anisosiz.c File Reference

Fonctions for anisotropic size map computation. More...

#include "mmgcommon.h"

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Functions
static double	MMG5_surf (MMG5_pMesh mesh, double m[3][6], MMG5_pTria ptt)
double	MMG5_surftri_ani (MMG5_pMesh mesh, MMG5_pSol met, MMG5_pTria ptt)
double	MMG5_surftri33_ani (MMG5_pMesh mesh, MMG5_pTria ptt, double ma[6], double mb[6], double mc[6])
void	MMG5_defUninitSize (MMG5_pMesh mesh, MMG5_pSol met, int8_t ismet)
void	MMG5_fillDefmetregSys (int k, MMG5_pPoint p0, int i0, MMG5_Bezier b, double r[3][3], double c[3], double *lispoi, double tAA[6], double tAb[3])
int	MMG5_solveDefmetregSys (MMG5_pMesh mesh, double r[3][3], double c[3], double tAA[6], double tAb[3], double *m, double isqhmin, double isqhmax, double hausd)
int	MMG5_solveDefmetrefSys (MMG5_pMesh mesh, MMG5_pPoint p0, int ipref[2], double r[3][3], double c[3], double tAA[6], double tAb[3], double *m, double isqhmin, double isqhmax, double hausd)
double	MMG5_ridSizeInTangentDir (MMG5_pMesh mesh, MMG5_pPoint p0, int idp, int *iprid, double isqhmin, double isqhmax)
double	MMG5_ridSizeInNormalDir (MMG5_pMesh mesh, int i0, double *bcu, MMG5_Bezier *b, double isqhmin, double isqhmax)
int	MMG5_grad2metSurf (MMG5_pMesh mesh, MMG5_pSol met, MMG5_pTria pt, int np1, int np2)
int	MMG5_simred (MMG5_pMesh mesh, double *m, double *n, double dm[2], double dn[2], double vp[2][2])
void	MMG5_gradEigenvreq (double *dm, double *dn, double difsiz, int8_t dir, int8_t *ier)
int	MMG5_updatemetreq_ani (double *n, double dn[2], double vp[2][2])
int	MMG5_grad2metSurfreq (MMG5_pMesh mesh, MMG5_pSol met, MMG5_pTria pt, int npmaster, int npslave)
int	MMG5_compute_meanMetricAtMarkedPoints_ani (MMG5_pMesh mesh, MMG5_pSol met)
int	MMG5_gradsiz_ani (MMG5_pMesh mesh, MMG5_pSol met, int *it)
int	MMG5_gradsizreq_ani (MMG5_pMesh mesh, MMG5_pSol met)

Detailed Description

Fonctions for anisotropic size map computation.

Author

Charles Dapogny (UPMC)

Cécile Dobrzynski (Bx INP/Inria/UBordeaux)

Pascal Frey (UPMC)

Algiane Froehly (Inria/UBordeaux)

Version

5

Copyright

GNU Lesser General Public License.

Function Documentation

MMG5_compute_meanMetricAtMarkedPoints_ani()

int MMG5_compute_meanMetricAtMarkedPoints_ani	(	MMG5_pMesh	mesh,
		MMG5_pSol	met
	)

Parameters

mesh	pointer toward the mesh structure.
met	pointer toward the metric structure.

Returns

1 if success, 0 if fail.

Compute the mean metric at mesh points with a non-nul s field. At the beginning, for a given point ip, contains the sum of n metrics and the s field of ip contains the number of metrics summed in the point. Set the flag of the processed points to 3.

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MMG5_defUninitSize()

void MMG5_defUninitSize	(	MMG5_pMesh	mesh,
		MMG5_pSol	met,
		int8_t	ismet
	)

Parameters

mesh	pointer toward the mesh structure.
met	pointer toward the metric structure.
ismet	1 if user provided metric.

Search for points with unintialized metric and define anisotropic size at this points.

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MMG5_fillDefmetregSys()

void MMG5_fillDefmetregSys	(	int	k,
		MMG5_pPoint	p0,
		int	i0,
		MMG5_Bezier	b,
		double	r[3][3],
		double	c[3],
		double *	lispoi,
		double	tAA[6],
		double	tAb[3]
	)

Parameters

k	index of the tetrahedra from which we come.
p0	pointer toward the point on which we want to def the metric.
i0	pointer toward the local index of the point in tria.
b	control polygon of triangle.
r	rotation matrix.
c	physical coordinates of the curve edge mid-point.
lispoi	list of incident vertices to p0
tAA	matrix to fill
tAb	second member

Fill matrice \sum tAA and second member \sum tAb with and with P_i the physical points at edge [i0;i1] extremities and middle. Compute the physical coor c of the curve edge's mid-point for a regular or reference point.

MMG5_grad2metSurf()

int MMG5_grad2metSurf	(	MMG5_pMesh	mesh,
		MMG5_pSol	met,
		MMG5_pTria	pt,
		int	np1,
		int	np2
	)

Parameters

mesh	pointer toward the mesh.
met	pointer toward the metric structure.
pt	pointer toward a triangle.
np1	global index of the first extremity of the edge.
np2	global index of the second extremity of the edge.

Returns

-1 if no gradation is needed, else index of graded point.

Enforces gradation of metric in one extremity of edge $f[ np1; np2]$f in tria pt with respect to the other, along the direction of the associated support curve first, then along the normal direction.

Warning

The gradation along the direction normal to the surface is made in an "isotropic way".

Remarks

ALGIANE: a mettre à plat : dans le cas d'une métrique très aniso avec la grande taille quasiment dans la direction de l'arête on se retrouve à modifier la grande taille uniquement (car proche de l'arête) sauf que cette modification n'a quasi pas d'influence sur le calcul de la longueur d'arête.

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MMG5_grad2metSurfreq()

int MMG5_grad2metSurfreq	(	MMG5_pMesh	mesh,
		MMG5_pSol	met,
		MMG5_pTria	pt,
		int	npmaster,
		int	npslave
	)

Parameters

mesh	pointer toward the mesh.
met	pointer toward the metric structure.
pt	pointer toward the processed triangle.
npmaster	edge extremity that cannot be modified
npslave	edge extremity to modify to respect the gradation.

Returns

0 if no gradation is needed, 1 otherwise.

Enforces gradation of metric of the extremity ±a npslave of edge $f[ npmaster; npslave]$f in tria pt with respect to the other, along the direction of the associated support curve first, then along the normal direction.

Warning

The gradation along the direction normal to the surface is made in an "isotropic way".

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MMG5_gradEigenvreq()

void MMG5_gradEigenvreq	(	double *	dm,
		double *	dn,
		double	difsiz,
		int8_t	dir,
		int8_t *	ier
	)

Parameters

dm	eigenvalues of the first matrix (not modified)
dn	eigenvalues of the second matrix (modified)
difsiz	maximal size gap authorized by the gradation.
dir	direction in which the sizes are graded.
ier	2 if dn has been updated, 0 otherwise.

Gradation of size dn = 1/sqrt(eigenv of the tensor) for required points in the idir direction.

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MMG5_gradsiz_ani()

int MMG5_gradsiz_ani	(	MMG5_pMesh	mesh,
		MMG5_pSol	met,
		int *	it
	)

Parameters

mesh	pointer toward the mesh structure.
met	pointer toward the metric structure.
it	number of performed iteration (to fill)

Returns

nup, the number of points updated.

Standard gradation procedure.

Mark the edges belonging to a required entity

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MMG5_gradsizreq_ani()

int MMG5_gradsizreq_ani	(	MMG5_pMesh	mesh,
		MMG5_pSol	met
	)

Parameters

mesh	pointer toward the mesh structure.
met	pointer toward the metric structure.

Returns

1

Enforces mesh gradation (on required entities) by truncating metric field.

Mark the edges belonging to a required entity (already done if the classic gradation is enabled)

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MMG5_ridSizeInNormalDir()

double MMG5_ridSizeInNormalDir	(	MMG5_pMesh	mesh,
		int	i0,
		double *	bcu,
		MMG5_Bezier *	b,
		double	isqhmin,
		double	isqhmax
	)

Parameters

mesh	pointer toward the mesh structure.
i0	local index in the face of the point on which we want to compute the metric
bcu	pointer toward the barycentric coordinates of vector u in the looked face.
b	bezier control polygon for the looked face.
isqhmin	minimum edge size.
isqhmax	maximum edge size.

Returns

the computed ridge size in first or second normal direction (depending of i0).

Compute the specific size of a ridge in the direction of the normal of the looked face.

MMG5_ridSizeInTangentDir()

double MMG5_ridSizeInTangentDir	(	MMG5_pMesh	mesh,
		MMG5_pPoint	p0,
		int	idp,
		int *	iprid,
		double	isqhmin,
		double	isqhmax
	)

Parameters

mesh	pointer toward the mesh structure.
p0	pointer toward the point at which we define the metric.
idp	global index of the point at which we define the metric.
iprid	pointer toward the two extremities of the ridge.
isqhmin	minimum edge size.
isqhmax	maximum edge size.

Returns

the computed ridge size in the tangent direction.

Compute the specific size of a ridge in the direction of the tangent of the ridge.

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MMG5_simred()

int MMG5_simred	(	MMG5_pMesh	mesh,
		double *	m,
		double *	n,
		double	dm[2],
		double	dn[2],
		double	vp[2][2]
	)

Parameters

mesh	pointer toward the mesh
m	first matrix
n	second matrix
dm	eigenvalues of m in the coreduction basis (to fill)
dn	eigenvalues of n in the coreduction basis (to fill)
vp	coreduction basis (to fill)

Returns

0 if fail 1 otherwise.

Perform simultaneous reduction of matrices m and n.

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MMG5_solveDefmetrefSys()

int MMG5_solveDefmetrefSys	(	MMG5_pMesh	mesh,
		MMG5_pPoint	p0,
		int	ipref[2],
		double	r[3][3],
		double	c[3],
		double	tAA[6],
		double	tAb[3],
		double *	m,
		double	isqhmin,
		double	isqhmax,
		double	hausd
	)

Parameters

mesh	pointer toward the mesh structure.
p0	pointer toward the point on which we want to define the metric.
ipref	table containing the indices of the edge extremities.
r	pointer toward the rotation matrix.
c	physical coordinates of the curve edge mid-point.
tAA	matrix of the system to solve.
tAb	second member.
m	pointer toward the metric.
isqhmax	maximum size for edge.
isqhmin	minimum size for edge.
hausd	hausdorff value at point.

Returns

1 if success, 0 if fail.

Solve tAA * tmp_m = tAb and fill m with tmp_m (after rotation) for a ref point.

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MMG5_solveDefmetregSys()

int MMG5_solveDefmetregSys	(	MMG5_pMesh	mesh,
		double	r[3][3],
		double	c[3],
		double	tAA[6],
		double	tAb[3],
		double *	m,
		double	isqhmin,
		double	isqhmax,
		double	hausd
	)

Parameters

mesh	pointer toward the mesh structure.
r	pointer toward the rotation matrix.
c	physical coordinates of the curve edge mid-point.
tAA	matrix of the system to solve.
tAb	second member.
m	pointer toward the metric.
isqhmax	maximum size for edge.
isqhmin	minimum size for edge.
hausd	hausdorff value at point.

Returns

1 if success, 0 if fail.

Solve tAA * tmp_m = tAb and fill m with tmp_m (after rotation) for a regular point.

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MMG5_surf()

static double MMG5_surf ( MMG5_pMesh  mesh, double  m[3][6], MMG5_pTria  ptt  )

inlinestatic

Parameters

mesh	pointer toward the mesh structure.
m	pointer toward the metric at triangle vertices.
ptt	pointer toward the triangle structure.

Returns

The double of the triangle area.

Compute the double of the area of the surface triangle ptt with respect to the anisotropic metric m.

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MMG5_surftri33_ani()

double MMG5_surftri33_ani	(	MMG5_pMesh	mesh,
		MMG5_pTria	ptt,
		double	ma[6],
		double	mb[6],
		double	mc[6]
	)

Parameters

mesh	pointer toward the mesh structure.
ptt	pointer toward the triangle structure.
ma	metric at triangle vertex.
mb	metric at triangle vertex.
mc	metric at triangle vertex.

Returns

The double of the triangle area.

Compute the double of the area of the surface triangle ptt with respect to the anisotropic metric met (for classic storage of ridges metrics).

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MMG5_surftri_ani()

double MMG5_surftri_ani	(	MMG5_pMesh	mesh,
		MMG5_pSol	met,
		MMG5_pTria	ptt
	)

Parameters

mesh	pointer toward the mesh structure.
met	pointer toward the metric structure.
ptt	pointer toward the triangle structure.

Returns

The double of the triangle area.

Compute the double of the area of the surface triangle ptt with respect to the anisotropic metric met (for special storage of ridges metrics).

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MMG5_updatemetreq_ani()

int MMG5_updatemetreq_ani	(	double *	n,
		double	dn[2],
		double	vp[2][2]
	)

Parameters

n	matrix to update
dn	eigenvalues of n in the coreduction basis
vp	coreduction basis

Returns

0 if fail, 1 otherwise

Update of the metric n = tP^-1 diag(dn0,dn1)P^-1, P = (vp[0], vp[1]) stored in columns

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