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Proceedings of CAD'15, 2015, 264-268
Variable Offsetting of Polygonal Structures Using Skeletons
Abstract. Offsetting is an important task in diverse applications in the manufacturing business. For a set C in the plane, the constant-radius offset with offset distance r is the set of all points of the plane whose minimum distance from C is exactly r. (We are interested in the Euclidean distance.) Formally, this offset curve can be defined as the boundary of the set ⋃_(p∈C) B(p,r), where B(p,r) denotes a disk with radius r centered at the point p. That is, the offset is the envelope of a set of disks of equal radius that have their centers along the input. Mathematically, the same offset curve can also be obtained as the Minkowski sum of C with a disk with radius r centered at the origin. For polygons such an offset curve will consist of one or more closed curves made up of line segments and circular arcs. Held describes how to use a Voronoi diagram, which is a versatile tool in computational geometry, to compute such an offset efficiently and reliably. Mitered offsets differ from constant-radius offsets in the handling of non-convex vertices of an input polygon: Instead of adding circular arcs to the offset curve, the offset segments of the two edges incident to a non-convex vertex get extended until they intersect. This type of offset can be generated in linear time from a straight skeleton. In order to avoid very sharp corners in the offset, the linear axis can be used in place of the straight skeleton, thus obtaining offsets with multi-segment bevels.
Keywords. Voronoi diagram, Variable-radius offset