org.apache.commons.math3.geometry.euclidean.twod.hull

## Class MonotoneChain

• java.lang.Object
• org.apache.commons.math3.geometry.euclidean.twod.hull.MonotoneChain
• All Implemented Interfaces:
ConvexHullGenerator2D, ConvexHullGenerator<Euclidean2D,Vector2D>

public class MonotoneChain
extends Object
Implements Andrew's monotone chain method to generate the convex hull of a finite set of points in the two-dimensional euclidean space.

The runtime complexity is O(n log n), with n being the number of input points. If the point set is already sorted (by x-coordinate), the runtime complexity is O(n).

The implementation is not sensitive to collinear points on the hull. The parameter includeCollinearPoints allows to control the behavior with regard to collinear points. If true, all points on the boundary of the hull will be added to the hull vertices, otherwise only the extreme points will be present. By default, collinear points are not added as hull vertices.

The tolerance parameter (default: 1e-10) is used as epsilon criteria to determine identical and collinear points.

Since:
3.3
Andrew's monotone chain algorithm (Wikibooks)
• ### Constructor Summary

Constructors
Constructor and Description
MonotoneChain()
Create a new MonotoneChain instance.
MonotoneChain(boolean includeCollinearPoints)
Create a new MonotoneChain instance.
MonotoneChain(boolean includeCollinearPoints, double tolerance)
Create a new MonotoneChain instance.
• ### Method Summary

Methods
Modifier and Type Method and Description
Collection<Vector2D> findHullVertices(Collection<Vector2D> points)
Find the convex hull vertices from the set of input points.
ConvexHull2D generate(Collection<Vector2D> points)
Builds the convex hull from the set of input points.
double getTolerance()
Get the tolerance below which points are considered identical.
boolean isIncludeCollinearPoints()
Returns if collinear points on the hull will be added as hull vertices.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### MonotoneChain

public MonotoneChain()
Create a new MonotoneChain instance.
• #### MonotoneChain

public MonotoneChain(boolean includeCollinearPoints)
Create a new MonotoneChain instance.
Parameters:
includeCollinearPoints - whether collinear points shall be added as hull vertices
• #### MonotoneChain

public MonotoneChain(boolean includeCollinearPoints,
double tolerance)
Create a new MonotoneChain instance.
Parameters:
includeCollinearPoints - whether collinear points shall be added as hull vertices
tolerance - tolerance below which points are considered identical
• ### Method Detail

• #### findHullVertices

public Collection<Vector2D> findHullVertices(Collection<Vector2D> points)
Find the convex hull vertices from the set of input points.
Parameters:
points - the set of input points
Returns:
the convex hull vertices in CCW winding
• #### getTolerance

public double getTolerance()
Get the tolerance below which points are considered identical.
Returns:
the tolerance below which points are considered identical
• #### isIncludeCollinearPoints

public boolean isIncludeCollinearPoints()
Returns if collinear points on the hull will be added as hull vertices.
Returns:
true if collinear points are added as hull vertices, or false if only extreme points are present.
• #### generate

public ConvexHull2D generate(Collection<Vector2D> points)
throws NullArgumentException,
ConvergenceException
Builds the convex hull from the set of input points.
Specified by:
generate in interface ConvexHullGenerator2D
Specified by:
generate in interface ConvexHullGenerator<Euclidean2D,Vector2D>
Parameters:
points - the set of input points
Returns:
the convex hull
Throws:
NullArgumentException - if the input collection is null
ConvergenceException - if generator fails to generate a convex hull for the given set of input points