Open Collections

Brown, Dylan

University of British Columbia

We introduce a new definition of center for a simple polygon P called the attention center, which is the point c inside P that minimizes the maximum geodesic distance from any p ∈ P to the visibility region of c. We survey various definitions of center which use geodesically convex distance metrics on simple polygons and their algorithms. We show attention distance is not geodesically convex but instead geodesically quasiconvex, a concept mostly seen to this point in the study of Riemannian manifolds, and present an algorithm which calculates the attention center of a simple polygon with n vertices to within error ε in O(n² log n/ε) time.

Text

2024-07-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/88711

Computer Science

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/