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We introduce additively-weighted straight skeletons as a new generalizationof straight skeletons. An additively-weighted straight skeleton is the resultof a wavefront-propagation process where, unlike in previous variants ofstraight skeletons, wavefront edges do not necessarily start to move at thebegin of the propagation process but at later points in time. We analyze theproperties of additively-weighted straight skeletons and show how to computestraight skeletons with both additive and multiplicative weights.  We then show how to use additively-weighted and multiplicatively-weightedstraight skeletons to generate roofs and terrains for polygonal shapes such asthe footprints of buildings or river networks. As a result, we get an automatedgeneration of roofs and terrains where the individual facets have differentinclinations and may start at different heights.

Straight Skeletons with Additive and Multiplicative Weights and Their Application to the Algorithmic Generation of Roofs and Terrains