List of combinatorial computational geometry topics enumerates the topics of computational geometry that states problems in terms of geometric objects as discrete entities and hence the methods of their solution are mostly theories and algorithms of combinatorial character.
See List of numerical computational geometry topics for another flavor of computational geometry that deals with geometric objects as continuous entities and applies methods and algorithms of nature characteristic to numerical analysis.
Construction/representation
Extremal shapes
Interaction/Search
- Boolean operations on polygons
- Collision detection
- Line segment intersection
- Point ___location
- Polygon intersection
- Range searching
- Ray shooting
- Closest pair of points
- Closest point problem
- Diameter of a point set
- Delaunay triangulation
- Voronoi diagram
Visibility
- Visibility (geometry)
- Art gallery problem (The museum problem)
- Visibility graph
- Watchman route problem
- Computer graphics applications:
Other
- Ray casting (also known as ray tracing)
- Ham sandwich problem
- shape assembly problems
- shape matching problems
- Klee's measure problem
- Problems on isothetic polygons and isothetic polyhedra
- Path planning
- Polygon containment
- Robust geometric computation addresses two main issues: fixed-precision representation of real numbers in computers and possible geometrical degeneracy (mathematics) of input data