org.dyn4j.geometry

Class Triangle

java.lang.Object

org.dyn4j.geometry.AbstractShape

org.dyn4j.geometry.Polygon

org.dyn4j.geometry.Triangle

All Implemented Interfaces:

DataContainer, Convex, Rotatable, Shape, Transformable, Translatable, Wound

public class Triangle
extends Polygon
implements Convex, Wound, Shape, Transformable, DataContainer

Implementation of a Triangle Convex Shape.

A Triangle must have one vertex which is not colinear with the other two.

This class is provided to enhance performance of some of the methods contained in the Convex and Shape interfaces.

Since:

1.0.0

Version:

3.2.0

Author:

William Bittle

Constructor Summary

Constructors

Constructor and Description
Triangle(Vector2 point1, Vector2 point2, Vector2 point3) Full constructor.

Method Summary

Modifier and Type	Method and Description
boolean	contains(Vector2 point, Transform transform) Returns true if the point is inside the Triangle.
java.lang.String	toString()

Methods inherited from class org.dyn4j.geometry.Polygon

createAABB, createMass, getAxes, getFarthestFeature, getFarthestPoint, getFoci, getNormalIterator, getNormals, getRadius, getVertexIterator, getVertices, project, rotate, translate

Methods inherited from class org.dyn4j.geometry.AbstractShape

contains, createAABB, getCenter, getId, getRadius, getUserData, hashCode, project, rotate, rotate, rotateAboutCenter, setUserData, translate

Methods inherited from class java.lang.Object

equals, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.dyn4j.geometry.Convex

getAxes, getFarthestFeature, getFarthestPoint, getFoci

Methods inherited from interface org.dyn4j.geometry.Wound

getNormalIterator, getNormals, getVertexIterator, getVertices

Methods inherited from interface org.dyn4j.geometry.Shape

contains, createAABB, createAABB, createMass, getCenter, getId, getRadius, getRadius, project, project, rotateAboutCenter

Constructor Detail

Triangle

public Triangle(Vector2 point1,
                Vector2 point2,
                Vector2 point3)

Full constructor.

Creates a new triangle using the given points. The center will be the area weighted center of the points.

A triangle must have 3 non-null points of which one is not colinear with the other two.

Parameters:

point1 - the first point

point2 - the second point

point3 - the third point

Throws:

java.lang.NullPointerException - if point1, point2, or point3 is null

java.lang.IllegalArgumentException - if point1, point2, and point3 contain coincident points or has clockwise winding

Method Detail

toString

public java.lang.String toString()

Overrides:

toString in class Polygon

contains

public boolean contains(Vector2 point,
                        Transform transform)

Returns true if the point is inside the Triangle.

The equation of a plane is:

N · (P - A) = 0

Where A is any point on the plane.
Create two axes (Vector2s), we will choose V_ab and V_ac.

V_ac = C - A V_ab = B - A

Where A, B, and C are the vertices of the Triangle.
From this we can say that you can get to any point on the plane by going some u distance on V_ac and some v distance on V_ab where A is the origin.

P = A + u * V_ac + v * V_ab

Simplifing P - A

V_pa = u * V_ac + v * V_ab

We still need another equation to solve for u and v:
Dot the equation by V_ac to get

V_pa · V_ac = (u * V_ac + v * V_ab) · V_ac

Dot the equation by V_ab to get the other

V_pa · V_ab = (u * V_ac + v * V_ab) · V_ab

Distribute out both equations

V_pa · V_ac = u * V_ac · V_ac + v * V_ab · V_ac V_pa · V_ab = u * V_ac · V_ab + v * V_ab · V_ab

Solving the first equation for u:

u = (V_pa · V_ac - v * V_ab · V_ac) / (V_ac · V_ac)

Substitute one into the other:

V_pa · V_ab = (V_pa · V_ac - v * V_ab · V_ac) / (V_ac · V_ac) * V_ac · V_ab + v * V_ab · V_ab V_pa · V_ab = (V_pa · V_ac / V_ac · V_ac) * V_ac · V_ab - v * (V_ab · V_ac / V_ac · V_ac) * V_ac · V_ab + v * V_ab · V_ab V_pa · V_ab = (V_pa · V_ac / V_ac · V_ac) * V_ac · V_ab + v * (V_ab · V_ab - (V_ab · V_ac / V_ac · V_ac) * V_ac · V_ab) v = (V_pa · V_ab - (V_pa · V_ac / V_ac · V_ac) * V_ac · V_ab) / (V_ab · V_ab - (V_ab · V_ac / V_ac · V_ac) * V_ac · V_ab)

Which reduces to:

v = ((V_pa · V_ab) * (V_ac · V_ac) - (V_pa · V_ac) * (V_ac · V_ab)) / ((V_ab · V_ab) * (V_ac · V_ac) - (V_ab · V_ac) * (V_ac · V_ab))

Once v is obtained use either equation to obtain u:

u = (v * V_ab · V_ab - V_pa · V_ab) / V_ac · V_ab

We know that the point is inside the Triangle if u and v are greater than zero and u + v is less than one.

Specified by:

contains in interface Shape

Overrides:

contains in class Polygon

Parameters:

point - world space point

transform - Transform the Shape's transform

Returns:

boolean