Computational geometry

Wikipedia says:

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry.

The main impetus for the development of computational geometry as a discipline was progress in computer graphics and computer-aided design and manufacturing (CAD/CAM), but many problems in computational geometry are classical in nature, and may come from mathematical visualization. Other important applications of computational geometry include robotics (motion planning and visibility problems), ,geographic information systems (GIS) (geometrical location and search, route planning), integrated circuit design (IC geometry design and verification), computer-aided engineering (CAE) (programming of numerically controlled (NC) machines).

The primary goal of research in

combinatorial computational geometryis to develop efficient algorithms and data structures for solving problems stated in terms of basic geometrical objects: points, line segments, polygons, polyhedra.

Here is a list of some problem areas:

- Binary Space Partition
- Convex hull
- Point location
- Quadtree
- Ray Tracing
- Triangulation
- Visibility Graph
- Voronoi Diagram

According to Wikipedia:

Numerical computational geometry. This branch is also known as geometric modelling and computer-aided geometric design (CAGD). Core problems are curve and surface modelling and representation. The most important instruments here are parametric curves and parametric surfaces, such as Bezier curves, spline curves and surfaces. An important non-parametric approach is the level set method.

- Computational Geometry Algorithms Library CGAL

The goal of the CGAL Open Source Project is to provide easy access to efficient and reliable geometric algorithms in the form of a C++ library. CGAL is used in various areas needing geometric computation, such as: computer graphics, scientific visualization, computer aided design and modeling, geographic information systems, molecular biology, medical imaging, robotics and motion planning, mesh generation, numerical methods. There are language bindings to Python.

- Computational geometry, Wikipedia

category: computational methods