Planar triangle mesh. ,. More...

#include <mesh.h>

Public Member Functions
	Mesh2 ()
	Create an empty mesh.

	Mesh2 (const QVector< Vector2 > &, const QVector< int > &)
	Create a mesh from a list of vertices and a indexes. More...

	Mesh2 (const Quadrangle2 &, int, int)
	Generate a grid geometry over an input quadrangle. More...

	Mesh2 (const Box2 &, int, int)
	Generate a grid geometry. More...

	Mesh2 (const Circle2 &, int)
	Create an n-adic subdivision of a circle. More...

	Mesh2 (const Ellipse2 &, int)
	Create an n-adic subdivision of an ellipse. More...

	Mesh2 (const Polygon2 &)
	Create triangle mesh from a polygon. More...

	~Mesh2 ()
	Empty.

Triangle2	GetTriangle (int) const
	Get a triangle. More...

Vector2	Vertex (int) const
	Get a vertex. More...

Vector2	Vertex (int, int) const
	Get a vertex from a specific triangle. More...

Box2	GetBox () const
	Compute the boudning box. More...

int	VertexSize () const
	Get the number of vertices in the geometry. More...

int	TriangleSize () const
	Get the number of triangles. More...

int	IndexSize () const
	Get the size of the index array. More...

int	index (int) const
	Get the vertex index. More...

int	index (int, int) const
	Get a vertex/normal index according to triangle information. More...

QVector< int >	Indexes () const
	Return the set of indexes.

QVector< int > &	Indexes ()
	Return the set of indexes.

QVector< Vector2 >	Vertices () const
	Get the array of vertices.

QVector< int >	Valences () const
	Compute the valence of the vertices. More...

void	Transform (const Frame2 &)
	Transform a mesh. More...

void	Translate (const Vector2 &)
	Translate a mesh. More...

void	Scale (const Vector2 &)
	Translate a mesh. More...

void	Rotate (const Matrix2 &)
	Rotate a mesh. More...

void	Draw (QGraphicsScene &, const QPen &=QPen(), bool=true) const
	Draw the mesh. More...

Static Public Member Functions
static Mesh2	Delaunay (QVector< Vector2 > &)
	Compute the Delaunay triangulation of a set of points. More...

static Mesh2	DelaunayN4 (const QVector< Vector2 > &)
	Compute the Delaunay triangulation of a set of points in the plane. More...

Protected Attributes
QVector< Vector2 >	vertices
	Vertices.

QVector< int >	indices
	Triangle vertex indices.

Detailed Description

Planar triangle mesh. ,.

Constructor & Destructor Documentation

◆ Mesh2() [1/6]

Mesh2::Mesh2	(	const QVector< Vector2 > &	v,
		const QVector< int > &	i
	)

explicit

Create a mesh from a list of vertices and a indexes.

Indices should be a multiple of three; the number of triangles is derived from the size of indices.

See also: Mesh2::TriangleSize

Parameters

v	Set of vertices.
i	Indexes that represent the triangles.

◆ Mesh2() [2/6]

Mesh2::Mesh2	(	const Quadrangle2 &	quad,
		int	nx,
		int	ny
	)

explicit

Generate a grid geometry over an input quadrangle.

Parameters

quad	Quadrangle.
nx,ny	Number of points in the subdivision.

◆ Mesh2() [3/6]

Mesh2::Mesh2	(	const Box2 &	box,
		int	x,
		int	y
	)

explicit

Generate a grid geometry.

Parameters

box	The box.
x,y	Number of points in the subdivision.

◆ Mesh2() [4/6]

Mesh2::Mesh2	(	const Circle2 &	circle,
		int	n
	)

explicit

Create an n-adic subdivision of a circle.

Creates an hexagon an applies an n-adic subdivision. The code of this function strongly relies on the more general function Polygon2::Subdivide().

Parameters

circle	The circle.
n	Subdivision level.

◆ Mesh2() [5/6]

Mesh2::Mesh2	(	const Ellipse2 &	ellipse,
		int	n
	)

explicit

Create an n-adic subdivision of an ellipse.

Create a circle and apply scaling and translation.

See also: Mesh2::Mesh2(const Circle&, int)

This constructor is the same as the following:

Ellipse2 ellipse(Vector2(2.0,3.0),4.0,2.0);
Mesh2 mesh(Circle(1.0),n);
mesh.Scale(ellipse.A(),ellipse.B());
mesh.Translate(ellipse.Center());

Parameters

ellipse	The ellipse.
n	Subdivision level.

◆ Mesh2() [6/6]

Mesh2::Mesh2 ( const Polygon2 & polygon )

explicit

Create triangle mesh from a polygon.

Perform a decomposition of the polygon into triangles using the ear-clipping algorithm.

See also: Polygon::EarClip()

Parameters

polygon The polygon.

Member Function Documentation

◆ Delaunay()

Mesh2 Mesh2::Delaunay ( QVector< Vector2 > & points )

static

Compute the Delaunay triangulation of a set of points.

Bowyer-Watson algorithm, O(n log n) complexity, C++ implementation of http://paulbourke.net/papers/triangulate.

◆ DelaunayN4()

Mesh2 Mesh2::DelaunayN4 ( const QVector< Vector2 > & p )

static

Compute the Delaunay triangulation of a set of points in the plane.

This function return the set of index of vertices

This function is only provided as a reference: it uses a brute force approach with an O(n⁴) complexity.

Basically it computes all the possible triangles and checks whether they are valid by testing if some points lie inside the circumscribed circle.

Parameters

p	Set of input points.

See also: Mesh2::Delaunay

◆ Draw()

void Mesh2::Draw	(	QGraphicsScene &	graphics,
		const QPen &	pen = `QPen()`,
		bool	vertexes = `true`
	)		const

Draw the mesh.

Parameters

graphics	Graphics scene.
pen	Pen used for the edges and vertexes.
vertexes	Boolean defining whether vertexes should be drawn as discs.

◆ GetBox()

Box2 Mesh2::GetBox ( ) const

Compute the boudning box.

Simply eqsuivalent as:

Mesh2 mesh;

Box2 box=Box2(mesh.Vertices());

Box2

Axis aligned box in the plane.

Definition: box.h:371

Mesh2::Vertices

QVector< Vector2 > Vertices() const

Get the array of vertices.

Definition: mesh.h:404

◆ GetTriangle()

Triangle2 Mesh2::GetTriangle ( int i ) const

inline

Get a triangle.

Parameters

i Index.

Returns: The triangle.

◆ index() [1/2]

int Mesh2::index ( int i ) const

inline

Get the vertex index.

Parameters

i	The number in indices of the wanted vertex.

Returns: The index of the wanted vertex.

◆ index() [2/2]

int Mesh2::index	(	int	t,
		int	v
	)		const

inline

Get a vertex/normal index according to triangle information.

Parameters

t	The triangle number.
v	The triangle vertex index.

Returns: The index of the wanted vertex.

◆ IndexSize()

int Mesh2::IndexSize ( ) const

inline

Get the size of the index array.

See also: Mesh2::TriangleSize()

◆ Rotate()

void Mesh2::Rotate ( const Matrix2 & r )

Rotate a mesh.

Parameters

r	Rotation matrix.

◆ Scale()

void Mesh2::Scale ( const Vector2 & s )

Translate a mesh.

Parameters

s	Scaling vector.

◆ Transform()

void Mesh2::Transform ( const Frame2 & f )

Transform a mesh.

Parameters

f	Transform.

◆ Translate()

void Mesh2::Translate ( const Vector2 & t )

Translate a mesh.

Parameters

t	Translation vector.

◆ TriangleSize()

int Mesh2::TriangleSize ( ) const

inline

Get the number of triangles.

This is the size of the array of indexes divided by three.

Returns: The effective number of triangle in the geometry.

◆ Valences()

QVector< int > Mesh2::Valences ( ) const

Compute the valence of the vertices.

Returns: A vector with the computed valences.

◆ Vertex() [1/2]

Vector2 Mesh2::Vertex ( int i ) const

inline

Get a vertex.

Parameters

i	The index of the wanted vertex.

Returns: The wanted vertex (as a 3D Vector).

◆ Vertex() [2/2]

Vector2 Mesh2::Vertex	(	int	t,
		int	v
	)		const

inline

Get a vertex from a specific triangle.

Parameters

t	The number of the triangle that contains the wanted vertex.
v	The triangle vertex: 0, 1, or 2.

Returns: The wanted vertex.

◆ VertexSize()

int Mesh2::VertexSize ( ) const

inline

Get the number of vertices in the geometry.

Returns: The number of vertices in the geometry, in other words the size of vertices.

Public Member Functions

Static Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Mesh2() [1/6]

◆ Mesh2() [2/6]

◆ Mesh2() [3/6]

◆ Mesh2() [4/6]

◆ Mesh2() [5/6]

◆ Mesh2() [6/6]

Member Function Documentation

◆ Delaunay()

◆ DelaunayN4()

◆ Draw()

◆ GetBox()

◆ GetTriangle()

◆ index() [1/2]

◆ index() [2/2]

◆ IndexSize()

◆ Rotate()

◆ Scale()

◆ Transform()

◆ Translate()

◆ TriangleSize()

◆ Valences()

◆ Vertex() [1/2]

◆ Vertex() [2/2]

◆ VertexSize()