Class ConvexHull3D

java.lang.Object

org.episteme.core.mathematics.geometry.ConvexHull3D

public final class ConvexHull3D
extends Object

3D Convex Hull implementation using the Quickhull algorithm.

Time complexity: O(n log n) average case, O(n²) worst case.

The Quickhull algorithm:

1. Find extreme points to form initial tetrahedron
2. Partition remaining points by which face they're "above"
3. Recursively process each face with associated points

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

See Also:

• Quickhull Algorithm

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	ConvexHull3D.Face	Represents a triangular face of the hull.

Method Summary

Modifier and Type	Method	Description
static List<ConvexHull3D.Face>	compute(List<Point3D> points)	Computes the 3D convex hull of a set of points.
static ConvexPolyhedron3D	computePolyhedron(List<Point3D> points)	Creates a ConvexPolyhedron3D from the hull.
static Real	computeSurfaceArea(List<Point3D> points)	Computes the surface area of the convex hull.
static Real	computeVolume(List<Point3D> points)	Computes the volume of the convex hull.
static boolean	contains(List<Point3D> hullPoints, Point3D query)	Checks if a point is inside the convex hull.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

compute

public static List<ConvexHull3D.Face> compute(List<Point3D> points)

Computes the 3D convex hull of a set of points.

Parameters:

points - input points

Returns:

list of triangular faces forming the hull

computePolyhedron

public static ConvexPolyhedron3D computePolyhedron(List<Point3D> points)

Creates a ConvexPolyhedron3D from the hull.

Parameters:

points - the input points

Returns:

a convex polyhedron boundary

computeVolume

public static Real computeVolume(List<Point3D> points)

Computes the volume of the convex hull.

Parameters:

points - the input points

Returns:

the volume

computeSurfaceArea

public static Real computeSurfaceArea(List<Point3D> points)

Computes the surface area of the convex hull.

Parameters:

points - the input points

Returns:

the surface area

contains

public static boolean contains(List<Point3D> hullPoints,
 Point3D query)

Checks if a point is inside the convex hull.

Parameters:

hullPoints - the points that define the hull

query - the point to test

Returns:

true if inside