Polyhedron

java.lang.Object
- Jcg.polyhedron.Polyhedron_3<X>

```
public class Polyhedron_3<X extends Point_>
extends java.lang.Object
```
Half-Edge data structure for polyhedral meshes (allowing to represent planar and surface orientable meshes)

Author:

Code by Luca Castelli Aleardi (Ecole Polytechnique, INF562, INF555, 2010-2016)

See Also:

for the Manipulation of an orientable surface

Field Summary

Fields
Modifier and Type Field and Description

java.util.ArrayList<Face<X>> facets

java.util.ArrayList<Halfedge<X>> halfedges

java.util.ArrayList<Vertex<X>> vertices

Fields
Modifier and Type	Field and Description
`java.util.ArrayList<Face<X>>`	`facets`
`java.util.ArrayList<Halfedge<X>>`	`halfedges`
`java.util.ArrayList<Vertex<X>>`	`vertices`

Constructor Summary

Constructors
Constructor and Description

Polyhedron_3()

Polyhedron_3(int n, int e, int f)

Constructors
Constructor and Description
`Polyhedron_3()`
`Polyhedron_3(int n, int e, int f)`

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`Halfedge<X>`	`addTriangleToBorder(Halfedge h, X point)` creates a new triangle facet within the hole incident to h by connecting the tip of h with two new halfedges and a new vertex.
`void`	`createCenterVertex(Face<X> f)` Split a face by inserting a new vertex
`void`	`DecorateVertices()`
`java.lang.String`	`edgesToString()` Return a string representing the list of faces
`void`	`eraseCenterVertex(Vertex<X> v)` replace the star of a vertex v by a new face
`java.lang.String`	`facesToString()` Return a string representing the list of faces
`Halfedge<X>`	`fillHole(Halfedge h)`
`void`	`flipEdge(Halfedge<X> e)` Perform the flip of an edge
`int`	`genus()` Return the genus of the mesh (given by Euler formula) Warning: works only for meshes with one connected component
`boolean`	`isClosed()` returns true if there are no border edges
`boolean`	`isPureBivalent()` returns true if all vertices have exactly two incident edges
`boolean`	`isPureQuad()` true iff the every face is a quadrangle
`boolean`	`isPureTriangle()` true iff the every face is a triangle
`boolean`	`isPureTrivalent()` returns true if all vertices have exactly three incident edges
`boolean`	`isTriangle(Halfedge<X> h)` true iff the connected component denoted by h is a triangle
`boolean`	`isValid(boolean borders)` returns true if the polyhedral surface is combinatorially consistent.
`Halfedge<X>`	`makeHole(Halfedge<X> h)`
`Halfedge<X>`	`makeTriangle(X p1, X p2, X p3)` a triangle with border edges is added to the polyhedral surface.
`int`	`numberOfBoundaries()` Compute and return the number of boundaries
`int`	`sizeOfFacets()`
`int`	`sizeOfHalfedges()`
`int`	`sizeOfVertices()`
`Halfedge<X>`	`splitEdge(Halfedge<X> h, X point)` splits the edge inserting a new vertex, with coordinates given by point.
`Halfedge<X>`	`splitFacet(Halfedge<X> h, Halfedge<X> g)` splits the facet incident to h and g into two facets with a new diagonal between the two vertices denoted by h and g respectively.
`int`	`vertexDegree(Vertex<X> v)` compute the degree of a vertex
`java.lang.String`	`verticesToString()` Return a string representing the list of vertices

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - vertices
```
public java.util.ArrayList<Vertex<X extends Point_>> vertices
```
  - facets
```
public java.util.ArrayList<Face<X extends Point_>> facets
```
  - halfedges
```
public java.util.ArrayList<Halfedge<X extends Point_>> halfedges
```
- Constructor Detail
  - Polyhedron_3
```
public Polyhedron_3()
```
  - Polyhedron_3
```
public Polyhedron_3(int n,
                    int e,
                    int f)
```
- Method Detail
  - DecorateVertices
```
public void DecorateVertices()
```
  - sizeOfVertices
```
public int sizeOfVertices()
```
  - sizeOfFacets
```
public int sizeOfFacets()
```
  - sizeOfHalfedges
```
public int sizeOfHalfedges()
```
  - vertexDegree
```
public int vertexDegree(Vertex<X> v)
```
    compute the degree of a vertex
  - isClosed
```
public boolean isClosed()
```
    returns true if there are no border edges
  - isPureBivalent
```
public boolean isPureBivalent()
```
    returns true if all vertices have exactly two incident edges
  - isPureTrivalent
```
public boolean isPureTrivalent()
```
    returns true if all vertices have exactly three incident edges
  - isPureTriangle
```
public boolean isPureTriangle()
```
    true iff the every face is a triangle
  - isPureQuad
```
public boolean isPureQuad()
```
    true iff the every face is a quadrangle
  - isTriangle
```
public boolean isTriangle(Halfedge<X> h)
```
    true iff the connected component denoted by h is a triangle
  - genus
```
public int genus()
```
    Return the genus of the mesh (given by Euler formula) Warning: works only for meshes with one connected component
  - numberOfBoundaries
```
public int numberOfBoundaries()
```
    Compute and return the number of boundaries
  - isValid
```
public boolean isValid(boolean borders)
```
    returns true if the polyhedral surface is combinatorially consistent. If borders==true normalization of the border edges is checked too. This method checks that each facet is at least a triangle and that the two incident facets of a non-border edge are distinct.
  - flipEdge
```
public void flipEdge(Halfedge<X> e)
```
    Perform the flip of an edge
  - createCenterVertex
```
public void createCenterVertex(Face<X> f)
```
    Split a face by inserting a new vertex
  - eraseCenterVertex
```
public void eraseCenterVertex(Vertex<X> v)
```
    replace the star of a vertex v by a new face
  - makeHole
```
public Halfedge<X> makeHole(Halfedge<X> h)
```
  - fillHole
```
public Halfedge<X> fillHole(Halfedge h)
```
  - addTriangleToBorder
```
public Halfedge<X> addTriangleToBorder(Halfedge h,
                                       X point)
```
    creates a new triangle facet within the hole incident to h by connecting the tip of h with two new halfedges and a new vertex. Returns the halfedge of the new edge that is incident to the new facet and the new vertex.
  - makeTriangle
```
public Halfedge<X> makeTriangle(X p1,
                                X p2,
                                X p3)
```
    a triangle with border edges is added to the polyhedral surface. Returns a non-border halfedge of the triangle.
  - splitFacet
```
public Halfedge<X> splitFacet(Halfedge<X> h,
                              Halfedge<X> g)
```
    splits the facet incident to h and g into two facets with a new diagonal between the two vertices denoted by h and g respectively. Returns h->next() after the operation, i.e., the new diagonal. The new face is to the right of the new diagonal, the old face is to the left. The time is proportional to the distance from h to g around the facet.
  - splitEdge
```
public Halfedge<X> splitEdge(Halfedge<X> h,
                             X point)
```
    splits the edge inserting a new vertex, with coordinates given by point.
  - verticesToString
```
public java.lang.String verticesToString()
```
    Return a string representing the list of vertices
  - facesToString
```
public java.lang.String facesToString()
```
    Return a string representing the list of faces
  - edgesToString
```
public java.lang.String edgesToString()
```
    Return a string representing the list of faces

Class Polyhedron_3<X extends Point_>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

vertices

facets

halfedges

Constructor Detail

Polyhedron_3

Polyhedron_3

Method Detail

DecorateVertices

sizeOfVertices

sizeOfFacets

sizeOfHalfedges

vertexDegree

isClosed

isPureBivalent

isPureTrivalent

isPureTriangle

isPureQuad

isTriangle

genus

numberOfBoundaries

isValid

flipEdge

createCenterVertex

eraseCenterVertex

makeHole

fillHole

addTriangleToBorder

makeTriangle

splitFacet

splitEdge

verticesToString

facesToString

edgesToString