# 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.
Ileana Streinu