Aim of the course
The aim of the course is to introduce the concepts of geometric modeling, the types of geometric models, their representations and methods of solving various problems emerging in the modeling of objects. Emphasis will be placed on IT issues - will address the problems of efficiency of geometric algorithms and implementation aspects.
Recalling the basic issues of computational geometry - area search, location of objects, issues of visibility, the nearest neighborhood, detecting intersections. Concepts of geometric modeling. Possible representations of the models, their effectiveness, conversions between different representations, the impact of the representation of geometric modeling on the accuracy with particular emphasis on means of implementation. Modeling curves, surfaces and solids with different description techniques and processing. Acquisition and processing of spatial data for the three-dimensional reconstruction of physical objects. 3D objects collision detection and handling.
Overview of the course elements
The course includes laboratory classes. Their realization will consolidate the gained theoretical knowledge and enrich them by the methods of effective implementation of object modeling for computer graphics.
1. Geometria obliczeniowa. Algorytmy i zastosowania, M. de Berg, M. van Kreveld, M. Overmars, O. Schwarzkopf , WNT, 2007.
2. Geometria obliczeniowa. Wprowadzenie, F.P. Preparata, M.I. Shamos, Helion, 2003.
3. Podstawy modelowania krzywych i powierzchni. Zastosowanie w grafice komputerowej, Przemysław Kiciak, WNT 2005.
4. Grafika Fizyka Metody Numeryczne, Symulacje fizyczne z wizualizacja˛ 3D, J. Matalewski, T. Dziubak, A. Sylwestrzak, PWN 2010
5. Geometric Folding Algorithms, E. D. Demaine, J. O’Rourke, Cambridge University Press, 2007.