RAY,
		const intersection::direction	dir = intersection::VECTOR ) const

inline

Return point intersection with a ray.

For a hit, the distance is signed. Positive number represents the point in front of triangle. In case of miss pointHit is set to nearest point on triangle and its distance to the distance between the original point and the plane intersection point

Definition at line 556 of file triangleI.H.

References areaNormal(), intersection::CONTACT_SPHERE, intersection::FULL_RAY, intersection::HALF_RAY, PointHit< PointType >::hit(), PointHit< PointType >::hitPoint(), intersection(), Foam::mag(), Foam::min(), n, nearestPoint(), p, intersection::planarTol(), PointHit< PointType >::point(), ray(), PointHit< PointType >::setDistance(), PointHit< PointType >::setMiss(), PointHit< PointType >::setPoint(), intersection::VECTOR, and intersection::VISIBLE.

Referenced by face::ray(), and ray().

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◆ intersection()

template<class Point, class PointRef>

Foam::pointHit intersection	(	const point &	p,
		const vector &	q,
		const intersection::algorithm	alg,
		const scalar	tol = 0.0 ) const

inline

Fast intersection with a ray.

For a hit, the pointHit.distance() is the line parameter t : intersection=p+t*q. Only defined for VISIBLE, FULL_RAY or HALF_RAY. tol increases the virtual size of the triangle by a relative factor.

Definition at line 671 of file triangleI.H.

References Foam::det(), intersection::FULL_RAY, intersection::HALF_RAY, intersection(), intersection::VISIBLE, and Foam::Zero.

Referenced by mappedPatchBase::facePoint(), treeDataPrimitivePatch< PatchType >::findIntersection(), triangleFuncs::intersectBb(), face::intersection(), intersection(), nearestPoint(), and ray().

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◆ nearestPointClassify()

template<class Point, class PointRef>

Foam::pointHit nearestPointClassify	(	const point &	p,
		label &	nearType,
		label &	nearLabel ) const

Find the nearest point to p on the triangle and classify it:

+ near point (nearType=POINT, nearLabel=0, 1, 2) + near edge (nearType=EDGE, nearLabel=0, 1, 2) Note: edges are counted from starting vertex so e.g. edge 2 is from f[2] to f[0]

Definition at line 753 of file triangleI.H.

References centre(), Foam::cp(), EDGE, Foam::mag(), NONE, p, and POINT.

Referenced by triSurfaceTools::calcInterpolationWeights(), classify(), nearestPoint(), and face::nearestPointClassify().

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◆ nearestPoint() [1/2]

template<class Point, class PointRef>

Foam::pointHit nearestPoint ( const point & p ) const

inline

Return nearest point to p on triangle.

Definition at line 902 of file triangleI.H.

References nearestPointClassify(), and p.

Referenced by wallBoundedStreamLine::findNearestTet(), cellPointWeight::findTriangle(), tetrahedron< Point, PointRef >::nearestPoint(), and ray().

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◆ classify()

template<class Point, class PointRef>

bool classify	(	const point &	p,
		label &	nearType,
		label &	nearLabel ) const

inline

Classify nearest point to p in triangle plane.

w.r.t. triangle edges and points. Returns inside (true)/outside (false).

Definition at line 916 of file triangleI.H.

References nearestPointClassify(), and p.

Referenced by triSurfaceTools::classify().

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◆ nearestPoint() [2/2]

template<class Point, class PointRef>

Foam::pointHit nearestPoint	(	const linePointRef &	edge,
		pointHit &	edgePoint ) const

inline

Return nearest point to line on triangle. Returns hit if.

point is inside triangle. Sets edgePoint to point on edge (hit if nearest is inside line)

Definition at line 928 of file triangleI.H.

References Vector< Cmpt >::dist(), PointHit< PointType >::distance(), intersection::FULL_RAY, PointHit< PointType >::hit(), PointHit< PointType >::hitPoint(), intersection(), Foam::ln(), Foam::mag(), PointHit< PointType >::point(), PointHit< PointType >::setDistance(), PointHit< PointType >::setMiss(), and PointHit< PointType >::setPoint().

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◆ sign()

template<class Point, class PointRef>

int sign	(	const point &	p,
		const scalar	tol = SMALL ) const

inline

The sign for which side of the face plane the point is on.

Uses the supplied tolerance for rounding around zero.

Returns

0: on plane
+1: above plane
-1: below plane

Definition at line 1052 of file triangleI.H.

References p, and unitNormal().

Referenced by face::sign().

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◆ sliceWithPlane()

template<class Point, class PointRef>

template<class AboveOp, class BelowOp>

void sliceWithPlane	(	const plane &	pln,
		AboveOp &	aboveOp,
		BelowOp &	belowOp ) const

inline

Decompose triangle into triangles above and below plane.

Definition at line 106 of file triangle.C.

◆ triangleOverlap()

template<class Point, class PointRef>

template<class InsideOp, class OutsideOp>

void triangleOverlap	(	const vector &	n,
		const triangle< Point, PointRef > &	tri,
		InsideOp &	insideOp,
		OutsideOp &	outsideOp ) const

inline

Decompose triangle into triangles inside and outside.

(with respect to user provided normal) other triangle.

Definition at line 119 of file triangle.C.

References a(), b(), c(), Foam::mag(), n, triangle< Point, PointRef >::storeOp::nTris_, s(), triangle(), and triangle< Point, PointRef >::storeOp::tris_.

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◆ operator>>

template<class Point, class PointRef>

Istream & operator>>	(	Istream &	,
		triangle< Point, PointRef > &	)

friend

◆ operator

template<class Point, class PointRef>

Ostream & operator	(	Ostream &	,
		const triangle< Point, PointRef > &	)

friend

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

src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.H
src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.C
src/OpenFOAM/meshes/primitiveShapes/triangle/triangleI.H

Classes

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Member Typedef Documentation

◆ point_type

◆ triIntersectionList

Member Enumeration Documentation

◆ proxType

Constructor & Destructor Documentation

◆ triangle() [1/5]

◆ triangle() [2/5]

◆ triangle() [3/5]

◆ triangle() [4/5]

◆ triangle() [5/5]

Member Function Documentation

◆ a()

◆ b()

◆ c()

◆ centre() [1/2]

◆ areaNormal() [1/2]

◆ unitNormal() [1/2]

◆ box() [1/2]

◆ centre() [2/2]

◆ areaNormal() [2/2]

◆ unitNormal() [2/2]

◆ FOAM_DEPRECATED_FOR()

◆ mag()

◆ magSqr()

◆ box() [2/2]

◆ vecA()

◆ vecB()

◆ vecC()

◆ circumCentre()

◆ circumRadius()

◆ quality()

◆ sweptVol()

◆ inertia()

◆ randomPoint()

◆ barycentricToPoint()

◆ pointToBarycentric() [1/2]

◆ pointToBarycentric() [2/2]

◆ intersects() [1/2]

◆ intersects() [2/2]

◆ ray()

◆ intersection()

◆ nearestPointClassify()

◆ nearestPoint() [1/2]

◆ classify()

◆ nearestPoint() [2/2]

◆ sign()

◆ sliceWithPlane()

◆ triangleOverlap()

Friends And Related Symbol Documentation

◆ operator>>

◆ operator