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

TL;DR

This paper introduces additively-weighted straight skeletons, a new variant that allows for more flexible wavefront propagation, and demonstrates their application in automatically generating complex roofs and terrains with varied inclinations.

Contribution

The paper presents the first analysis and computation methods for additively-weighted straight skeletons, extending existing models to include both additive and multiplicative weights for practical terrain and roof generation.

Findings

Additively-weighted straight skeletons enable flexible wavefront propagation.

Combined additive and multiplicative weights facilitate complex shape modeling.

Application to generate roofs and terrains with varied inclinations and heights.

Abstract

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 start to move at the begin 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. 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 get an automated generation of roofs and terrains where the individual facets have different inclinations and may start at different heights.