Straight Skeleton Implementations Computational Geometry and - PowerPoint PPT Presentation

UNIVERSITY OF SALZBURG Straight Skeleton Implementations Computational Geometry and Applications Lab based on Exact Arithmetic Günther Eder, Martin Held, and Peter Palfrader Online Conference, March 2020

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. edge events r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. edge events r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the split event vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation, Roof modeling Straight Skeleton Implementations – Peter Palfrader 2/10

Straight Skeleton UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Defined as a result of a wavefront propagation . r The Straight Skeleton is the trace of the vertices of the wavefront over time. r Edge Events, Split Events. r Applications: Tool path generation, Roof modeling, Origami. ✂ Straight Skeleton Implementations – Peter Palfrader 2/10

Algorithms UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab Best worst-case complexity: r Eppstein and Erickson (1998) and Cheng et al. (2016). With implementations: r Cacciola (2004), based on Felkel and Obdržálek (1998). r Aichholzer and Aurenhammer (1998) ∗ . r For monotone polygons: Biedl et al. (2015) ∗ . Straight Skeleton Implementations – Peter Palfrader 3/10

Algorithms UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab Best worst-case complexity: r Eppstein and Erickson (1998) and Cheng et al. (2016). With implementations: r Cacciola (2004), based on Felkel and Obdržálek (1998). r Aichholzer and Aurenhammer (1998) ∗ . r For monotone polygons: Biedl et al. (2015) ∗ . Straight Skeleton Implementations – Peter Palfrader 3/10

Algorithms UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab Best worst-case complexity: r Eppstein and Erickson (1998) and Cheng et al. (2016). With implementations: r Cacciola (2004), based on Felkel and Obdržálek (1998). r Aichholzer and Aurenhammer (1998) ∗ . r For monotone polygons: Biedl et al. (2015) ∗ . ∗ New implementation! Straight Skeleton Implementations – Peter Palfrader 3/10

Algorithms UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab Best worst-case complexity: r Eppstein and Erickson (1998) and Cheng et al. (2016). With implementations: r Cacciola (2004), based on Felkel and Obdržálek (1998). r Aichholzer and Aurenhammer (1998) ∗ . r For monotone polygons: Biedl et al. (2015) ∗ . ∗ New implementation! Straight Skeleton Implementations – Peter Palfrader 3/10

Cacciola UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Part of CGAL . r Input: polygons and polygons with holes. r Priority queue of edge events and all potential split events. r There are quadratic many such potential split events. Straight Skeleton Implementations – Peter Palfrader 4/10

Cacciola UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Part of CGAL . r Input: polygons and polygons with holes. r Priority queue of edge events and all potential split events. r There are quadratic many such potential split events. Straight Skeleton Implementations – Peter Palfrader 4/10

Cacciola UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Part of CGAL . r Input: polygons and polygons with holes. r Priority queue of edge events and all potential split events. r There are quadratic many such potential split events. edge events Straight Skeleton Implementations – Peter Palfrader 4/10

Cacciola UNIVERSITY OF SALZBURG Computational Geometry and Applications Lab r Part of CGAL . r Input: polygons and polygons with holes. r Priority queue of edge events and all potential split events. r There are quadratic many such potential split events. split event edge events Straight Skeleton Implementations – Peter Palfrader 4/10