Package org.episteme.core.mathematics.geometry.boundaries

package org.episteme.core.mathematics.geometry.boundaries

Comprehensive boundary and region support for geometric modeling.

This package provides a complete framework for representing spatial boundaries in 2D and 3D, including support for complex territorial shapes with enclaves and exclaves.

Core Interfaces

• Boundary - Base interface for all boundaries
• Boundary2D - 2D boundary interface (polygons)
• Boundary3D - 3D boundary interface (polyhedra)
• BoundingBox - Axis-aligned bounding box interface

2D Boundaries

• ConvexPolygon2D - Convex polygon
• CompositeBoundary2D - Multiple regions with enclaves/exclaves
• FuzzyBoundary2D - Fuzzy membership boundaries
• BoundingBox2D - 2D axis-aligned box

3D Boundaries

• ConvexPolyhedron3D - Convex polyhedron
• CompositeBoundary3D - Multiple volumes with cavities
• BoundingBox3D - 3D axis-aligned box

Special Boundaries

• PointBoundary - Zero-dimensional point

Utilities

• BoundaryConverter - 2D↔3D conversion

Enclave/Exclave Support

The composite boundary classes support complex territorial configurations:

• Exclaves - Multiple disjoint regions belonging to the same entity
• Enclaves - Holes/exclusions within a region
• Third-degree cases - Enclaves within enclaves (counter-enclaves)

Example: Modeling Baarle-Hertog/Baarle-Nassau (Belgium/Netherlands border):

CompositeBoundary2D belgium = new CompositeBoundary2D();
belgium.addInclusion(mainBelgiumTerritory);
belgium.addInclusion(baarleHertogExclave1);

// Dutch enclave within Belgian exclave
CompositeBoundary2D baarleWithEnclave = new CompositeBoundary2D(baarleHertogExclave2);
baarleWithEnclave.addExclusion(dutchCounterEnclave);
belgium.addInclusion(baarleWithEnclave);

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Related Packages

Package	Description
org.episteme.core.mathematics.geometry

Class	Description
Boundary<P>	Base interface for all geometric boundaries.
Boundary2D	Interface for two-dimensional boundaries (regions in a plane).
Boundary3D	Interface for three-dimensional boundaries (volumes).
Boundary3D.Face	Represents a face of the 3D boundary.
BoundaryConverter	Utility class for converting between boundary dimensions.
BoundingBox<P>	Axis-aligned bounding box for any boundary.
BoundingBox2D	Axis-aligned bounding box in 2D.
BoundingBox3D	Axis-aligned bounding box in 3D.
CompositeBoundary<P>	A composite boundary supporting inclusions (exclaves) and exclusions (enclaves).
CompositeBoundary2D	A composite 2D boundary supporting exclaves and enclaves.
CompositeBoundary2D.ContainmentResult	Result of a containment check with detailed status.
CompositeBoundary2D.ContainmentResult.Status
CompositeBoundary3D	A composite 3D boundary supporting exclaves and enclaves.
CompositeBoundary3D.ContainmentResult	Containment result with detailed status.
CompositeBoundary3D.ContainmentResult.Status
ConvexPolygon2D	A convex polygon in 2D space.
ConvexPolyhedron3D	A convex polyhedron in 3D space.
ConvexPolyhedron3D.TriangularFace	Represents a triangular face.
FuzzyBoundary2D	A 2D boundary with fuzzy (graded) membership.
PointBoundary<P>	A zero-dimensional boundary representing a single point.