#### CSC274b

Spring 1998

Ileana Streinu

#
Lecture 21

#### Monday, April 6, 1998

- 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.

Last modified April 6, 1998.