#include <triangle.hpp>

Detailed Description

template<uint8_t dim>
class bem::Triangle< dim >

Triangle primitive class.

Template Parameters

dim	- The dimension of the triangle (2 or 3).

Definition at line 44 of file triangle.hpp.

Constructor & Destructor Documentation

◆ Triangle() [1/3]

template<uint8_t dim>

bem::Triangle< dim >::Triangle ( )

inline

Constructs a default reference Triangle object.

Definition at line 51 of file triangle.hpp.

◆ Triangle() [2/3]

template<uint8_t dim>

bem::Triangle< dim >::Triangle	(	ConstEigRef< EigMatMN< Float, dim, 3 > >	v,
		EigRowVecN< Float, 3 >	edge_polarities = `EigRowVecN<Float, 3>::Constant(1, 3, 1)`
	)

inline

Constructs a Triangle with given vertices.

Parameters

[in]	v	- Vertices of the triangle.
[in]	edge_polarities	- Polarity of each edge of the triangle (optional).

Definition at line 63 of file triangle.hpp.

◆ Triangle() [3/3]

template<uint8_t dim>

bem::Triangle< dim >::Triangle	(	std::array< EigColVecN< Float, dim >, 3 >	v_array,
		EigRowVecN< Float, 3 >	edge_polarities = `EigRowVecN<Float, 3>::Constant(1, 3, 1)`
	)

inline

Constructs a Triangle with given vertices.

Parameters

[in]	v_array	- Array of vertices of the triangle.
[in]	edge_polarities	- Polarity of each edge of the triangle (optional).

Definition at line 78 of file triangle.hpp.

Member Function Documentation

◆ set_v()

template<uint8_t dim>

void bem::Triangle< dim >::set_v	(	ConstEigRef< EigMatMN< Float, dim, 3 > >	v,
		EigRowVecN< Float, 3 >	edge_polarities = `EigRowVecN<Float, 3>::Constant(1, 3, 1)`
	)

Sets the vertices of this Triangle.

Parameters

[in]	v	- Vertices of the triangle.
[in]	edge_polarities	- Polarity of each edge of the triangle (optional).

Definition at line 33 of file triangle.cpp.

◆ v() [1/2]

template<uint8_t dim>

const EigMatMN< Float, dim, 3 > & bem::Triangle< dim >::v ( ) const

inline

Returns the vertices of this Triangle.

Returns: Vertices of the triangle.

Definition at line 106 of file triangle.hpp.

◆ v() [2/2]

template<uint8_t dim>

EigColVecN< Float, dim > bem::Triangle< dim >::v ( const uint8_t idx ) const

inline

Returns the vertex of this Triangle at a given index.

Parameters

[in] idx - Index of the desired vertex (0, 1, or 2).

Returns: Vertex of the triangle at the given index.

Definition at line 117 of file triangle.hpp.

◆ edge_polarities() [1/2]

template<uint8_t dim>

const EigRowVecN< Float, 3 > & bem::Triangle< dim >::edge_polarities ( ) const

inline

Returns the edge polarities of this Triangle.

Returns: Edge polarities of the triangle.

Definition at line 129 of file triangle.hpp.

◆ edge_polarities() [2/2]

template<uint8_t dim>

Float bem::Triangle< dim >::edge_polarities ( const uint8_t idx ) const

inline

Returns the edge polarity of this Triangle at a given index.

Parameters

[in] idx - Index of the desired edge (0, 1, or 2).

Returns: Edge polarity of the triangle at the given index.

Definition at line 140 of file triangle.hpp.

◆ reverse()

template<uint8_t dim>

void bem::Triangle< dim >::reverse ( )

inline

Reverses the orientation of this Triangle.

Definition at line 151 of file triangle.hpp.

◆ area() [1/2]

template<uint8_t dim>

Float bem::Triangle< dim >::area ( ) const

inline

Returns the area of this Triangle.

Returns: Area of the triangle.

Definition at line 162 of file triangle.hpp.

◆ normal() [1/2]

template<uint8_t dim>

EigColVecN< Float, 3 > bem::Triangle< dim >::normal ( ) const

inline

Returns the unit normal vector for this Triangle.

Returns: Unit normal vector of the triangle.

Definition at line 170 of file triangle.hpp.

◆ centroid() [1/2]

template<uint8_t dim>

EigColVecN< Float, dim > bem::Triangle< dim >::centroid ( ) const

inline

Returns the centroid of this Triangle.

Returns: Centroid of the triangle.

Definition at line 178 of file triangle.hpp.

◆ mean_edge_length()

template<uint8_t dim>

Float bem::Triangle< dim >::mean_edge_length ( ) const

inline

Returns the mean edge length of this Triangle.

Returns: Mean edge length of the triangle.

Definition at line 186 of file triangle.hpp.

◆ to_2d()

template<uint8_t dim>

Triangle< 2 > bem::Triangle< dim >::to_2d ( ) const

Returns an equivalent triangle with coordinates in a local 2D system, with the local origin at this triangle's first vertex, and with its edge connecting the first two vertices lying along the local x axis.

Returns: 2D Triangle with coordinates in a local 2D system.

Definition at line 48 of file triangle.cpp.

◆ to_3d()

template<uint8_t dim>

Triangle< 3 > bem::Triangle< dim >::to_3d ( const Float z = 0.0 ) const

Adds a 0-valued third dimension if this Triangle is in 2D, otherwise just returns a copy of this Triangle.

Returns: 3D Triangle.

Definition at line 74 of file triangle.cpp.

◆ local_origin()

template<uint8_t dim>

EigColVecN< Float, dim > bem::Triangle< dim >::local_origin ( ) const

inline

Returns the local origin of this Triangle in the global coordinate system. The local origin is just the first vertex of the triangle.

Returns: Local origin of the triangle in the global coordinate system (i.e., its first vertex).

Definition at line 217 of file triangle.hpp.

◆ local_coordinate_basis()

template<uint8_t dim>

EigMatMN< Float, dim, dim > bem::Triangle< dim >::local_coordinate_basis ( ) const

Returns the unit vectors of a local coordinate system, defined in the global system, such that the edge connecting the first two vertices lie along the local x axis, and the Triangle lies in the local xy plane.

Returns: Local coordinate basis of the triangle in the global coordinate system.

Definition at line 83 of file triangle.cpp.

◆ get_plane_projection()

template<uint8_t dim>

void bem::Triangle< dim >::get_plane_projection	(	EigMatNX< Float, dim > &	r_proj,
		EigRowVec< Float > &	d,
		ConstEigRef< EigMatNX< Float, 3 > >	r,
		uint8_t	ref_idx = `0`
	)		const

Returns the projection of given points on to the triangle's plane, along with the normal distance to the plane. For a 2D Triangle, its third (z) dimension is assumed to be 0.

Parameters

[out]	r_proj	- Projected points.
[out]	d	- Perpendicular distances of the original points to the triangle's plane.
[in]	r	- Points to be projected onto the triangle's plane.
[in]	ref_idx	- Index of the reference vertex to be used for the projection (optional).

Definition at line 111 of file triangle.cpp.

◆ reference_triangle()

template<uint8_t dim>

Triangle< dim > bem::Triangle< dim >::reference_triangle ( )

static

Returns a reference triangle in the specified dimension.

Returns: Reference edge with vertices (0, 0, ...), (1, 0, ...), (0, 1, ...).

Definition at line 129 of file triangle.cpp.

◆ edge_lengths()

template<uint8_t dim>

EigColVecN< Float, 3 > bem::Triangle< dim >::edge_lengths ( ) const

inline

Returns the lengths of each edge of this Triangle.

Returns: Lengths of the triangle's edges.

Definition at line 259 of file triangle.hpp.

◆ longest_edge_index()

template<uint8_t dim>

uint8_t bem::Triangle< dim >::longest_edge_index ( ) const

inline

Returns the index associated with the longest edge of this Triangle.

Returns: Index of the triangle's longest edge.

Definition at line 272 of file triangle.hpp.

◆ shortest_edge_index()

template<uint8_t dim>

uint8_t bem::Triangle< dim >::shortest_edge_index ( ) const

inline

Returns the index associated with the shortest edge of this Triangle.

Returns: Index of the triangle's shortest edge.

Definition at line 285 of file triangle.hpp.

◆ longest_edge_length()

template<uint8_t dim>

Float bem::Triangle< dim >::longest_edge_length ( ) const

inline

Length of the longest edge of this Triangle.

Returns: Length of the triangle's longest edge.

Definition at line 298 of file triangle.hpp.

◆ shortest_edge_length()

template<uint8_t dim>

Float bem::Triangle< dim >::shortest_edge_length ( ) const

inline

Length of the shortest edge of this Triangle.

Returns: Length of the triangle's shortest edge.

Definition at line 308 of file triangle.hpp.

◆ barycentric_coords()

template<uint8_t dim>

EigMatNX< Float, 3 > bem::Triangle< dim >::barycentric_coords ( ConstEigRef< EigMatNX< Float, dim > > p ) const

Returns barycentric coordinates of given points lying in the Triangle's plane.

Parameters

[in] p - Points in the triangle's plane for which to compute barycentric coordinates.

Returns: Barycentric coordinates of the points.

Definition at line 141 of file triangle.cpp.

◆ projection_loc()

template<uint8_t dim>

EigRowVec< uint8_t > bem::Triangle< dim >::projection_loc ( ConstEigRef< EigMatNX< Float, 3 > > r ) const

Returns flags that indicate whether the given points project inside or outside the triangle, or onto a vertex or edge.

Parameters

[in] r - Points to be projected.

Returns: 0 if strictly inside, 1 if on a vertex, 2 if on an edge, 3 if strictly outside.

Definition at line 172 of file triangle.cpp.

◆ point_in_triangle()

template<uint8_t dim>

bool bem::Triangle< dim >::point_in_triangle	(	ConstEigRef< EigColVecN< Float, dim > >	r,
		const Float	tol = `TRIANGLE_DEFAULT_TOL`
	)		const

Checks whether a given point is inside the triangle, inclusive of edges and vertices.

Parameters

[in]	r	- Point to be tested.
[in]	tol	- Comparison tolerance (optional).

Returns: True if the point is inside the triangle, inclusive of edges and vertices, false otherwise.

Definition at line 241 of file triangle.cpp.

◆ map_points()

template<uint8_t dim>

template<uint8_t dim_out>

EigColVecN< Float, dim_out > bem::Triangle< dim >::map_points	(	ConstEigRef< EigColVecN< Float, dim > >	points,
		const Triangle< dim_out > &	tri_out
	)		const

inline

Performs an affine transform to map points lying in this triangle's plane to the output triangle's plane.

Template Parameters

dim_out - Output triangle's dimension (2 or 3).

Parameters

[in]	points	- Coordinates in this triangle's plane.
[in]	tri_out	- Target `Triangle` into whose plane `points` will be mapped.

Returns: Output coordinates in tri_out's plane.

Definition at line 349 of file triangle.hpp.

◆ area() [2/2]

template<uint8_t dim>

Float bem::Triangle< dim >::area ( ConstEigRef< EigMatMN< Float, dim, 3 > > v )

static

Computes the area of the triangle formed by the given vertices.

Parameters

[in] v - Vertices.

Returns: Area of the triangle.

Definition at line 287 of file triangle.cpp.

◆ normal() [2/2]

template<uint8_t dim>

EigColVecN< Float, 3 > bem::Triangle< dim >::normal ( ConstEigRef< EigMatMN< Float, dim, 3 > > v )

static

Computes the unit normal vector for the triangle formed by the given vertices.

Parameters

[in] v - Vertices.

Returns: Unit normal vector of the triangle.

Definition at line 307 of file triangle.cpp.

◆ centroid() [2/2]

template<uint8_t dim>

static EigColVecN< Float, dim > bem::Triangle< dim >::centroid ( ConstEigRef< EigMatMN< Float, dim, 3 > > v )

inlinestatic

Computes the centroid of the triangle formed by the given vertices.

Parameters

[in] v - Vertices.

Returns: Centroid of the triangle.

protected

Definition at line 393 of file triangle.hpp.

The documentation for this class was generated from the following files:

source/geometry/operations.hpp
source/geometry/primitives/triangle.hpp
source/geometry/primitives/triangle.cpp