[IPGeo] - [2024Winter] - [en] - [Practical Geometry]


Practical Geometry [2024 SoSe]
Code
IPGeo
Name
Practical Geometry
CP
4
Duration
one semester
Offered
irregularly
Format
Lecture 2 SWS + Exercise course 1 SWS
Workload
120h, thereof
45 h lecture
60 h self-study and working on assignments
15h preparation for exam
Availability
M.Sc. Angewandte Informatik
M.Sc. Data and Computer Science
M.Sc. Scientific Computing
Language
English
Lecturer(s)
Susanne Krömker
Examination scheme
Learning objectives Understanding of basic geometric concepts for data analysis as well as efficient point search and further processing of measurement data
Confident handling of projections and descriptions beyond the three-dimensional world of experience
Calculation of geometric invariants, distances, curvatures from measurement data, reconstructed and generated surfaces
Learning content Basic areas of geometry with relevance in computer graphics, image processing, pattern recognition, computer vision and geometric modeling.
(i) Analytic geometry: operations on vector spaces with appropriate coordinates and mappings (affine mappings, collinearities), geometric fitting of point clouds to linear structures or planes from error-prone measurement data
(ii) Projective geometry: central projection and inverse reconstruction of 3D objects from planar images (computer vision, geodesy), differences between B-spline curves and surfaces and the class of NURBS, freeform geometries in CAD systems
(iii) Differential geometry: parameter representations in geometric data processing, implicit representations (level sets), estimation of invariants from discrete data (triangulations, point clouds).
Requirements for participation recommended are: linear algebra, computational geometry and any programming language (e.g. C/C++/Pascal/python)
Requirements for the assignment of credits and final grade The module is completed with a graded oral examination. The final grade of the module is determined by the grade of the examination. The requirements for the assignment of credits follows the regulations in section modalities for examinations.
Useful literature Geometrie für Informatiker, Script TU Vienna 2004, Helmut Pottmann, current publications