Basic Geometric Tools. More...

Classes
class	torus_structure
	torus_structure which extends a 2 dimensional structure with a radial dimension More...

class	Comma_initializer
	Template class which forwards insertions to the container class. More...

class	convex
	generic definition of a convex ( bgeot::convex_structure + vertices coordinates ) More...

struct	stored_point_tab
	Point tab storage. More...

class	convex_of_reference
	Base class for reference convexes. More...

class	convex_structure
	Structure of a convex. More...

class	geometric_trans
	Description of a geometric transformation between a reference element and a real element. More...

class	geotrans_precomp_
	precomputed geometric transformation operations use this for repetitive evaluation of a geometric transformations on a set of points "pspt" in the reference convex which do not change. More...

class	geotrans_precomp_pool
	The object geotrans_precomp_pool Allow to allocate a certain number of geotrans_precomp and automatically delete them when it is deleted itself. More...

class	geotrans_interpolation_context
	the geotrans_interpolation_context structure is passed as the argument of geometric transformation interpolation functions. More...

class	geotrans_inv_convex
	does the inversion of the geometric transformation for a given convex More...

class	geotrans_inv
	handles the geometric inversion for a given (supposedly quite large) set of points More...

struct	index_node_pair
	store a point and the associated index for the kdtree. More...

class	kdtree
	Balanced tree over a set of points. More...

class	mesh_structure
	Mesh structure definition. More...

class	node_tab
	Store a set of points, identifying points that are nearer than a certain very small distance. More...

class	permutation
	generation of permutations, and ranking/unranking of these. More...

class	power_index
	Vector of integer (16 bits type) which represent the powers of a monomial. More...

class	polynomial
	This class deals with plain polynomials with several variables. More...

struct	imbricated_box_less
	A comparison function for bgeot::base_node. More...

class	rtree
	Balanced tree of n-dimensional rectangles. More...

class	small_vector
	container for small vectors of POD (Plain Old Data) types. More...

struct	torus_geom_trans
	An adaptor that adapts a two dimensional geometric_trans to include radial dimension. More...

Typedefs
typedef gmm::uint16_type	short_type
	used as the common short type integer in the library

typedef std::shared_ptr< const convex_structure >	pconvex_structure
	Pointer on a convex structure description.

typedef std::shared_ptr< const bgeot::geometric_trans >	pgeometric_trans
	pointer type for a geometric transformation

typedef std::vector< index_node_pair >	kdtree_tab_type
	store a set of points with associated indexes.

typedef size_t	size_type
	used as the common size type in the library

Functions
pconvex_ref	simplex_of_reference (dim_type nc, short_type k=1)
	returns a simplex of reference of dimension nc and degree k

pconvex_ref	Q2_incomplete_of_reference (dim_type d)
	incomplete Q2 quadrilateral/hexahedral of reference of dimension d = 2 or 3

pconvex_ref	pyramid_QK_of_reference (dim_type k)
	pyramidal element of reference of degree k (k = 1 or 2 only)

pconvex_ref	pyramid_Q2_incomplete_of_reference ()
	incomplete quadratic pyramidal element of reference (13-node)

pconvex_ref	prism_incomplete_P2_of_reference ()
	incomplete quadratic prism element of reference (15-node)

pconvex_ref	convex_ref_product (pconvex_ref a, pconvex_ref b)
	tensorial product of two convex ref. More...

pconvex_ref	parallelepiped_of_reference (dim_type nc, dim_type k=1)
	parallelepiped of reference of dimension nc (and degree 1)

pconvex_ref	prism_of_reference (dim_type nc)
	prism of reference of dimension nc (and degree 1)

pconvex_ref	equilateral_simplex_of_reference (dim_type nc)
	equilateral simplex (degree 1). More...

pconvex_ref	generic_dummy_convex_ref (dim_type nc, size_type n, short_type nf)
	generic convex with n global nodes

bool	operator== (const pconvex_structure &p1, const pconvex_structure &p2)
	Stored objects must be compared by keys, because there is a possibility that they are duplicated in storages of multiple threads and pointers to them are never equal.

bool	operator== (const pconvex_structure &p1, std::nullptr_t)
	these operators still use comparison by addresses against nullptr

int	get_token (std::istream &ist, std::string &st, bool ignore_cr=true, bool to_up=true, bool read_un_pm=true, int *linenb=0)
	Very simple lexical analysis of general interest for reading small languages with a "MATLAB like" syntax : spaces are ignored, '' indicates a commentary until the end of the line, '...' indicates that the instruction continue on the next line (or separate two sub part of the same character string). More...

void	cuthill_mckee_on_convexes (const bgeot::mesh_structure &ms, std::vector< size_type > &cmk)
	Return the cuthill_mc_kee ordering on the convexes.

size_type	alpha (short_type n, short_type d)
	Return the value of $\frac{(n+p)!}{n!p!}$ which is the number of monomials of a polynomial of variables and degree .

base_poly	read_base_poly (short_type n, std::istream &f)
	read a base_poly on the stream ist.

base_poly	read_base_poly (short_type n, const std::string &s)
	read a base_poly on the string s.

void	structured_mesh_for_convex (pconvex_ref cvr, short_type k, pbasic_mesh &pm, pmesh_precomposite &pmp, bool force_simplexification)
	This function returns a mesh in pm which contains a refinement of the convex cvr if force_simplexification is false, refined convexes have the same basic_structure than cvr, if it is set to true, the cvr is decomposed into simplexes which are then refined. More...

const basic_mesh *	refined_simplex_mesh_for_convex (pconvex_ref cvr, short_type k)
	simplexify a convex_ref. More...

const std::vector< std::unique_ptr< mesh_structure > > &	refined_simplex_mesh_for_convex_faces (pconvex_ref cvr, short_type k)
	simplexify the faces of a convex_ref More...

pconvex_ref	basic_convex_ref (pconvex_ref cvr)
	return the associated order 1 reference convex.

pconvex_structure	basic_structure (pconvex_structure cv)
	Original structure (if concerned)

template<typename T >
std::ostream &	operator<< (std::ostream &o, const polynomial< T > &P)
	Print P to the output stream o. for instance cout << P;.

template<typename T >
polynomial< T >	poly_substitute_var (const polynomial< T > &P, const polynomial< T > &S, size_type subs_dim)
	polynomial variable substitution More...

template<typename T >
rational_fraction< T >	operator+ (const polynomial< T > &P, const rational_fraction< T > &Q)
	Add Q to P.

template<typename T >
rational_fraction< T >	operator- (const polynomial< T > &P, const rational_fraction< T > &Q)
	Subtract Q from P.

functions on convex structures
std::ostream &	operator<< (std::ostream &o, const convex_structure &cv)
	Print the details of the convex structure cvs to the output stream o. More...

pconvex_structure	simplex_structure (dim_type d)
	Give a pointer on the structures of a simplex of dimension d.

pconvex_structure	simplex_structure (dim_type n, short_type k)
	Simplex structure with the Lagrange grid of degree k. More...

pconvex_structure	polygon_structure (short_type)
	Give a pointer on the structures of a polygon with n vertex.

pconvex_structure	convex_product_structure (pconvex_structure, pconvex_structure)
	Give a pointer on the structures of a convex which is the direct product of the convexes represented by pcvs1 and pcvs2.

pconvex_structure	parallelepiped_structure (dim_type d, dim_type k=1)
	Give a pointer on the structures of a parallelepiped of dimension d.

pconvex_structure	Q2_incomplete_structure (dim_type d)
	Give a pointer on the structures of a incomplete Q2 quadrilateral/hexahedral of dimension d = 2 or 3.

pconvex_structure	pyramid_QK_structure (short_type k)
	Give a pointer on the 3D pyramid structure for a degree k = 1 or 2.

pconvex_structure	pyramid_Q2_incomplete_structure ()
	Give a pointer on the 3D quadratic incomplete pyramid structure.

pconvex_structure	prism_incomplete_P2_structure ()
	Give a pointer on the 3D quadratic incomplete prism structure.

pconvex_structure	generic_dummy_structure (dim_type nc, size_type n, short_type nf)
	Generic convex with n global nodes.

pconvex_structure	prism_P1_structure (dim_type nc)
	Give a pointer on the structures of a prism of dimension d. More...

IS_DEPRECATED pconvex_structure	prism_structure (dim_type nc)

IS_DEPRECATED pconvex_structure	pyramid_structure (short_type k)

functions on geometric transformations
typedef std::shared_ptr< const geotrans_precomp_ >	pgeotrans_precomp

typedef dal::naming_system< geometric_trans >::param_list	gt_param_list

void	mat_mult (const scalar_type A, const scalar_type B, scalar_type *C, size_type M, size_type N, size_type P)

void	mat_tmult (const scalar_type A, const scalar_type B, scalar_type *C, size_type M, size_type N, size_type P)

scalar_type	lu_det (const scalar_type *A, size_type N)

scalar_type	lu_inverse (scalar_type *A, size_type N, bool doassert)

pgeometric_trans	Q2_incomplete_geotrans (dim_type nc)

pgeometric_trans	pyramid_QK_geotrans (short_type k)

pgeometric_trans	pyramid_Q2_incomplete_geotrans ()

pgeometric_trans	prism_incomplete_P2_geotrans ()

base_small_vector	compute_normal (const geotrans_interpolation_context &c, size_type face)
	norm of returned vector is the ratio between the face surface on the real element and the face surface on the reference element IT IS NOT UNITARY More...

base_matrix	compute_local_basis (const geotrans_interpolation_context &c, size_type face)
	return the local basis (i.e. More...

void	add_geometric_trans_name (std::string name, dal::naming_system< geometric_trans >::pfunction f)

pgeometric_trans	geometric_trans_descriptor (std::string name)
	Get the geometric transformation from its string name. More...

std::string	name_of_geometric_trans (pgeometric_trans p)
	Get the string name of a geometric transformation. More...

pgeometric_trans	simplex_geotrans (size_type n, short_type k)

pgeometric_trans	parallelepiped_geotrans (size_type n, short_type k)

pgeometric_trans	parallelepiped_linear_geotrans (size_type n)

pgeometric_trans	prism_linear_geotrans (size_type n)

pgeometric_trans	linear_product_geotrans (pgeometric_trans pg1, pgeometric_trans pg2)

pgeometric_trans	prism_geotrans (size_type n, short_type k)

pgeometric_trans	product_geotrans (pgeometric_trans pg1, pgeometric_trans pg2)

pgeometric_trans	default_trans_of_cvs (pconvex_structure cvs)

pgeotrans_precomp	geotrans_precomp (pgeometric_trans pg, pstored_point_tab pspt, dal::pstatic_stored_object dep)

void	delete_geotrans_precomp (pgeotrans_precomp pgp)

IS_DEPRECATED pgeometric_trans APIDECL	pyramid_geotrans (short_type k)

scalar_type	lu_det (const base_matrix &A)

scalar_type	lu_inverse (base_matrix &A, bool doassert=true)

Detailed Description

Basic Geometric Tools.

Function Documentation

◆ convex_ref_product()

pconvex_ref bgeot::convex_ref_product	(	pconvex_ref	a,
		pconvex_ref	b
	)

tensorial product of two convex ref.

in order to ensure unicity, it is required the a->dim() >= b->dim()

Definition at line 720 of file bgeot_convex_ref.cc.

◆ equilateral_simplex_of_reference()

pconvex_ref bgeot::equilateral_simplex_of_reference ( dim_type nc )

equilateral simplex (degree 1).

used only for mesh quality estimations

Definition at line 822 of file bgeot_convex_ref.cc.

◆ operator<<()

std::ostream & bgeot::operator<<	(	std::ostream &	o,
		const convex_structure &	cv
	)

Print the details of the convex structure cvs to the output stream o.

For debuging purpose.

Definition at line 71 of file bgeot_convex_structure.cc.

◆ simplex_structure()

pconvex_structure bgeot::simplex_structure	(	dim_type	n,
		short_type	k
	)

Simplex structure with the Lagrange grid of degree k.

Parameters

n	the simplex dimension.
k	the simplex degree.

Definition at line 238 of file bgeot_convex_structure.cc.

◆ get_token()

int bgeot::get_token	(	std::istream &	ist,
		std::string &	st,
		bool	ignore_cr = `true`,
		bool	to_up = `true`,
		bool	read_un_pm = `true`,
		int *	linenb = `0`
	)

Very simple lexical analysis of general interest for reading small languages with a "MATLAB like" syntax : spaces are ignored, '' indicates a commentary until the end of the line, '...' indicates that the instruction continue on the next line (or separate two sub part of the same character string).

The function returns 0 if there is nothing else to read in the file 1 if an end line has been found (st is empty in this case) 2 if a number as been read 3 if a string has been read 4 if a alphanumeric name has been read 5 for a one character symbol 6 for a two characters symbol (<=, >=, ==, !=, &&, ||)

Note that when the end of line is not significant the option ignore_cr allows to consider the carriage return as a space character.

Definition at line 50 of file bgeot_ftool.cc.

◆ compute_normal()

base_small_vector APIDECL bgeot::compute_normal	(	const geotrans_interpolation_context &	c,
		size_type	face
	)

norm of returned vector is the ratio between the face surface on the real element and the face surface on the reference element IT IS NOT UNITARY

pt is the position of the evaluation point on the reference element

Definition at line 1082 of file bgeot_geometric_trans.cc.

◆ compute_local_basis()

base_matrix APIDECL bgeot::compute_local_basis	(	const geotrans_interpolation_context &	c,
		size_type	face
	)

return the local basis (i.e.

the normal in the first column, and the tangent vectors in the other columns

Definition at line 1094 of file bgeot_geometric_trans.cc.

◆ geometric_trans_descriptor()

pgeometric_trans APIDECL bgeot::geometric_trans_descriptor ( std::string name )

Get the geometric transformation from its string name.

See also: name_of_geometric_trans

Definition at line 1163 of file bgeot_geometric_trans.cc.

◆ name_of_geometric_trans()

std::string APIDECL bgeot::name_of_geometric_trans ( pgeometric_trans p )

Get the string name of a geometric transformation.

List of possible names: GT_PK(N,K) : Transformation on simplexes, dim N, degree K

GT_QK(N,K) : Transformation on parallelepipeds, dim N, degree K GT_PRISM(N,K) : Transformation on prisms, dim N, degree K GT_PYRAMID_QK(K) : Transformation on pyramids, dim 3, degree K=0,1,2 GT_Q2_INCOMPLETE(N) : Q2 incomplete transformation in dim N=2 or 3. GT_PYRAMID_Q2_INCOMPLETE : incomplete quadratic pyramid transformation in dim 3 GT_PRISM_INCOMPLETE_P2 : incomplete quadratic prism transformation in dim 3 GT_PRODUCT(a,b) : tensorial product of two transformations GT_LINEAR_PRODUCT(a,b) : Linear tensorial product of two transformations GT_LINEAR_QK(N) : shortcut for GT_LINEAR_PRODUCT(GT_LINEAR_QK(N-1), GT_PK(1,1))

Definition at line 1173 of file bgeot_geometric_trans.cc.

◆ structured_mesh_for_convex()

void bgeot::structured_mesh_for_convex	(	pconvex_ref	cvr,
		short_type	k,
		pbasic_mesh &	pm,
		pmesh_precomposite &	pmp,
		bool	force_simplexification
	)

This function returns a mesh in pm which contains a refinement of the convex cvr if force_simplexification is false, refined convexes have the same basic_structure than cvr, if it is set to true, the cvr is decomposed into simplexes which are then refined.

TODO: move it into another file and separate the pmesh_precomposite part ?

Definition at line 499 of file bgeot_poly_composite.cc.

◆ refined_simplex_mesh_for_convex()

const basic_mesh * bgeot::refined_simplex_mesh_for_convex	(	pconvex_ref	cvr,
		short_type	k
	)

simplexify a convex_ref.

Parameters

cvr	the convex_ref.
k	the refinement level.

Returns: a pointer to a statically allocated mesh. Do no free it!

Definition at line 558 of file bgeot_poly_composite.cc.

◆ refined_simplex_mesh_for_convex_faces()

const std::vector< std::unique_ptr< mesh_structure > > & bgeot::refined_simplex_mesh_for_convex_faces	(	pconvex_ref	cvr,
		short_type	k
	)

simplexify the faces of a convex_ref

Parameters

cvr	the convex_ref.
k	the refinement level.

Returns: vector of pointers to a statically allocated mesh_structure objects. Do no free them! The point numbers in the mesh_structure refer to the points of the mesh given by refined_simplex_mesh_for_convex.

Definition at line 565 of file bgeot_poly_composite.cc.

◆ prism_P1_structure()

pconvex_structure bgeot::prism_P1_structure ( dim_type nc )

inline

Give a pointer on the structures of a prism of dimension d.

i.e. the direct product of a simplex of dimension d-1 and a segment.

Definition at line 206 of file bgeot_convex_structure.h.

◆ poly_substitute_var()

template<typename T >

polynomial<T> bgeot::poly_substitute_var	(	const polynomial< T > &	P,
		const polynomial< T > &	S,
		size_type	subs_dim
	)

polynomial variable substitution

Parameters

P	the original polynomial
S	the substitution poly (not a multivariate one)
subs_dim	: which variable is substituted example: poly_subs(x+yx^2, x+1, 0) = x+1 + y(x+1)^2

Definition at line 587 of file bgeot_poly.h.

Classes

Typedefs

Functions

functions on geometric transformations

Detailed Description

Function Documentation

◆ convex_ref_product()

◆ equilateral_simplex_of_reference()

◆ operator<<()

◆ simplex_structure()

◆ get_token()

◆ compute_normal()

◆ compute_local_basis()

◆ geometric_trans_descriptor()

◆ name_of_geometric_trans()

◆ structured_mesh_for_convex()

◆ refined_simplex_mesh_for_convex()

◆ refined_simplex_mesh_for_convex_faces()

◆ prism_P1_structure()

◆ poly_substitute_var()