Straight skeletons with additive and multiplicative weights and their application to the algorithmic generation of roofs and terrains

- Additively-weighted straight skeletons based on wavefront propagation.
- Wavefront edges are allowed to start at different points in time.
- Combination of additive and multiplicative weights.
- Automated generation of roofs and terrains.
- Facets have different inclinations and may start at different heights.

We introduce additively-weighted straight skeletons as a new generalization of straight skeletons. An additively-weighted straight skeleton is the result of a wavefront-propagation process where, unlike in previous variants of straight skeletons, wavefront edges do not necessarily begin to move at the start of the propagation process but at later points in time. We analyze the properties of additively-weighted straight skeletons and show how to compute straight skeletons with both additive and multiplicative weights, i.e., where input edges are allowed to move at different speeds and may start at different times.We then show how to use additively-weighted and multiplicatively-weighted straight skeletons to generate roofs and terrains for polygonal shapes such as the footprints of buildings or river networks. As a result, we are able to automatically generate roofs and terrains where the individual facets have different inclinations and may start at different heights.

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