Examples and Tutorials

Explore practical implementations of geometric algorithms through detailed, step-by-step examples.

📐 Basic Geometry

Fundamental operations such as constructing closed polygons, computing plane normals, and verifying coplanarity.

• Generate closed polygons from unordered point sets

• Compute plane normals from 3D coplanar points

• Verify coplanarity of 3D point sets

📍 Point Queries

Techniques for determining spatial relationships between points and other primitives (lines, polygons, polyhedra).

• Determine point-line coincidence (2D/3D)

• Test point-in-polygon containment (2D/3D)

• Check point-in-polyhedron containment

📏 Line & Surface Queries

Intersection detection and distance computations between lines, polygons, and polyhedra.

• Compute minimum distance between two 3D line primitives

• Detect line-line intersections (2D/3D)

• Determine line-polygon intersections (2D/3D)

• Identify line-polyhedron intersections.

📦 Oriented Bounding Containers

Compute oriented bounding boxes and rectangles, useful for collision detection and spatial queries.

• Generate oriented bounding boxes (PCA-aligned and minimum-volume)

🧹 Point Filtering

Filter points based on containment within geometric boundaries.

• Filter 2D points by polygon containment

• Filter 3D points by polyhedron containment

📷 Pinhole Camera

Project 3D world coordinates to 2D image planes.

• Project 3D points to 2D camera coordinates.

🧱 Rasterisation Toolkit

Convert continuous geometric shapes into discrete grid representations.

• Rasterization data structures

• Rasterize lines via Bresenham's algorithm (2D/3D)

• Rasterize polygon (2D/3D)

• Rasterize polyhedron surfaces

🧭 Path Planning

Implement and optimize 3D Jump Point Search (JPS) algorithms for large-scale environments.

• JPS environment models

• High-precision JPS with CGAL-AABB

• Voxel-accelerated JPS