List of combinatorial computational geometry topics
From Wikipedia, the free encyclopedia
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.
Contents |
[edit] Construction/representation
- Convex hull
- Happy end problem
- Hyperplane arrangement
- Polygon decomposition
- Polygon triangulation
- Minimal convex decomposition
- Minimal convex cover problem (NP-hard)
- Minimal rectangular decomposition
- Tessellation problems
- Polygon triangulation
- Shape dissection problems
- Smallest bounding sphere (smallest bounding circle)
- Stabbing line problem
- Triangulation
- Voronoi diagram
[edit] Interaction/Search
- Boolean operations on polygons
- Collision detection
- Line segment intersection
- Point location
- Polygon intersection
- Range searching
- Orthogonal range searching
- Simplex range searching
- Ray shooting
[edit] Distances
- Closest pair of points
- Closest point problem
- Diameter of a point set
[edit] Visibility
- Visibility (geometry)
- Art gallery problem (The museum problem)
- Visibility graph
- Watchman route problem
- Computer graphics applications:
[edit] 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
- Paths among obstacles
- Shortest path in a polygon
- Polygon containment
- Robust geometric computation addresses two main isssues: fixed-precision representation of real numbers in computers and possible geometrical degeneracy (mathematics) of input data
