Lecturers

Description

This activity is intended to provide practical knowledge about important software tools relevant to researchers dealing with geometric problems. It will include lectures as well as practicum.

Contents and organization

Andreas Fabri & Sébastien Loriot – CGAL: The Computational Geometry Algorithms Library, by Example
Requirements: In order to be productive you should have installed the latest release of CGAL, either on Linux or Windows together with its dependencies.
CGAL is an open source project that provides a library of geometric data structures and algorithms. The course consists of three sessions in the morning and programming exercises in the afternoon. In the first 30min session you learn how the CGAL project evolved, how it is organized, how researchers can potentially contribute, what the license is, etc. The second and third 60min session cover two topics in depth, namely:

  1. Polygon Mesh: Processing mesh simplification, remeshing, skeletonization, segmentation, Boolean operations, hole filling, slicing, AABB tree, etc.
  2. Mesh Generation: Surface and tetrahedral volume mesh generation for input coming from voxel data, implicit functions, polyhedral surfaces, Nurbs patches. Periodic mesh generation.

In these sessions we switch between life demos so that you see what the algorithms are about, give the intuition of the underlying theory, and explain the principles of the API. In the afternoon you develop software using CGAL. Ideally you identify a CGAL package that might be helpful in your own research, and you start playing around with it. You most probably start from the examples provided for the CGAL package you are interested in. During this session we look over your shoulder, give hints how to quickly find information in the manuals.

Michael Joswig – Polyhedral Computations with polymake
Requirements: Attendees should bring their laptops. They should read and follow the technical advice at http://page.math.tu-berlin.de/~joswig/software/polymake/DCCG2018/index.html
We will start with an introduction to computations in high-dimensional polyhedral geometry, with applications to, e.g., optimization and tropical geometry. Then we will review several algorithms for computing convex hulls and survey their advantages and disadvantages by analyzing explicit examples. The course will end with some reports about the current frontiers of polyhedral computation.

Zoltán Kovács – Modeling computational geometry with GeoGebra
Requirements: Attendees should bring their laptops.
We will learn about methods in GeoGebra to visualize experiments in computational geometry. We will focus on creating basic and more advanced applets, connect them with datasets, control the details via JavaScript programming, and publish the results as a dynamic web applet. The planned topics include visualizing well-known static problems (like presentation of a Voronoi diagram, Delaunay triangulation or a minimum spanning tree), tesselations, parametric curves and surfaces. We will discuss some connections between parametric and implicit curves related to modeling planar linkages and automated reasoning by using fast elimination from recent algebraic geometry methods. The goal of the course is to get an overview of the possible techniques on doing own research experiments with GeoGebra. We will also learn how the obtained results can be communicated by publishing them as a dynamic web page.

Room

All scientific activities will take place in the Auditorium.

Material

You will find here slides and links provided by the lecturers for this course.

Program

Monday, April 30

  • Registration

  • Welcome

  • CGAL: The Computational Geometry Algorithms Library, by Example

    Andreas Fabri Andreas Fabri

  • Coffee break

  • CGAL: The Computational Geometry Algorithms Library, by Example

    Andreas Fabri Andreas Fabri

  • Lunch time

  • CGAL: The Computational Geometry Algorithms Library, by Example

    Andreas Fabri Andreas Fabri

Tue, May 1

Wednesday, May 2

  • Modeling computational geometry with GeoGebra

    Zoltán Kovács Zoltán Kovács

  • Group photo

  • Coffee break

  • Modeling computational geometry with GeoGebra

    Zoltán Kovács Zoltán Kovács

  • Lunch time

  • Working & interacting

Thursday, May 3

  • Polyhedral Computations with polymake

    Michael Joswig Michael Joswig

  • Coffee break

  • Polyhedral Computations with polymake

    Michael Joswig Michael Joswig

  • Lunch time

  • Polyhedral Computations with polymake

    Michael Joswig Michael Joswig

Friday, May 4

  • Modeling computational geometry with GeoGebra

    Zoltán Kovács Zoltán Kovács

  • Coffee break

  • Modeling computational geometry with GeoGebra

    Zoltán Kovács Zoltán Kovács

  • Lunch time

  • Working & interacting

Group picture