Computational Geometry

What is Computational Geometry? Finding efficient algorithmic solutions for computational problems with a geometric contents.
Applications: graphics, robotics, computer vision, database visualization, geographical information systems, virtual reality, etc.
Examples:
- Robot arm motion: is point x accessible by robot arm R?
- Can robot R move from point a to point b in a given environment (with obstacles)? Robot path planning.
- Motion planning:
  - without collision
  - point/disk/convex robot. General?
  - research problems
- visibility problems: is point A visible from point B (in an environment with obstacles)?
  - simple case: inside a polygon.
  - visibility graph computation. See applet (used in cs2 hwk).
Basic ideas in Computational Geometry.
- Orientation of triangles and area function.
- Convex hull.
- Applet for area, sign of area and convex hull.
- Visibility graphs.
- Polygon triangulation. Art gallery problems.
Student Research Projects.
- Roxana.
- Lilla.
- Ling.