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Proceedings of CAD'18, 2018, 37-41
Straight Skeletons and Mitered Offsets of Polyhedral Terrains in 3D
Abstract. Offsetting is a fundamental operation both in CAD as well as in several
application areas. In a nutshell, offsetting a plane polygon P by a constant-radius offset with offset distance t requires us to determine all points of the plane that are within distance t from P. The resulting offset curve will contain straight-line segments and circular arcs. A mitered offset is obtained by dropping the offset arcs and extending the offset segments in order to make them meet. For mitered offsets, an offset segment is not at a fixed distance to its source segment but instead to the line supporting the source segment. Nowadays it is generally uncontested that computing an appropriate skeletal data structure as preprocessing constitutes the premier choice for offsetting polygons with regard to both speed and reliability. See, e.g., constant-radius offsets based on Voronoi diagrams and mitered offsets based on straight skeletons. Hence, it seems natural to apply a similar approach to mitered offsetting in 3D and to resort to 3D pendants of straight skeletons.
Keywords. Straight Skeleton, Monotone Surface, Mitered Offset, 3D