A universal predictor-corrector type incremental algorithm for the construction of weighted straight skeletons based on the notion of deforming polygon

TL;DR

This paper introduces a novel predictor-corrector incremental algorithm for constructing weighted straight skeletons of 2D polygons, eliminating the need for complex auxiliary structures and enabling interactive, exact results.

Contribution

It presents the first predictor-corrector approach for weighted straight skeletons that directly uses polygon input, avoiding kinetic triangulation and motorcycle graphs.

Findings

Successfully constructed roof topologies from various complex floor plans.

The algorithm operates interactively, allowing real-time modifications.

Developed a C++ graphical tool for building and testing the algorithm.

Abstract

A new predictor-corrector type incremental algorithm is proposed for the exact construction of weighted straight skeletons of 2D general planar polygons of arbitrary complexity based on the notion of deforming polygon. In the proposed algorithm, the raw input provided by the polygon itself is enough to resolve edge collapse and edge split events. Neither the construction of a kinetic triangulation nor the computation of a motorcycle graph is required. Due to its incremental nature, there is always a room in the algorithm for the interactive construction of the straight skeleton. The proposed algorithm is of predictor-corrector type. In the algorithm, the edge collapse and edge split events are tackled by a completely different novel original approach which is first of its kind. In the predictor step, the position of the vertices is advanced in time by direct integration assuming no event. Then predicted positions are corrected by using linear interpolation if there are edge collapse or edge split events within the same increment. In the algorithm edge collapse and edge split events are detected by, respectively, edge swap and edge penetration. The proposed algorithm has been used to construct roof topology starting from a floor plan of various complexity ranging from simple convex to highly nonconvex with holes. In order to construct, improve and test the building blocks of the underlying algorithm, a graphical user interface, Straight Skeleton Development Kit, has also been developed in parallel by the author using C++ programming language.