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## Path Curvature on a Convex Roof

##### Date

2007-12-15##### Author

Ford, Robert

##### Type of Degree

Dissertation##### Department

Mathematics and Statistics##### Metadata

Show full item record##### Abstract

Given a set of rectangles, R1 through Rk, where Ri and Ri+1 share a common
edge and these common edges are congruent and parallel to each other. The resulting
”roof” is part of the surface of a convex body. We’ll consider paths from one corner
of this “roof” to the opposite corner. Extending the common edges to lines we’ll call
ridges and rectangles to planar strips, we can allow such paths to go “off the roof”.
Path curvature is computed for a polygonal path by simple adding up the curvatures
of each intermediate vertex. More general paths use a sequence of polygonal approximations
to compute curvature. We’ll discern when the path of least curvature goes
off the roof or when it is the shortest path.