1st Meeting Industrial Geometry Project S09205 “Computational Geometry” Oswin Aichholzer, Franz Aurenhammer, Thomas Hackl, Bernhard Kornberger, Students: Odo Benda, Birgit Vogtenhuber IST & IGI TU-Graz Industrial Geometry

1st Meeting Industrial Geometry Project S09205 „Computational Geometry“ - Introduction 1 Introduction  Computational Geometry:  Algorithms and data structures for elementary geometric questions  Traditionally: basic geometric objects (points, lines … )  Real world applications: advanced geometric primitives (surfaces, location query structures …)  Objectives  Provide algorithmic background for subprojects within the JRP  Develop novel techniques and geometric structures for applications  Utilize existing CG libraries to guarantee robustness and efficiency

1st Meeting Industrial Geometry Project S09205 „Computational Geometry“ - Introduction 2 Activities  5.1: Mesh generation & geometric graphs  5.2: Distances and clustering  5.3: Efficient geometric data structures for quick information retrieval  5.4: Geometric graphs and segmentation  5.5: Advanced geometric representations

1st Meeting Industrial Geometry Project S09205 „Computational Geometry“ - Introduction 3 And now: Real Talks  Computational Geometry - Some Basic Structures Franz Aurenhammer (25 Min.)  Approximating Solids by Balls Bernhard Kornberger (20 Min.)  Approximation Theory and Computational Geometry - New Allies Thomas Hackl (15 Min.)