Weighted skeletal structures for computing variable-radius offsets

Held et al. [CAD&A 2016] introduced generalized weighted Voronoi diagrams as a tool to construct variable-radius offsets. We revisit this structure and provide two algorithms to compute it. We also introduce variable-radius skeletons of polygons as a closely related structure which inherits most properties of generalized weighted Voronoi diagrams except that its skeletal regions are always connected. Experimental results obtained by our implementation of variable-radius skeletons are discussed. In addition to variable-radius offsets we demonstrate how this structure can be used to generate intricate roofs for polygonal footprints of buildings in an automated way. © 2021 CAD Solutions, LLC.