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 &)
	Scale 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	SetTrigonometric (bool=true)
	Set all triangles in the same trigonometric order.
double	AverageEdgeLength () const
	Compute the average edge length.
Ia	EdgeLengthRange () 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.
void	EdgeCollapse (int)
	Collapse an edge of the mesh.
Mesh2	SubMesh (const QVector< int > &, const QSet< int > &={}) const
	Create a mesh by removing vertices that are not in the list (and the triangles connected to these vertices).
Mesh2	SubMesh (const Box2 &) const
	Select the sub-mesh by removing all vertices outside the given box.
Mesh2	SubMesh (const ScalarField2 &) const
	Select the sub-mesh by removing all vertices outside the given mask.
Mesh2	SubMesh (const Polygon2 &) const
	Select the sub-mesh by removing all vertices and triangles outside the given polygon.
Mesh2	SubMesh (const Circle2 &) const
	Select the sub-mesh by removing all vertices outside the given circle.

Static Public Member Functions
static Mesh2	Delaunay (const QVector< Vector2 > &)
	Compute the Delaunay triangulation of a set of points.
static Mesh2	Alpha (const QVector< Vector2 > &, const double &)
	Compute the alpha shape 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.

Protected Member Functions
bool	FindEdge (int, int, int &, int=0) const
	Find a half-edge from a vertex to another vertex.

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.

Friends
std::ostream &	operator<< (std::ostream &s, const Mesh2 &mesh)
	Overloaded.

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

Alpha()

Mesh2 Mesh2::Alpha ( const QVector< Vector2 > & points, const double & radius )

static

Compute the alpha shape of a set of points.

The Delaunay triangulation of the points is computed, then the triangles whose circumscribed circle has a radius greater than radius are removed: the larger the radius, the closer the result is to the convex hull of the points, and the smaller the radius, the more the boundary of the shape follows the points. The order of the remaining triangles is not preserved. The mesh is empty if there are less than three points.

Parameters

points	The points.
radius	Maximum radius of the circumscribed circle of the triangles which are kept.

Returns

The mesh made of the triangles of the Delaunay triangulation which pass the radius criterion.

See also

Mesh2::Delaunay

Aspect()

double Mesh2::Aspect

(

)

const

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

Returns

The average aspect ratio, or 0 if the mesh is empty.

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.

AverageEdgeLength()

double Mesh2::AverageEdgeLength

(

)

const

Compute the average edge length.

Returns

The average length, or 0 if the mesh is empty.

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.

In some cases, the triangulation may contain anti-trigonometric order triangles. Therefore the function calls SetTrigonometric(true) to guarantee that all triangles are properly oriented.

Parameters

p	Point set.

Bowyer-Watson algorithm, \( O(n^2) \) complexity.

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 \( O(n^4) \) 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() [1/2]

void Mesh2::EdgeCollapse

(

const double &

epsilon

)

Run a simple edge collapse algorithm over a triangle mesh.

This algorithm runs in \( O(n^2) \) where n denotes the number of triangles in the mesh.

Parameters

epsilon

Threshold length for collapsing an edge.

EdgeCollapse() [2/2]

void Mesh2::EdgeCollapse

(

int

i

)

Collapse an edge of the mesh.

The half-edge i, from the vertex ia to the vertex ib, and the opposite half-edge of the adjacent triangle are collapsed: the two vertexes are replaced by their middle point, and the two triangles which share the edge are removed. The vertex with the smallest index is kept, and the one with the largest index is replaced by the last vertex of the array. Nothing is done if the edge is on the boundary of the mesh, i.e., if there is no opposite half-edge.

Parameters

i	Index of the half-edge.

See also

Mesh2::EdgeCollapse(const double&)

FindEdge()

bool Mesh2::FindEdge ( int a, int b, int & k, int s = 0 ) const

protected

Find a half-edge from a vertex to another vertex.

The half-edge k of a triangle goes from the vertex indices[k] to the vertex indices[NextIndex(k)]. The search starts at the half-edge s and stops at the first half-edge from a to b.

Parameters

a,b	Indexes of the starting and ending vertexes of the half-edge.
k	Index of the half-edge in the array of vertex indexes, set to the end of the array if there is no such half-edge.
s	Index of the first half-edge of the search.

Returns

True if the half-edge has been found.

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

)

Scale a mesh.

Parameters

s	Scaling vector.

SetTrigonometric()

void Mesh2::SetTrigonometric

(

bool

trigo = true

)

Set all triangles in the same trigonometric order.

Parameters

trigo

Trigonometric (counterclockwise) is true, clockwise if false.

Author

Hugo Schott

SubMesh() [1/5]

Mesh2 Mesh2::SubMesh

(

const Box2 &

box

)

const

Select the sub-mesh by removing all vertices outside the given box.

Parameters

box

The box.

Author

Benoit Huftier

SubMesh() [2/5]

Mesh2 Mesh2::SubMesh

(

const Circle2 &

circle

)

const

Select the sub-mesh by removing all vertices outside the given circle.

Parameters

circle

The circle.

Author

Benoit Huftier

SubMesh() [3/5]

Mesh2 Mesh2::SubMesh

(

const Polygon2 &

poly

)

const

Select the sub-mesh by removing all vertices and triangles outside the given polygon.

Parameters

poly	The polygon

Author

Benoit Huftier

SubMesh() [4/5]

Mesh2 Mesh2::SubMesh	(	const QVector< int > &	verticesInd,
		const QSet< int > &	removedTrianglesInd = {} ) const

Create a mesh by removing vertices that are not in the list (and the triangles connected to these vertices).

Parameters

verticesInd	Indexes of the preserved vertexes.
removedTrianglesInd	Extra triangles to remove within the submesh.

Author

Benoit Huftier

SubMesh() [5/5]

Mesh2 Mesh2::SubMesh

(

const ScalarField2 &

mask

)

const

Select the sub-mesh by removing all vertices outside the given mask.

Parameters

mask	The mask, negative values mean that the vertex is not in the mask, positive values inside.

Author

Benoit Huftier

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.

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.

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & s, const Mesh2 & mesh )

friend

Overloaded.

Parameters

s	Stream.
mesh	The mesh.