- What is Computational Geometry? Finding efficient
algorithmic solutions for computational problems with a geometric
- Applications: graphics, robotics, computer vision, database
visualization, geographical information systems, virtual reality,
- 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.