cs_scheme_geometry.cpp File Reference

#include "cs_defs.h"
#include <assert.h>
#include <float.h>
#include "cs_quadrature.h"
#include "cs_scheme_geometry.h"

Include dependency graph for cs_scheme_geometry.cpp:

Macros
#define	CS_SCHEME_GEOMETRY_DBG   0
#define	_dp3   cs_math_3_dot_product

Functions
static void	_add_tria_to_covariance (const cs_real_t x1[3], const cs_real_t x2[3], const cs_real_t x3[3], const cs_nvec3_t ax, const cs_nvec3_t ay, const cs_real_t center[3], cs_real_t area, cs_real_t tensor[3])
	Update the covariance tensor with the contribution of the current triangle. More...
static void	_add_tetra_to_inertia3 (const cs_real_t x1[3], const cs_real_t x2[3], const cs_real_t x3[3], const cs_real_t x4[3], const cs_real_t center[3], cs_real_t vol, cs_real_33_t tensor)
	Update the computation of the inertia tensor with the contribution of a tetrahedron. More...
static void	_add_tetra_to_inertia (const cs_real_t x1[3], const cs_real_t x2[3], const cs_real_t x3[3], const cs_real_t x4[3], const cs_real_t center[3], cs_real_t vol, cs_real_33_t tensor)
	Update the computation of the inertia tensor with the contribution of a tetrahedron Ref.: F. Tonon "Explicit exact formulas for the 3D tetrahedron inertia tensor in terms of its vertex coordinates" (2004) J. of Mathematics and Statistics. More...
void	cs_compute_face_covariance_tensor (const cs_cell_mesh_t *cm, short int f, const cs_nvec3_t ax, const cs_nvec3_t ay, const cs_real_t center[3], cs_real_t cov[3])
	Compute the inertial matrix of a cell with respect to the point called "center". This computation is performed exactly thanks to quadrature based on a "tetrahedrization" of the cell. More...
void	cs_compute_inertia_tensor (const cs_cell_mesh_t *cm, const cs_real_t center[3], cs_real_t inertia[3][3])
	Compute the inertial matrix of a cell with respect to the point called "center". This computation is performed exactly thanks to quadrature based on a "tetrahedrization" of the cell. More...
void	cs_compute_grd_ve (const short int v1, const short int v2, const cs_nvec3_t deq, const cs_real_3_t uvc[], const cs_real_t lvc[], cs_real_t *grd_v1, cs_real_t *grd_v2)
	Compute the gradient of a Lagrange hat function related to primal vertices in a p_{ef,c} subvolume of a cell c where e is an edge belonging to the face f with vertices v1 and v2. More...
void	cs_compute_wef_wvf (short int f, const cs_cell_mesh_t *cm, cs_real_t *wvf, cs_real_t *wef)
	Compute for a face the weight related to each vertex w_{v,f} and the weight related to each edge w_{v,f} = |dc(v) cap f|/|f| Sum of w_{v,f} over the face vertices is equal to 1 Sum of w_{e,f} over the face edges is equal to 1. More...

Macro Definition Documentation

_dp3

#define _dp3   cs_math_3_dot_product

CS_SCHEME_GEOMETRY_DBG

#define CS_SCHEME_GEOMETRY_DBG   0

Function Documentation

_add_tetra_to_inertia()

static void _add_tetra_to_inertia ( const cs_real_t  x1[3], const cs_real_t  x2[3], const cs_real_t  x3[3], const cs_real_t  x4[3], const cs_real_t  center[3], cs_real_t  vol, cs_real_33_t  tensor  )

inlinestatic

Update the computation of the inertia tensor with the contribution of a tetrahedron Ref.: F. Tonon "Explicit exact formulas for the 3D tetrahedron inertia tensor in terms of its vertex coordinates" (2004) J. of Mathematics and Statistics.

Parameters

[in]	x1	1st vertex coordinate
[in]	x2	2nd vertex coordinate
[in]	x3	3rd vertex coordinate
[in]	x4	4th vertex coordinate
[in]	center	center used for the computation
[in]	vol	volume of the tetrahedron
[in,out]	tensor	inertia tensor to update

_add_tetra_to_inertia3()

static void _add_tetra_to_inertia3 ( const cs_real_t  x1[3], const cs_real_t  x2[3], const cs_real_t  x3[3], const cs_real_t  x4[3], const cs_real_t  center[3], cs_real_t  vol, cs_real_33_t  tensor  )

inlinestatic

Update the computation of the inertia tensor with the contribution of a tetrahedron.

Parameters

[in]	x1	1st vertex coordinate
[in]	x2	2nd vertex coordinate
[in]	x3	3rd vertex coordinate
[in]	x4	4th vertex coordinate
[in]	center	center used for the computation
[in]	vol	volume of the tetrahedron
[in,out]	tensor	inertia tensor to update

_add_tria_to_covariance()

static void _add_tria_to_covariance ( const cs_real_t  x1[3], const cs_real_t  x2[3], const cs_real_t  x3[3], const cs_nvec3_t  ax, const cs_nvec3_t  ay, const cs_real_t  center[3], cs_real_t  area, cs_real_t  tensor[3]  )

inlinestatic

Update the covariance tensor with the contribution of the current triangle.

Parameters

[in]	x1	1st vertex coordinate
[in]	x2	2nd vertex coordinate
[in]	x3	3rd vertex coordinate
[in]	ax	main X-axis for the face-related coordinate system
[in]	ay	main Y-axis for the face-related coordinate system
[in]	center	center used for the computation
[in]	area	area of the triangle
[in,out]	tensor	covariance tensor to update

cs_compute_face_covariance_tensor()

void cs_compute_face_covariance_tensor	(	const cs_cell_mesh_t *	cm,
		short int	f,
		const cs_nvec3_t	ax,
		const cs_nvec3_t	ay,
		const cs_real_t	center[3],
		cs_real_t	cov[3]
	)

Compute the inertial matrix of a cell with respect to the point called "center". This computation is performed exactly thanks to quadrature based on a "tetrahedrization" of the cell.

Parameters

[in]	cm	pointer to a cs_cell_mesh_t structure
[in]	f	id of the face in the cell numbering
[in]	ax	main X-axis for the face-related coordinate system
[in]	ay	main Y-axis for the face-related coordinate system
[in]	center	coordinates of the face center
[in,out]	cov	2x2 symmetric covariance matrix to compute

cs_compute_grd_ve()

void cs_compute_grd_ve	(	const short int	v1,
		const short int	v2,
		const cs_nvec3_t	deq,
		const cs_real_3_t	uvc[],
		const cs_real_t	lvc[],
		cs_real_t *	grd_v1,
		cs_real_t *	grd_v2
	)

Compute the gradient of a Lagrange hat function related to primal vertices in a p_{ef,c} subvolume of a cell c where e is an edge belonging to the face f with vertices v1 and v2.

Compute the gradient of a Lagrange function related to primal vertices in a p_{ef,c} subvolume of a cell c where e is an edge belonging to the face f with vertices v1 and v2.

Parameters

[in]	v1	number of the first vertex in cell numbering
[in]	v2	number of the second vertex in cell numbering
[in]	deq	dual edge quantities
[in]	uvc	xc --> xv unit tangent vector
[in]	lvc	xc --> xv vector length
[in,out]	grd_v1	gradient of Lagrange function related to v1
[in,out]	grd_v2	gradient of Lagrange function related to v2

cs_compute_inertia_tensor()

void cs_compute_inertia_tensor	(	const cs_cell_mesh_t *	cm,
		const cs_real_t	center[3],
		cs_real_t	inertia[3][3]
	)

Compute the inertial matrix of a cell with respect to the point called "center". This computation is performed exactly thanks to quadrature based on a "tetrahedrization" of the cell.

Parameters

[in]	cm	pointer to a cs_cell_mesh_t structure
[in]	center	coordinates of the cell center
[in,out]	inertia	inertia matrix to compute

cs_compute_wef_wvf()

void cs_compute_wef_wvf	(	short int	f,
		const cs_cell_mesh_t *	cm,
		cs_real_t *	wvf,
		cs_real_t *	wef
	)

Compute for a face the weight related to each vertex w_{v,f} and the weight related to each edge w_{v,f} = |dc(v) cap f|/|f| Sum of w_{v,f} over the face vertices is equal to 1 Sum of w_{e,f} over the face edges is equal to 1.

Parameters

[in]	f	id of the face in the cell-wise numbering
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	wvf	weights of each face vertex
[in,out]	wef	weights of each face edge