meshGFaceDelaunayInsertion.cpp File Reference

#include <limits>
#include <set>
#include <map>
#include <algorithm>
#include <numeric>
#include "GmshConfig.h"
#include "GmshMessage.h"
#include "OS.h"
#include "robustPredicates.h"
#include "BackgroundMesh.h"
#include "meshGFaceDelaunayInsertion.h"
#include "meshGFaceOptimize.h"
#include "meshGFace.h"
#include "GModel.h"
#include "GFace.h"
#include "Numeric.h"
#include "STensor3.h"
#include "Context.h"
#include "discreteFace.h"
#include "intersectCurveSurface.h"
#include "HilbertCurve.h"
#include "fullMatrix.h"

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Functions
static void	getDegeneratedVertices (GFace *gf, std::set< GEntity * > &degenerated)
static bool	intersection_segments_2 (double *p1, double *p2, double *q1, double *q2)
template<class ITERATOR >
void	_printTris (char *name, ITERATOR it, ITERATOR end, bidimMeshData *data, GFace *gf=nullptr, std::set< GEntity * > *degenerated=nullptr)
static bool	isActive (MTri3 *t, double limit_, int &active)
static bool	isActive (MTri3 *t, double limit_, int &i, std::set< MEdge, MEdgeLessThan > *front)
static void	updateActiveEdges (MTri3 *t, double limit_, std::set< MEdge, MEdgeLessThan > &front)
static void	circumCenterMetric (double *pa, double *pb, double *pc, const double *metric, double *x, double &Radius2)
static void	circumCenterMetricXYZ (double *p1, double *p2, double *p3, SMetric3 &metric, double *res, double *uv, double &radius)
static void	circumCenterMetric (MTriangle *base, const double *metric, bidimMeshData &data, double *x, double &Radius2)
void	buildMetric (GFace *gf, double *uv, double *metric)
static double	computeTolerance (const double radius)
int	inCircumCircleAniso (GFace *gf, double *p1, double *p2, double *p3, double *uv, double *metric)
int	inCircumCircleAniso (GFace *gf, MTriangle *base, const double *uv, const double *metricb, bidimMeshData &data)
static void	fourthPoint (double *p1, double *p2, double *p3, double *p4)
int	inCircumCircle (MTriangle *base, const double *p, const double *param, bidimMeshData &data)
template<class Iterator >
static void	connectTris (Iterator beg, Iterator end, std::vector< edgeXface > &conn)
void	connectTriangles (std::list< MTri3 * > &l)
void	connectTriangles (std::vector< MTri3 * > &l)
void	connectTriangles (std::set< MTri3 *, compareTri3Ptr > &l)
static int	inCircumCircleXY (MTriangle *t, MVertex *v)
static void	recurFindCavity (std::vector< edgeXface > &shell, std::vector< MTri3 * > &cavity, MVertex *v, MTri3 *t)
static void	recurFindCavityAniso (GFace *gf, std::list< edgeXface > &shell, std::list< MTri3 * > &cavity, double *metric, double *param, MTri3 *t, bidimMeshData &data)
static bool	circUV (MTriangle *t, bidimMeshData &data, double *res, GFace *gf)
static bool	invMapUV (MTriangle *t, double *p, bidimMeshData &data, double *uv, double tol)
double	getSurfUV (MTriangle *t, bidimMeshData &data)
static int	insertVertexB (std::list< edgeXface > &shell, std::list< MTri3 * > &cavity, bool force, GFace *gf, MVertex *v, double *param, MTri3 *t, std::set< MTri3 *, compareTri3Ptr > &allTets, std::set< MTri3 *, compareTri3Ptr > *activeTets, bidimMeshData &data, double *metric, MTri3 **oneNewTriangle, bool verifyStarShapeness=true)
static bool	invMapXY (MTriangle *t, MVertex *v)
static MTri3 *	search4Triangle (MTri3 *t, MVertex *v, int maxx, int &ITER)
static MTri3 *	search4Triangle (MTri3 *t, double pt[2], bidimMeshData &data, std::set< MTri3 *, compareTri3Ptr > &AllTris, double uv[2], bool force=false)
static bool	insertAPoint (GFace *gf, std::set< MTri3 *, compareTri3Ptr >::iterator it, double center[2], double metric[3], bidimMeshData &data, std::set< MTri3 *, compareTri3Ptr > &AllTris, std::set< MTri3 *, compareTri3Ptr > *ActiveTris=nullptr, MTri3 *worst=nullptr, MTri3 **oneNewTriangle=nullptr, bool testStarShapeness=false)
void	bowyerWatson (GFace *gf, int MAXPNT, std::map< MVertex *, MVertex * > *equivalence, std::map< MVertex *, SPoint2 > *parametricCoordinates)
static double	lengthInfniteNorm (const double p[2], const double q[2], const double quadAngle)
static void	circumCenterInfinite (MTriangle *base, double quadAngle, bidimMeshData &data, double *x)
static double	lengthMetric (const double p[2], const double q[2], const double metric[3])
static double	optimalPointFrontal (GFace *gf, MTri3 *worst, int active_edge, bidimMeshData &data, double newPoint[2], double metric[3])
static bool	optimalPointFrontalB (GFace *gf, MTri3 *worst, int active_edge, bidimMeshData &data, double newPoint[2], double metric[3])
void	bowyerWatsonFrontal (GFace *gf, std::map< MVertex *, MVertex * > *equivalence, std::map< MVertex *, SPoint2 > *parametricCoordinates, std::vector< SPoint2 > *true_boundary)
static void	optimalPointFrontalQuad (GFace *gf, MTri3 *worst, int active_edge, bidimMeshData &data, double newPoint[2], double metric[3])
void	buildBackgroundMesh (GFace *gf, bool crossFieldClosestPoint, std::map< MVertex *, MVertex * > *equivalence, std::map< MVertex *, SPoint2 > *parametricCoordinates)
void	bowyerWatsonFrontalLayers (GFace *gf, bool quad, std::map< MVertex *, MVertex * > *equivalence, std::map< MVertex *, SPoint2 > *parametricCoordinates)
void	bowyerWatsonParallelograms (GFace *gf, std::map< MVertex *, MVertex * > *equivalence, std::map< MVertex *, SPoint2 > *parametricCoordinates)
void	bowyerWatsonParallelogramsConstrained (GFace *gf, const std::set< MVertex * > &constr_vertices, std::map< MVertex *, MVertex * > *equivalence, std::map< MVertex *, SPoint2 > *parametricCoordinates)
static void	initialSquare (std::vector< MVertex * > &v, MVertex *box[4], std::vector< MTri3 * > &t)
static MTri3 *	getTriToBreak (MVertex *v, std::vector< MTri3 * > &t, int &ITER)
static bool	triOnBox (MTriangle *t, MVertex *box[4])
void	recoverEdges (std::vector< MTri3 * > &t, std::vector< MEdge > &edges)
void	delaunayMeshIn2D (std::vector< MVertex * > &v, std::vector< MTriangle * > &result, bool removeBox, std::vector< MEdge > *edgesToRecover, bool hilbertSort)
bool	swapedge (MVertex *v1, MVertex *v2, MVertex *v3, MVertex *v4, MTri3 *t1, int iLocalEdge)
bool	diffend (MVertex *v1, MVertex *v2, MVertex *p1, MVertex *p2)
static bool	recoverEdgeBySwaps (std::vector< MTri3 * > &t, MVertex *mv1, MVertex *mv2, std::vector< MEdge > &edges)

Variables
static double	LIMIT_ = 0.5 * std::sqrt(2.0) * 1

Function Documentation

_printTris()

template<class ITERATOR >

void _printTris	(	char *	name,
		ITERATOR	it,
		ITERATOR	end,
		bidimMeshData *	data,
		GFace *	gf = nullptr,
		std::set< GEntity * > *	degenerated = nullptr
	)

Definition at line 64 of file meshGFaceDelaunayInsertion.cpp.

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bowyerWatson()

void bowyerWatson	(	GFace *	gf,
		int	MAXPNT,
		std::map< MVertex *, MVertex * > *	equivalence,
		std::map< MVertex *, SPoint2 > *	parametricCoordinates
	)

Definition at line 1033 of file meshGFaceDelaunayInsertion.cpp.

Referenced by buildBackgroundMesh(), meshGenerator(), and meshGeneratorPeriodic().

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bowyerWatsonFrontal()

void bowyerWatsonFrontal	(	GFace *	gf,
		std::map< MVertex *, MVertex * > *	equivalence,
		std::map< MVertex *, SPoint2 > *	parametricCoordinates,
		std::vector< SPoint2 > *	true_boundary
	)

Definition at line 1289 of file meshGFaceDelaunayInsertion.cpp.

Referenced by meshGenerator(), and meshGeneratorPeriodic().

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bowyerWatsonFrontalLayers()

void bowyerWatsonFrontalLayers	(	GFace *	gf,
		bool	quad,
		std::map< MVertex *, MVertex * > *	equivalence,
		std::map< MVertex *, SPoint2 > *	parametricCoordinates
	)

Definition at line 1497 of file meshGFaceDelaunayInsertion.cpp.

Referenced by meshGenerator(), and meshGeneratorPeriodic().

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bowyerWatsonParallelograms()

void bowyerWatsonParallelograms	(	GFace *	gf,
		std::map< MVertex *, MVertex * > *	equivalence,
		std::map< MVertex *, SPoint2 > *	parametricCoordinates
	)

Definition at line 1621 of file meshGFaceDelaunayInsertion.cpp.

Referenced by meshGenerator(), and meshGeneratorPeriodic().

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bowyerWatsonParallelogramsConstrained()

void bowyerWatsonParallelogramsConstrained	(	GFace *	gf,
		const std::set< MVertex * > &	constr_vertices,
		std::map< MVertex *, MVertex * > *	equivalence,
		std::map< MVertex *, SPoint2 > *	parametricCoordinates
	)

Definition at line 1711 of file meshGFaceDelaunayInsertion.cpp.

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buildBackgroundMesh()

void buildBackgroundMesh	(	GFace *	gf,
		bool	crossFieldClosestPoint,
		std::map< MVertex *, MVertex * > *	equivalence,
		std::map< MVertex *, SPoint2 > *	parametricCoordinates
	)

Definition at line 1453 of file meshGFaceDelaunayInsertion.cpp.

Referenced by meshGenerator(), and meshGeneratorPeriodic().

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buildMetric()

void buildMetric	(	GFace *	gf,
		double *	uv,
		double *	metric
	)

Definition at line 332 of file meshGFaceDelaunayInsertion.cpp.

Referenced by _relocate(), bowyerWatson(), bowyerWatsonParallelograms(), bowyerWatsonParallelogramsConstrained(), edgeSwapTestDelaunayAniso(), inCircumCircleAniso(), MTri3::MTri3(), optimalPointFrontal(), and optimalPointFrontalQuad().

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circumCenterInfinite()

static void circumCenterInfinite ( MTriangle *  base, double  quadAngle, bidimMeshData &  data, double *  x  )

static

Definition at line 1108 of file meshGFaceDelaunayInsertion.cpp.

Referenced by optimalPointFrontalQuad().

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circumCenterMetric() [1/2]

static void circumCenterMetric ( double *  pa, double *  pb, double *  pc, const double *  metric, double *  x, double &  Radius2  )

static

Definition at line 246 of file meshGFaceDelaunayInsertion.cpp.

Referenced by bowyerWatson(), circumCenterMetric(), circumCenterMetricXYZ(), inCircumCircleAniso(), and optimalPointFrontal().

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circumCenterMetric() [2/2]

static void circumCenterMetric ( MTriangle *  base, const double *  metric, bidimMeshData &  data, double *  x, double &  Radius2  )

static

Definition at line 319 of file meshGFaceDelaunayInsertion.cpp.

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circumCenterMetricXYZ()

static void circumCenterMetricXYZ ( double *  p1, double *  p2, double *  p3, SMetric3 &  metric, double *  res, double *  uv, double &  radius  )

static

Definition at line 278 of file meshGFaceDelaunayInsertion.cpp.

Referenced by MTri3::MTri3().

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circUV()

static bool circUV ( MTriangle *  t, bidimMeshData &  data, double *  res, GFace *  gf  )

static

Definition at line 623 of file meshGFaceDelaunayInsertion.cpp.

Referenced by bowyerWatson(), and optimalPointFrontal().

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computeTolerance()

static double computeTolerance ( const double  radius )

static

Definition at line 341 of file meshGFaceDelaunayInsertion.cpp.

Referenced by inCircumCircleAniso().

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connectTriangles() [1/3]

void connectTriangles

(

std::list< MTri3 * > &

l

)

Definition at line 543 of file meshGFaceDelaunayInsertion.cpp.

Referenced by buildMeshGenerationDataStructures(), and initialSquare().

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connectTriangles() [2/3]

void connectTriangles

(

std::set< MTri3 *, compareTri3Ptr > &

l

)

Definition at line 555 of file meshGFaceDelaunayInsertion.cpp.

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connectTriangles() [3/3]

void connectTriangles

(

std::vector< MTri3 * > &

l

)

Definition at line 549 of file meshGFaceDelaunayInsertion.cpp.

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connectTris()

template<class Iterator >

static void connectTris ( Iterator  beg, Iterator  end, std::vector< edgeXface > &  conn  )

static

Definition at line 515 of file meshGFaceDelaunayInsertion.cpp.

Referenced by connectTriangles(), delaunayMeshIn2D(), insertVertexB(), and swapedge().

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delaunayMeshIn2D()

void delaunayMeshIn2D	(	std::vector< MVertex * > &	v,
		std::vector< MTriangle * > &	result,
		bool	removeBox,
		std::vector< MEdge > *	edgesToRecover,
		bool	hilbertSort
	)

Definition at line 1834 of file meshGFaceDelaunayInsertion.cpp.

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diffend()

bool diffend	(	MVertex *	v1,
		MVertex *	v2,
		MVertex *	p1,
		MVertex *	p2
	)

Definition at line 1947 of file meshGFaceDelaunayInsertion.cpp.

Referenced by recoverEdgeBySwaps().

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fourthPoint()

static void fourthPoint ( double *  p1, double *  p2, double *  p3, double *  p4  )

static

Definition at line 394 of file meshGFaceDelaunayInsertion.cpp.

Referenced by MTri3::inCircumCircle().

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getDegeneratedVertices()

static void getDegeneratedVertices ( GFace *  gf, std::set< GEntity * > &  degenerated  )

static

Definition at line 37 of file meshGFaceDelaunayInsertion.cpp.

Referenced by bowyerWatsonFrontal().

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getSurfUV()

double getSurfUV ( MTriangle *  t, bidimMeshData &  data  )

inline

Definition at line 665 of file meshGFaceDelaunayInsertion.cpp.

Referenced by insertVertexB().

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getTriToBreak()

static MTri3* getTriToBreak ( MVertex *  v, std::vector< MTri3 * > &  t, int &  ITER  )

static

Definition at line 1806 of file meshGFaceDelaunayInsertion.cpp.

Referenced by delaunayMeshIn2D().

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inCircumCircle()

int inCircumCircle	(	MTriangle *	base,
		const double *	p,
		const double *	param,
		bidimMeshData &	data
	)

Definition at line 499 of file meshGFaceDelaunayInsertion.cpp.

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inCircumCircleAniso() [1/2]

int inCircumCircleAniso	(	GFace *	gf,
		double *	p1,
		double *	p2,
		double *	p3,
		double *	uv,
		double *	metric
	)

Definition at line 348 of file meshGFaceDelaunayInsertion.cpp.

Referenced by edgeSwapTestDelaunayAniso(), insertAPoint(), and recurFindCavityAniso().

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inCircumCircleAniso() [2/2]

int inCircumCircleAniso	(	GFace *	gf,
		MTriangle *	base,
		const double *	uv,
		const double *	metricb,
		bidimMeshData &	data
	)

Definition at line 363 of file meshGFaceDelaunayInsertion.cpp.

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inCircumCircleXY()

static int inCircumCircleXY ( MTriangle *  t, MVertex *  v  )

static

Definition at line 561 of file meshGFaceDelaunayInsertion.cpp.

Referenced by getTriToBreak(), and recurFindCavity().

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initialSquare()

static void initialSquare ( std::vector< MVertex * > &  v, MVertex *  box[4], std::vector< MTri3 * > &  t  )

static

Definition at line 1786 of file meshGFaceDelaunayInsertion.cpp.

Referenced by delaunayMeshIn2D().

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insertAPoint()

static bool insertAPoint ( GFace *  gf, std::set< MTri3 *, compareTri3Ptr >::iterator  it, double  center[2], double  metric[3], bidimMeshData &  data, std::set< MTri3 *, compareTri3Ptr > &  AllTris, std::set< MTri3 *, compareTri3Ptr > *  ActiveTris = nullptr, MTri3 *  worst = nullptr, MTri3 **  oneNewTriangle = nullptr, bool  testStarShapeness = false  )

static

Definition at line 923 of file meshGFaceDelaunayInsertion.cpp.

Referenced by bowyerWatson(), bowyerWatsonFrontal(), bowyerWatsonFrontalLayers(), bowyerWatsonParallelograms(), and bowyerWatsonParallelogramsConstrained().

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insertVertexB()

static int insertVertexB ( std::list< edgeXface > &  shell, std::list< MTri3 * > &  cavity, bool  force, GFace *  gf, MVertex *  v, double *  param, MTri3 *  t, std::set< MTri3 *, compareTri3Ptr > &  allTets, std::set< MTri3 *, compareTri3Ptr > *  activeTets, bidimMeshData &  data, double *  metric, MTri3 **  oneNewTriangle, bool  verifyStarShapeness = true  )

static

Definition at line 684 of file meshGFaceDelaunayInsertion.cpp.

Referenced by insertAPoint().

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intersection_segments_2()

static bool intersection_segments_2 ( double *  p1, double *  p2, double *  q1, double *  q2  )

inlinestatic

Definition at line 51 of file meshGFaceDelaunayInsertion.cpp.

Referenced by search4Triangle().

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invMapUV()

static bool invMapUV ( MTriangle *  t, double *  p, bidimMeshData &  data, double *  uv, double  tol  )

static

Definition at line 635 of file meshGFaceDelaunayInsertion.cpp.

Referenced by insertAPoint(), and search4Triangle().

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invMapXY()

static bool invMapXY ( MTriangle *  t, MVertex *  v  )

static

Definition at line 825 of file meshGFaceDelaunayInsertion.cpp.

Referenced by search4Triangle().

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isActive() [1/2]

static bool isActive ( MTri3 *  t, double  limit_, int &  active  )

static

Definition at line 199 of file meshGFaceDelaunayInsertion.cpp.

Referenced by bowyerWatsonFrontal(), bowyerWatsonFrontalLayers(), and insertVertexB().

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isActive() [2/2]

static bool isActive ( MTri3 *  t, double  limit_, int &  i, std::set< MEdge, MEdgeLessThan > *  front  )

static

Definition at line 215 of file meshGFaceDelaunayInsertion.cpp.

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lengthInfniteNorm()

static double lengthInfniteNorm ( const double  p[2], const double  q[2], const double  quadAngle  )

static

Definition at line 1094 of file meshGFaceDelaunayInsertion.cpp.

Referenced by optimalPointFrontalQuad().

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lengthMetric()

static double lengthMetric ( const double  p[2], const double  q[2], const double  metric[3]  )

static

Definition at line 1131 of file meshGFaceDelaunayInsertion.cpp.

Referenced by optimalPointFrontal().

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optimalPointFrontal()

static double optimalPointFrontal ( GFace *  gf, MTri3 *  worst, int  active_edge, bidimMeshData &  data, double  newPoint[2], double  metric[3]  )

static

Definition at line 1163 of file meshGFaceDelaunayInsertion.cpp.

Referenced by optimalPointFrontalB().

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optimalPointFrontalB()

static bool optimalPointFrontalB ( GFace *  gf, MTri3 *  worst, int  active_edge, bidimMeshData &  data, double  newPoint[2], double  metric[3]  )

static

Definition at line 1235 of file meshGFaceDelaunayInsertion.cpp.

Referenced by bowyerWatsonFrontal(), and bowyerWatsonFrontalLayers().

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optimalPointFrontalQuad()

static void optimalPointFrontalQuad ( GFace *  gf, MTri3 *  worst, int  active_edge, bidimMeshData &  data, double  newPoint[2], double  metric[3]  )

static

Definition at line 1366 of file meshGFaceDelaunayInsertion.cpp.

Referenced by bowyerWatsonFrontalLayers().

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recoverEdgeBySwaps()

static bool recoverEdgeBySwaps ( std::vector< MTri3 * > &  t, MVertex *  mv1, MVertex *  mv2, std::vector< MEdge > &  edges  )

static

Definition at line 1953 of file meshGFaceDelaunayInsertion.cpp.

Referenced by recoverEdges().

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recoverEdges()

void recoverEdges	(	std::vector< MTri3 * > &	t,
		std::vector< MEdge > &	edges
	)

Definition at line 1991 of file meshGFaceDelaunayInsertion.cpp.

Referenced by delaunayMeshIn2D().

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recurFindCavity()

static void recurFindCavity ( std::vector< edgeXface > &  shell, std::vector< MTri3 * > &  cavity, MVertex *  v, MTri3 *  t  )

static

Definition at line 575 of file meshGFaceDelaunayInsertion.cpp.

Referenced by delaunayMeshIn2D().

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recurFindCavityAniso()

static void recurFindCavityAniso ( GFace *  gf, std::list< edgeXface > &  shell, std::list< MTri3 * > &  cavity, double *  metric, double *  param, MTri3 *  t, bidimMeshData &  data  )

static

Definition at line 597 of file meshGFaceDelaunayInsertion.cpp.

Referenced by insertAPoint().

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search4Triangle() [1/2]

static MTri3* search4Triangle ( MTri3 *  t, double  pt[2], bidimMeshData &  data, std::set< MTri3 *, compareTri3Ptr > &  AllTris, double  uv[2], bool  force = false  )

static

Definition at line 874 of file meshGFaceDelaunayInsertion.cpp.

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search4Triangle() [2/2]

static MTri3* search4Triangle ( MTri3 *  t, MVertex *  v, int  maxx, int &  ITER  )

static

Definition at line 847 of file meshGFaceDelaunayInsertion.cpp.

Referenced by getTriToBreak(), and insertAPoint().

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swapedge()

bool swapedge	(	MVertex *	v1,
		MVertex *	v2,
		MVertex *	v3,
		MVertex *	v4,
		MTri3 *	t1,
		int	iLocalEdge
	)

Definition at line 1912 of file meshGFaceDelaunayInsertion.cpp.

Referenced by recoverEdgeBySwaps().

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triOnBox()

static bool triOnBox ( MTriangle *  t, MVertex *  box[4]  )

static

Definition at line 1820 of file meshGFaceDelaunayInsertion.cpp.

Referenced by delaunayMeshIn2D().

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updateActiveEdges()

static void updateActiveEdges ( MTri3 *  t, double  limit_, std::set< MEdge, MEdgeLessThan > &  front  )

static

Definition at line 231 of file meshGFaceDelaunayInsertion.cpp.

Referenced by bowyerWatsonFrontalLayers().

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Variable Documentation

LIMIT_

double LIMIT_ = 0.5 * std::sqrt(2.0) * 1

static

Definition at line 34 of file meshGFaceDelaunayInsertion.cpp.

Referenced by bowyerWatsonFrontal(), bowyerWatsonFrontalLayers(), and insertVertexB().