Mesh2 Class Reference

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.
	Mesh2 (const Quadrangle2 &, int, int)
	Generate a grid geometry over an input quadrangle.
	Mesh2 (const Box2 &, int, int)
	Generate a grid geometry.
	Mesh2 (const Circle2 &, int)
	Create an n-adic subdivision of a circle.
	Mesh2 (const Ellipse2 &, int)
	Create an n-adic subdivision of an ellipse.
	Mesh2 (const Polygon2 &)
	Create triangle mesh from a polygon.
	~Mesh2 ()
	Empty.
Triangle2	GetTriangle (int) const
	Get a triangle.
Vector2	Vertex (int) const
	Get a vertex.
Vector2	Vertex (int, int) const
	Get a vertex from a specific triangle.
Box2	GetBox () const
	Compute the boudning box.
int	VertexSize () const
	Get the number of vertices in the geometry.
int	TriangleSize () const
	Get the number of triangles.
int	IndexSize () const
	Get the size of the index array.
int	index (int) const
	Get the vertex index.
int	index (int, int) const
	Get a vertex/normal index according to triangle information.
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.
void	Transform (const Frame2 &)
	Transform a mesh.
void	Translate (const Vector2 &)
	Translate a mesh.
void	Scale (const Vector2 &)
	Translate a mesh.
void	Rotate (const Matrix2 &)
	Rotate a mesh.
void	Draw (QGraphicsScene &, const QPen &=QPen(), bool=true) const
	Draw the mesh.
double	Aspect () const
	Compute the average aspect ratio of the triangles of the mesh.
Mesh2	Intersect (const Box2 &) const
	Keep triangles that intersect the a box.
void	SetTrigoOrder (bool trigo=true)
	Set all triangles in the same trigonometric order.
double	AverageEdgeLength () const
	Compute the average edge length.
void	EdgeLengthRange (double &, double &) const
	Compute the range of edge lengths.
QVector< int >	AspectRatios (int=4) const
	Compute the histogram of the aspect ratio of the triangles of the mesh.
void	EdgeCollapse (const double &)
	Run a simple edge collapse algorithm over a triangle mesh.

Static Public Member Functions
static Mesh2	Delaunay (const QVector< Vector2 > &)
	Compute the Delaunay triangulation of a set of points.
static Mesh2	DelaunayN4 (const QVector< Vector2 > &)
	Compute the Delaunay triangulation of a set of points in the plane.
static int	NextIndex (int)
	Compute the next index of an edge in a triangle.

Static Protected Member Functions
static int	PrevIndex (int)
	Compute the previous index of an edge in a triangle.
static int	BaseIndex (int)
	Compute the base triangle index given an edge index.

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.

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

AspectRatios()

QVector< int > Mesh2::AspectRatios

(

int

n = 4

)

const

Compute the histogram of the aspect ratio of the triangles of the mesh.

Parameters

n	Number of classes.

BaseIndex()

int Mesh2::BaseIndex ( int i )

inlinestaticprotected

Compute the base triangle index given an edge index.

Parameters

i	Edge index.

Delaunay()

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

static

Compute the Delaunay triangulation of a set of points.

Parameters

p	Point set.

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.

EdgeCollapse()

void Mesh2::EdgeCollapse

(

const double &

epsilon

)

Run a simple edge collapse algorithm over a triangle mesh.

This algorithm runs in O(n²) where n denotes the number of triangles in the mesh.

Parameters

epsilon

Threshold length for collapsing an edge.

EdgeLengthRange()

void Mesh2::EdgeLengthRange	(	double &	a,
		double &	b ) const

Compute the range of edge lengths.

Parameters

a,b

Range.

GetBox()

Box2 Mesh2::GetBox

(

)

const

Compute the boudning box.

Simply eqsuivalent as:

Mesh2 mesh;
Box2 box=Box2(mesh.Vertices());

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()

Intersect()

Mesh2 Mesh2::Intersect

(

const Box2 &

box

)

const

Keep triangles that intersect the a box.

Parameters

box

The box.

NextIndex()

int Mesh2::NextIndex ( int i )

inlinestatic

Compute the next index of an edge in a triangle.

Parameters

i	Index of the starting vertex of an edge.

PrevIndex()

int Mesh2::PrevIndex ( int i )

inlinestaticprotected

Compute the previous index of an edge in a triangle.

Parameters

i	Index of the starting vertex of an edge.

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.

SetTrigoOrder()

void Mesh2::SetTrigoOrder

(

bool

trigo = true

)

Set all triangles in the same trigonometric order.

Parameters

trigo

Trigonometric (counterclockwise) is true, clockwise if false.

Author

Hugo Schott

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.