Definitions of triangle-specific functions. More...

#include <t8_element.h>
#include <t8_schemes/t8_default/t8_default_tri/t8_dtri.h>

Functions
void	t8_dtri_copy (const t8_dtri_t t, t8_dtri_t dest)
	Copy the values of one triangle to another. More...

int	t8_dtri_compare (const t8_dtri_t t1, const t8_dtri_t t2)
	Compare two triangle in their linear order. More...

void	t8_dtri_parent (const t8_dtri_t t, t8_dtri_t parent)
	Compute the parent of a triangle. More...

void	t8_dtri_ancestor (const t8_dtri_t t, int level, t8_dtri_t ancestor)
	Compute the ancestor of a triangle at a given level. More...

void	t8_dtri_compute_coords (const t8_dtri_t *elem, const int vertex, t8_dtri_coord_t coordinates[2])
	Compute the coordinates of a vertex of a triangle. More...

void	t8_dtri_compute_vertex_ref_coords (const t8_dtri_t *elem, const int vertex, double coordinates[2])
	Compute the reference coordinates of a vertex of a triangle when the tree (level 0 triangle) is embedded in [0,1]^2. More...

void	t8_dtri_compute_all_coords (const t8_dtri_t *elem, t8_dtri_coord_t coordinates[3][2])
	Compute the coordinates of the four vertices of a triangle. More...

void	t8_dtri_child (const t8_dtri_t t, int childid, t8_dtri_t child)
	Compute the childid-th child in Morton order of a triangle. More...

void	t8_dtri_childrenpv (const t8_dtri_t t, t8_dtri_t c[T8_DTRI_CHILDREN])
	Compute the 4 children of a triangle, array version. More...

int	t8_dtri_is_familypv (const t8_dtri_t *f[])
	Check whether a collection of eight triangles is a family in Morton order. More...

void	t8_dtri_sibling (const t8_dtri_t elem, int sibid, t8_dtri_t sibling)
	Compute a specific sibling of a triangle. More...

int	t8_dtri_face_neighbour (const t8_dtri_t t, int face, t8_dtri_t n)
	Compute the face neighbor of a triangle. More...

void	t8_dtri_nearest_common_ancestor (const t8_dtri_t t1, const t8_dtri_t t2, t8_dtri_t *r)
	Computes the nearest common ancestor of two triangles in the same tree. More...

void	t8_dtri_children_at_face (const t8_dtri_t tri, int face, t8_dtri_t children[], int num_children, int *child_indices)
	Given a triangle and a face of the triangle, compute all children of the triangle that touch the face. More...

int	t8_dtri_face_child_face (const t8_dtri_t *triangle, int face, int face_child)
	Given a face of a triangle and a child number of a child of that face, return the face number of the child of the triangle that matches the child face. More...

int	t8_dtri_face_parent_face (const t8_dtri_t *triangle, int face)
	Given a face of an triangle return the face number of the parent of the triangle that matches the triangle's face. More...

int	t8_dtri_tree_face (t8_dtri_t *t, int face)
	Given a triangle and a face of this triangle. More...

int	t8_dtri_root_face_to_face (t8_dtri_t *t, int root_face)
	Given a triangle and a face of the root triangle. More...

void	t8_dtri_transform_face (const t8_dtri_t trianglein, t8_dtri_t triangle2, int orientation, int sign, int is_smaller_face)
	Suppose we have two trees that share a common triangle f. More...

int	t8_dtri_is_inside_root (t8_dtri_t *t)
	Test if a triangle lies inside of the root triangle, that is the triangle of level 0, anchor node (0,0) and type 0. More...

int	t8_dtri_is_root_boundary (const t8_dtri_t *t, int face)
	Compute whether a given triangle shares a given face with its root tree. More...

int	t8_dtri_is_equal (const t8_dtri_t t1, const t8_dtri_t t2)
	Test if two triangles have the same coordinates, type and level. More...

int	t8_dtri_is_sibling (const t8_dtri_t t1, const t8_dtri_t t2)
	Test if two triangles are siblings. More...

int	t8_dtri_is_parent (const t8_dtri_t t, const t8_dtri_t c)
	Test if a triangle is the parent of another triangle. More...

int	t8_dtri_is_ancestor (const t8_dtri_t t, const t8_dtri_t c)
	Test if a triangle is an ancestor of another triangle. More...

t8_linearidx_t	t8_dtri_linear_id (const t8_dtri_t *t, int level)
	Computes the linear position of a triangle in a uniform grid. More...

void	t8_dtri_init_linear_id_with_level (t8_dtri_t *t, t8_linearidx_t id, const int start_level, const int end_level, t8_dtri_type_t parenttype)
	Same as init_linear_id, but we only consider the subtree. More...

void	t8_dtri_init_linear_id (t8_dtri_t *t, t8_linearidx_t id, int level)
	Initialize a triangle as the triangle with a given global id in a uniform refinement of a given level. More...

void	t8_dtri_init_root (t8_dtri_t *t)
	Initialize a triangle as the root triangle (type 0 at level 0) More...

void	t8_dtri_successor (const t8_dtri_t t, t8_dtri_t s, int level)
	Computes the successor of a triangle in a uniform grid of level level. More...

void	t8_dtri_first_descendant (const t8_dtri_t t, t8_dtri_t s, int level)
	Compute the first descendant of a triangle at a given level. More...

void	t8_dtri_last_descendant (const t8_dtri_t t, t8_dtri_t s, int level)
	Compute the last descendant of a triangle at a given level. More...

void	t8_dtri_corner_descendant (const t8_dtri_t t, t8_dtri_t s, int corner, int level)
	Compute the descendant of a triangle in a given corner. More...

void	t8_dtri_predecessor (const t8_dtri_t t, t8_dtri_t s, int level)
	Computes the predecessor of a triangle in a uniform grid of level level. More...

int	t8_dtri_ancestor_id (const t8_dtri_t *t, int level)
	Compute the position of the ancestor of this child at level level within its siblings. More...

int	t8_dtri_child_id (const t8_dtri_t *t)
	Compute the position of the ancestor of this child at level level within its siblings. More...

int	t8_dtri_get_level (const t8_dtri_t *t)
	Return the level of a triangle. More...

int	t8_dtri_is_valid (const t8_dtri_t *t)
	Query whether all entries of a triangle are in valid ranges. More...

void	t8_dtri_debug_print (const t8_dtri_t *t)
	Print a triangle. More...

Detailed Description

Definitions of triangle-specific functions.

Function Documentation

◆ t8_dtri_ancestor()

void t8_dtri_ancestor	(	const t8_dtri_t *	t,
		int	level,
		t8_dtri_t *	ancestor
	)

Compute the ancestor of a triangle at a given level.

Parameters

[in]	t	Input triangle.
[in]	level	A smaller level than t.
[in,out]	ancestor	Existing triangle whose data will be filled with the data of t's ancestor on level level.

Note: The triangle ancestor may point to the same triangle as t.

◆ t8_dtri_ancestor_id()

int t8_dtri_ancestor_id	(	const t8_dtri_t *	t,
		int	level
	)

Compute the position of the ancestor of this child at level level within its siblings.

Parameters

[in]	t	triangle to be considered.
[in]	level	level to be considered.

Returns: Returns its child id in 0..3

◆ t8_dtri_child()

void t8_dtri_child	(	const t8_dtri_t *	t,
		int	childid,
		t8_dtri_t *	child
	)

Compute the childid-th child in Morton order of a triangle.

Parameters

[in]	t	Input triangle.
[in,out]	childid	The id of the child, 0..7 in Morton order.
[out]	child	Existing triangle whose data will be filled with the date of t's childid-th child.

◆ t8_dtri_child_id()

int t8_dtri_child_id ( const t8_dtri_t * t )

Compute the position of the ancestor of this child at level level within its siblings.

Parameters

[in] t triangle to be considered.

Returns: Returns its child id in 0..3

◆ t8_dtri_children_at_face()

void t8_dtri_children_at_face	(	const t8_dtri_t *	tri,
		int	face,
		t8_dtri_t *	children[],
		int	num_children,
		int *	child_indices
	)

Given a triangle and a face of the triangle, compute all children of the triangle that touch the face.

Parameters

[in]	tri	The triangle.
[in]	face	A face of tri.
[in,out]	children	Allocated triangles, in which the children of tri that share a face with face are stored. They will be stored in order of their child_id.
[in]	num_children	The number of triangles in children. Must match the number of children that touch face.

◆ t8_dtri_childrenpv()

void t8_dtri_childrenpv	(	const t8_dtri_t *	t,
		t8_dtri_t *	c[T8_DTRI_CHILDREN]
	)

Compute the 4 children of a triangle, array version.

Parameters

[in]	t	Input triangle.
[in,out]	c	Pointers to the 4 computed children in Morton order. t may point to the same quadrant as c[0].

◆ t8_dtri_compare()

int t8_dtri_compare	(	const t8_dtri_t *	t1,
		const t8_dtri_t *	t2
	)

Compare two triangle in their linear order.

Parameters

[in]	t1	Triangle one.
[in]	t2	Triangle two.

Returns: Returns negativ if t1 < t2, zero if t1 = t2, positive if t1 > t2

◆ t8_dtri_compute_all_coords()

void t8_dtri_compute_all_coords	(	const t8_dtri_t *	elem,
		t8_dtri_coord_t	coordinates[3][2]
	)

Compute the coordinates of the four vertices of a triangle.

Parameters

[in]	elem	Input triangle.
[out]	coordinates	An array of 4x3 t8_dtri_coord_t that will be filled with the coordinates of t's vertices.

◆ t8_dtri_compute_coords()

void t8_dtri_compute_coords	(	const t8_dtri_t *	elem,
		const int	vertex,
		t8_dtri_coord_t	coordinates[2]
	)

Compute the coordinates of a vertex of a triangle.

Parameters

[in]	elem	Input triangle.
[in]	vertex	The number of the vertex.
[out]	coordinates	An array of 2 t8_dtri_coord_t that will be filled with the coordinates of the vertex.

◆ t8_dtri_compute_vertex_ref_coords()

void t8_dtri_compute_vertex_ref_coords	(	const t8_dtri_t *	elem,
		const int	vertex,
		double	coordinates[2]
	)

Compute the reference coordinates of a vertex of a triangle when the tree (level 0 triangle) is embedded in [0,1]^2.

Parameters

[in]	elem	Input triangle.
[in]	vertex	The number of the vertex.
[out]	coordinates	An array of 2 double that will be filled with the reference coordinates of the vertex.

◆ t8_dtri_copy()

void t8_dtri_copy	(	const t8_dtri_t *	t,
		t8_dtri_t *	dest
	)

Copy the values of one triangle to another.

Parameters

[in]	t	Triangle whose values will be copied.
[in,out]	dest	Existing triangle whose data will be filled with the data of t. *

◆ t8_dtri_corner_descendant()

void t8_dtri_corner_descendant	(	const t8_dtri_t *	t,
		t8_dtri_t *	s,
		int	corner,
		int	level
	)

Compute the descendant of a triangle in a given corner.

Parameters

[in]	t	Triangle whose descendant is computed.
[out]	s	Existing triangle whose data will be filled with the data of t's descendant in corner.
[in]	corner	The corner in which the descendant should lie.
[in]	level	The refinement level of the descendant. Must be greater or equal to t's level.

◆ t8_dtri_debug_print()

void t8_dtri_debug_print ( const t8_dtri_t * t )

Print a triangle.

Parameters

[in] t triangle to be considered.

◆ t8_dtri_face_child_face()

int t8_dtri_face_child_face	(	const t8_dtri_t *	triangle,
		int	face,
		int	face_child
	)

Given a face of a triangle and a child number of a child of that face, return the face number of the child of the triangle that matches the child face.

Parameters

[in]	triangle	The triangle.
[in]	face	Then number of the face.
[in]	face_child	The child number of a child of the face triangle.

Returns: The face number of the face of a child of triangle that conincides with face_child.

◆ t8_dtri_face_neighbour()

int t8_dtri_face_neighbour	(	const t8_dtri_t *	t,
		int	face,
		t8_dtri_t *	n
	)

Compute the face neighbor of a triangle.

Parameters

[in]	t	Input triangle.
[in]	face	The face across which to generate the neighbor.
[in,out]	n	Existing triangle whose data will be filled.

Note: t may point to the same triangle as n.

◆ t8_dtri_face_parent_face()

int t8_dtri_face_parent_face	(	const t8_dtri_t *	triangle,
		int	face
	)

Given a face of an triangle return the face number of the parent of the triangle that matches the triangle's face.

Or return -1 if no face of the parent matches the face.

Parameters

[in]	triangle	The triangle.
[in]	face	Then number of the face.

Returns: If face of elem is also a face of elem's parent, the face number of this face. Otherwise -1.

◆ t8_dtri_first_descendant()

void t8_dtri_first_descendant	(	const t8_dtri_t *	t,
		t8_dtri_t *	s,
		int	level
	)

Compute the first descendant of a triangle at a given level.

This is the descendant of the triangle in a uniform maxlevel refinement that has the smaller id.

Parameters

[in]	t	Triangle whose descendant is computed.
[in]	level	A given level. Must be grater or equal to t's level.
[out]	s	Existing triangle whose data will be filled with the data of t's first descendant.

◆ t8_dtri_get_level()

int t8_dtri_get_level ( const t8_dtri_t * t )

Return the level of a triangle.

Parameters

[in] t triangle to be considered.

Returns: The level of t.

◆ t8_dtri_init_linear_id()

void t8_dtri_init_linear_id	(	t8_dtri_t *	t,
		t8_linearidx_t	id,
		int	level
	)

Initialize a triangle as the triangle with a given global id in a uniform refinement of a given level.

Parameters

[in,out] t Existing triangle whose data will be filled.

[in] id Index to be considered.

[in] level level of uniform grid to be considered.

◆ t8_dtri_init_linear_id_with_level()

void t8_dtri_init_linear_id_with_level	(	t8_dtri_t *	t,
		t8_linearidx_t	id,
		const int	start_level,
		const int	end_level,
		t8_dtri_type_t	parenttype
	)

Same as init_linear_id, but we only consider the subtree.

Used for computing the index of a tetrahedron lying in a pyramid

Parameters

[in,out]	t	Existing triangle whose data will be filled
[in]	id	Index to be considered
[in]	start_level	The level of the root of the subtree
[in]	end_level	Level of uniform grid to be considered
[in]	parenttype	The type of the parent.

◆ t8_dtri_init_root()

void t8_dtri_init_root ( t8_dtri_t * t )

Initialize a triangle as the root triangle (type 0 at level 0)

Parameters

[in,out] t Existing triangle whose data will be filled.

◆ t8_dtri_is_ancestor()

int t8_dtri_is_ancestor	(	const t8_dtri_t *	t,
		const t8_dtri_t *	c
	)

Test if a triangle is an ancestor of another triangle.

Parameters

[in]	t	triangle to be tested.
[in]	c	Descendent triangle.

Returns: true if t is equal to or an ancestor of c.

◆ t8_dtri_is_equal()

int t8_dtri_is_equal	(	const t8_dtri_t *	t1,
		const t8_dtri_t *	t2
	)

Test if two triangles have the same coordinates, type and level.

Returns: true if t1 describes the same triangle as t2.

◆ t8_dtri_is_familypv()

int t8_dtri_is_familypv ( const t8_dtri_t * f[] )

Check whether a collection of eight triangles is a family in Morton order.

Parameters

[in] f An array of eight triangles.

Returns: Nonzero if f is a family of triangles.

◆ t8_dtri_is_inside_root()

int t8_dtri_is_inside_root ( t8_dtri_t * t )

Test if a triangle lies inside of the root triangle, that is the triangle of level 0, anchor node (0,0) and type 0.

Parameters

[in] t Input triangle.

Returns: true If t lies inside of the root triangle.

◆ t8_dtri_is_parent()

int t8_dtri_is_parent	(	const t8_dtri_t *	t,
		const t8_dtri_t *	c
	)

Test if a triangle is the parent of another triangle.

Parameters

[in]	t	triangle to be tested.
[in]	c	Possible child triangle.

Returns: true if t is the parent of c.

◆ t8_dtri_is_root_boundary()

int t8_dtri_is_root_boundary	(	const t8_dtri_t *	t,
		int	face
	)

Compute whether a given triangle shares a given face with its root tree.

Parameters

[in]	t	The input triangle.
[in]	face	A face of t.

Returns: True if face is a subface of the triangle's root element.

◆ t8_dtri_is_sibling()

int t8_dtri_is_sibling	(	const t8_dtri_t *	t1,
		const t8_dtri_t *	t2
	)

Test if two triangles are siblings.

Parameters

[in]	t1	First triangle to be tested.
[in]	t2	Second triangle to be tested.

Returns: true if t1 is equal to or a sibling of t2. *

◆ t8_dtri_is_valid()

int t8_dtri_is_valid ( const t8_dtri_t * t )

Query whether all entries of a triangle are in valid ranges.

Parameters

[in] t triangle to be considered.

Returns: True, if t is a valid triangle and it is safe to call any function on t. False otherwise.

◆ t8_dtri_last_descendant()

void t8_dtri_last_descendant	(	const t8_dtri_t *	t,
		t8_dtri_t *	s,
		int	level
	)

Compute the last descendant of a triangle at a given level.

This is the descendant of the triangle in a uniform maxlevel refinement that has the biggest id.

Parameters

[in]	t	Triangle whose descendant is computed.
[in]	level	A given level. Must be grater or equal to t's level.
[out]	s	Existing triangle whose data will be filled with the data of t's last descendant.

◆ t8_dtri_linear_id()

t8_linearidx_t t8_dtri_linear_id	(	const t8_dtri_t *	t,
		int	level
	)

Computes the linear position of a triangle in a uniform grid.

Parameters

[in]	t	triangle whose id will be computed.
[in]	level	level of uniform grid to be considered.

Returns: Returns the linear position of this triangle on a grid of level level.

Note: This id is not the Morton index.

◆ t8_dtri_nearest_common_ancestor()

void t8_dtri_nearest_common_ancestor	(	const t8_dtri_t *	t1,
		const t8_dtri_t *	t2,
		t8_dtri_t *	r
	)

Computes the nearest common ancestor of two triangles in the same tree.

Parameters

[in]	t1	First input triangle.
[in]	t2	Second input triangle.
[in,out]	r	Existing triangle whose data will be filled.

Note: t1, t2, r may point to the same quadrant.

◆ t8_dtri_parent()

void t8_dtri_parent	(	const t8_dtri_t *	t,
		t8_dtri_t *	parent
	)

Compute the parent of a triangle.

Parameters

[in]	elem	Input triangle.
[in,out]	parent	Existing triangle whose data will be filled with the data of elem's parent.

Note: elem may point to the same triangle as parent.

◆ t8_dtri_predecessor()

void t8_dtri_predecessor	(	const t8_dtri_t *	t,
		t8_dtri_t *	s,
		int	level
	)

Computes the predecessor of a triangle in a uniform grid of level level.

Parameters

[in]	t	triangle whose id will be computed.
[in,out]	s	Existing triangle whose data will be filled with the data of t's predecessor on level level.
[in]	level	level of uniform grid to be considered.

◆ t8_dtri_root_face_to_face()

int t8_dtri_root_face_to_face	(	t8_dtri_t *	t,
		int	root_face
	)

Given a triangle and a face of the root triangle.

If the triangle lies on the tree boundary, return the corresponding face number of the triangle. If not the return value is arbitrary.

Parameters

[in]	t	The triangle.
[in]	face	The index of a face of the root element.

Returns: The index of the face of t that is a subface of face, if t is on the tree boundary. Any arbitrary integer if t is not at a tree boundary.

Note: For boundary triangles, this function is the inverse of t8_dtri_tree_face

◆ t8_dtri_sibling()

void t8_dtri_sibling	(	const t8_dtri_t *	elem,
		int	sibid,
		t8_dtri_t *	sibling
	)

Compute a specific sibling of a triangle.

Parameters

[in]	elem	Input triangle.
[in,out]	sibling	Existing triangle whose data will be filled with the data of sibling no. sibling_id of elem.
[in]	sibid	The id of the sibling computed, 0..7 in Bey order.

◆ t8_dtri_successor()

void t8_dtri_successor	(	const t8_dtri_t *	t,
		t8_dtri_t *	s,
		int	level
	)

Computes the successor of a triangle in a uniform grid of level level.

Parameters

[in]	t	triangle whose id will be computed.
[in,out]	s	Existing triangle whose data will be filled with the data of t's successor on level level.
[in]	level	level of uniform grid to be considered.

◆ t8_dtri_transform_face()

void t8_dtri_transform_face	(	const t8_dtri_t *	trianglein,
		t8_dtri_t *	triangle2,
		int	orientation,
		int	sign,
		int	is_smaller_face
	)

Suppose we have two trees that share a common triangle f.

Given a triangle e that is a subface of f in one of the trees and given the orientation of the tree connection, construct the face triangle of the respective tree neighbor that logically coincides with e but lies in the coordinate system of the neighbor tree.

Parameters

[in]	trianglein	The face triangle.
[in,out]	triangle2	On return the face triangle triangle1 with respective to the coordinate system of the other tree.
[in]	orientation	The orientation of the tree-tree connection.

See also: t8_cmesh_set_join

Parameters

[in]	sign	Depending on the topological orientation of the two tree faces, either 0 (both faces have opposite orientation) or 1 (both faces have the same top. orientattion). t8_eclass_face_orientation
[in]	is_smaller_face	Flag to declare whether triangle1 belongs to the smaller face. A face f of tree T is smaller than f' of T' if either the eclass of T is smaller or if the classes are equal and f<f'. The orientation is defined in relation to the smaller face.

Note: trianglein and triangle2 may point to the same element.

◆ t8_dtri_tree_face()

int t8_dtri_tree_face	(	t8_dtri_t *	t,
		int	face
	)

Given a triangle and a face of this triangle.

If the face lies on the tree boundary, return the face number of the tree face. If not the return value is arbitrary.

Parameters

[in]	t	The triangle.
[in]	face	The index of a face of t.

Returns: The index of the tree face that face is a subface of, if face is on a tree boundary. Any arbitrary integer if t is not at a tree boundary.

Note: For boundary triangles, this function is the inverse of t8_dtri_root_face_to_face

Functions

Detailed Description

Function Documentation

◆ t8_dtri_ancestor()

◆ t8_dtri_ancestor_id()

◆ t8_dtri_child()

◆ t8_dtri_child_id()

◆ t8_dtri_children_at_face()

◆ t8_dtri_childrenpv()

◆ t8_dtri_compare()

◆ t8_dtri_compute_all_coords()

◆ t8_dtri_compute_coords()

◆ t8_dtri_compute_vertex_ref_coords()

◆ t8_dtri_copy()

◆ t8_dtri_corner_descendant()

◆ t8_dtri_debug_print()

◆ t8_dtri_face_child_face()

◆ t8_dtri_face_neighbour()

◆ t8_dtri_face_parent_face()

◆ t8_dtri_first_descendant()

◆ t8_dtri_get_level()

◆ t8_dtri_init_linear_id()

◆ t8_dtri_init_linear_id_with_level()

◆ t8_dtri_init_root()

◆ t8_dtri_is_ancestor()

◆ t8_dtri_is_equal()

◆ t8_dtri_is_familypv()

◆ t8_dtri_is_inside_root()

◆ t8_dtri_is_parent()

◆ t8_dtri_is_root_boundary()

◆ t8_dtri_is_sibling()

◆ t8_dtri_is_valid()

◆ t8_dtri_last_descendant()

◆ t8_dtri_linear_id()

◆ t8_dtri_nearest_common_ancestor()

◆ t8_dtri_parent()

◆ t8_dtri_predecessor()

◆ t8_dtri_root_face_to_face()

◆ t8_dtri_sibling()

◆ t8_dtri_successor()

◆ t8_dtri_transform_face()

◆ t8_dtri_tree_face()