We study optimization problems for polyhedral terrains in the presence of data imprecision. An imprecise terrain is given by a triangulated point set where the height component of the vertices is speci¯ed by an interval of possible values. We restrict ourselves to terrains with a one-dimensional projection, usually referred to as 1.5-dimensional terrains, where an imprecise terrain is given by an x-monotone polyline, and the y-coordinate of each vertex is not ¯xed but only constrained to a given interval. Motivated mainly by applications in terrain analysis, in this paper we study ¯ve di®erent optimization measures related to obtaining smooth terrains, for the 1.5-dimensional case. In particular, we present exact algorithms to minimize and maximize the average turning angle, as well as to minimize the maximum slope change. Furthermore, we also give approximation algorithms to minimize the largest turning angle and to maximize the smallest turning angle.
|Title of host publication||Abstracts 24th European Workshop on Computational Geometry (EuroCG'08, Nancy, France, March 18-20, 2008)|
|Place of Publication||Vandoeuvre-lès-Nancy|
|Publication status||Published - 2008|