CSC274b
Spring 1998
Ileana Streinu

• Wrap up Convex Hull topic: lower bound for convex hulls. Textbook, Ch. 3.6, page 96.
• 3d Convex hull Java applet. Illustrates all the algorithms we discussed last week.
• Duality. Duality applet from Jim Henle's page. Textbook, Ch. 6.5, page 214.
• Duality properties: dual of dual gets you back to where you started. Preserves incidences (point on line, line through point; line through two points, point of intersection of two lines). [parabola duality] Preserves above/below properties.
• A dictionary of dual terms: Arrangements of lines vs. configurations of points. Upper and lower envelopes vs. convex hulls. Solving a problem for lines by reducing it (via duality) to a problem for points (upper envelope; intersection of half-planes).
• Reading: Textbook, Ch.6.