Triangulation

java.lang.Object
- Jcg.triangulations2D.Triangulation_2

Direct Known Subclasses:

Delaunay_2
```
public class Triangulation_2
extends java.lang.Object
```
Incremental Triangulation using Face/Vertex data structure (TriangulationDS_2).

Author:

Java-code by Luca Castelli-Aleardi and Steve Oudot

Constructor Summary

Constructors
Constructor and Description
`Triangulation_2()` Constuctor: builds an empty triangulation.
`Triangulation_2(Point_2 a, Point_2 b, Point_2 c)` Constuctor: builds a triangulation consisting of a triangle.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`java.util.Collection<HalfedgeHandle<Point_2>>`	`convexHullEdges()` Computes and returns the collection of all edges on the convex hull (collects only one HalfedgeHandle per geometric edge).
`java.util.Collection<HalfedgeHandle<Point_2>>`	`finiteEdges()` Computes and returns the collection of all finite edges in the triangulation (that is, all edges connecting vertices in the interior of the bounding box).
`java.util.Collection<TriangulationDSFace_2<Point_2>>`	`finiteFaces()` Computes and returns the collection of all finite faces of the triangulation (that is, faces lying in the interior of the bounding box).
`java.util.Collection<TriangulationDSVertex_2<Point_2>>`	`finiteVertices()` Computes and returns the collection of all finite vertices of the triangulation (that is, vertices lying in the interior of the bounding box).
`TriangulationDSVertex_2<Point_2>`	`insert(Point_2 p)` Inserts point p in the triangulation and returns the newly created vertex
`boolean`	`isInfinite(HalfedgeHandle<Point_2> e)` Returns true if Edge e is infinite, i.e.
`boolean`	`isInfinite(Point_2 p)` Returns true if Point p is infinite, i.e.
`boolean`	`isInfinite(TriangulationDSFace_2<Point_2> f)` Returns true if Face f is infinite, i.e.
`boolean`	`isInfinite(TriangulationDSVertex_2<Point_2> v)` Returns true if Vertex v is infinite, i.e.
`boolean`	`isValid()` checks the combinatorial validity of the triangulation.
`TriangulationDSFace_2<Point_2>`	`locate(Point_2 p)` Locates point p in the triangulation and returns a triangle containing p.
`java.lang.String`	`toString()`

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

- Constructor Detail
  - Triangulation_2
```
public Triangulation_2()
```
    Constuctor: builds an empty triangulation.
  - Triangulation_2
```
public Triangulation_2(Point_2 a,
                       Point_2 b,
                       Point_2 c)
```
    Constuctor: builds a triangulation consisting of a triangle.
- Method Detail
  - locate
```
public TriangulationDSFace_2<Point_2> locate(Point_2 p)
```
    Locates point p in the triangulation and returns a triangle containing p.
    
    Parameters:
    
    p - the point to locate
    
    Returns:
    
    one of the triangles containing p
  - insert
```
public TriangulationDSVertex_2<Point_2> insert(Point_2 p)
```
    Inserts point p in the triangulation and returns the newly created vertex
    
    Parameters:
    
    p - the point to insert
  - isInfinite
```
public boolean isInfinite(Point_2 p)
```
    Returns true if Point p is infinite, i.e. if it is a vertex of the bounding box
  - isInfinite
```
public boolean isInfinite(TriangulationDSVertex_2<Point_2> v)
```
    Returns true if Vertex v is infinite, i.e. if it is a vertex of the bounding box
  - isInfinite
```
public boolean isInfinite(TriangulationDSFace_2<Point_2> f)
```
    Returns true if Face f is infinite, i.e. if it is connected to a vertex of the bounding box.
  - isInfinite
```
public boolean isInfinite(HalfedgeHandle<Point_2> e)
```
    Returns true if Edge e is infinite, i.e. if it is connected to a vertex of the bounding box.
  - finiteVertices
```
public java.util.Collection<TriangulationDSVertex_2<Point_2>> finiteVertices()
```
    Computes and returns the collection of all finite vertices of the triangulation (that is, vertices lying in the interior of the bounding box).
  - finiteFaces
```
public java.util.Collection<TriangulationDSFace_2<Point_2>> finiteFaces()
```
    Computes and returns the collection of all finite faces of the triangulation (that is, faces lying in the interior of the bounding box).
  - finiteEdges
```
public java.util.Collection<HalfedgeHandle<Point_2>> finiteEdges()
```
    Computes and returns the collection of all finite edges in the triangulation (that is, all edges connecting vertices in the interior of the bounding box).
  - convexHullEdges
```
public java.util.Collection<HalfedgeHandle<Point_2>> convexHullEdges()
```
    Computes and returns the collection of all edges on the convex hull (collects only one HalfedgeHandle per geometric edge).
  - isValid
```
public boolean isValid()
```
    checks the combinatorial validity of the triangulation.
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

Class Triangulation_2

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

Triangulation_2

Triangulation_2

Method Detail

locate

insert

isInfinite

isInfinite

isInfinite

isInfinite

finiteVertices

finiteFaces

finiteEdges

convexHullEdges

isValid

toString