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. 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) ∗ . ∗ 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. 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

Straight Skeleton Implementations Computational Geometry and - PowerPoint PPT Presentation

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

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Bone s a nd Ske le ta l T issue s The Skeleton What are the components of the skeletal

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Straight Skeleton Implementations Computational Geometry and - PowerPoint PPT Presentation

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

Straight Skeleton Computational Geometry and Geometric Computing Seminar Lavinia Dinu

Computing the Straight Skeleton of an Orthogonal Monotone Polygon in Linear Time G unther Eder,

Approximating a Motorcycle Graph by a Straight Skeleton Stefan Huber Martin Held Universit

CLIC near CERN Tunnel implementations (laser straight) Central MDI &amp; Interaction Region 1

Skeleton and Dual Complex Chenyang Xu Beijing International Center of Mathematics Research

(laser straight) Central MDI &amp; Interaction 1 -Introduction -Feasibility Studies -CDR

The Visibility Skeleton Frdo Durand, George Drettakis, Claude Puech Visibility Skeleton Graph

Hamilton-Jacobi Skeleton and Shock Graphs Peihong Zhu University of Utah Papers:

Skeletons Animated characters are usually built on top of an underlying skeleton The

Skeleton and Skin What is skinning? Skinning is the process of creating association between

Straight Talk, Straight Answers on VECTOR 1:00 2:00 p.m. February 7, 2018 Presented by the

Threshold Implementations Svetla Nikova Threshold Implementations A provably secure

The Skeleton Consists of bones, cartilage, joints, and ligaments Composed of 206 named

Curve-Skeleton Applications Nicu D. Cornea, Deborah Silver, Rutgers University, New Jersey

On Computing Straight Skeletons by Means of Kinetic Triangulations Peter Palfrader Martin Held

Bone s a nd Ske le ta l T issue s The Skeleton What are the components of the skeletal

Optimal shape of sensors or actuators for heat and wave equations with random initial data Yannick

( z , t ) = A cos( kz t + ) Which of these do you prefer for a &quot;le fu moving&quot;

Unique Continuation for Waves, Carleman Estimates, and Applications Arick Shao Queen Mary

Coq LASER 2011 Summerschool Elba Island, Italy Christine Paulin-Mohring Universit Paris Sud

Lecture 12 - GPU Ray Tracing (2) Welcome! , = (, )

The equality of the homogeneous and the Gabor wave front set Patrik Wahlberg Universit` a di

Pluto Scheduling Algorithm By Athanasios Konstantinidis Supervisor Paul H. J. Kelly About Me

C REATE E VENT , CONT . Consecutive edges along a polygon boundary. e x e j e i C REATE E VENT ,

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( z , t ) = A cos( kz t + ) Which of these do you prefer for a "le fu moving"