Width-bounded geodesic strips for surface tiling

Joe Kahlert, Matt Olson, Hao Zhang

Abstract: We present an algorithm for computing families of geodesic curves over an open mesh patch to partition the patch into strip-like segments. Specifically, the segments can be well approximated using strips obtained by trimming long, rectangular pieces of material having a prescribed width δ. We call this the width-bounded geodesic strip tiling of a curved surface, a problem with practical applications such as the surfacing of curved roofs. The strips are said to be straight since they are constrained to fit within rectangles of width δ, in contrast to arbitrary, possible highly curved, strip segments. The straightness criterion, as well as a bound on strip widths, distinguishes our problem from ones previously studied for developable surface decomposition.