ICS 266, Spring 1996, Homework Set 1

Due Tuesday, April 16, in class

Plücker coordinates.
Find formulas in Plücker coordinates (for lines in 3-dimensional space) that test
- Whether two given lines meet at a point
- Whether two given lines are parallel
Projective duality.
Write down the projective duals to the following problem statements.
(Do not solve the problems.)
- Find the two points where a given line crosses a given convex polygon.
- Determine whether some line passes through all of a set of (non-vertical) line segments.
- Find the point in 4-dimensional space where some pair of (2-dimensional) planes crosses.
Möbius transformations.
Find a fractional linear transformation of complex numbers,
f(z)=(az+b)/(cz+d), for which f(0)=1, f(1)=i, and f(i)=0.