Course Overview – GEAGT232-Ma
Geometric Modelling and its Applications
Computer Science Engineering, MSc, Second Semester
Requirements
Active participation in lectures Implementing and demonstrating the semester projects (a CAD projects) An examination in the exam period
Examination
The examination is basically a written examination. In the hope of better results, there can be an additional oral examination part. The exam paper will contain both theoretical questions and computational tasks. These are selected from the Questions and the Exercises parts of the lecture notes respectively. There are available a large number of sample exam papers, which formats are identical to the exam, and the exam questions and tasks are the subset of them (at least with different constant values in the computational tasks). In the final result of the course the result of the semester projects also will be considered in the ratio of 1 : 2 (project : examination).
Literature
Imre Juhász: Curve and Surface Modeling, lecture notes, 2020.
Imre Piller: Geometric Modeling, lecture notes, 2025.
Hoschek, J., Lasser, D.: Fundamentals of Computer Aided Geometric Design, AK Peters, Wellesley, 1993.
Jean Gallier: Curves and Surfaces in Geometric modelling: Theory and Algorithms, Department of Computer and Information Science, University of Pennsylvania, 2025.
Farin, J. Hoschek, M.-S. Kim: Handbook of Computer Aided Geometric Design, Elsevier, 2002.
PTC Creo Parametric - Primer
Topics and Schedule
| Week | Topic |
| 1 | Curves and their description methods and properties |
| 2 | Interpolation curves: Lagrange, Hermite arc, Overhauser spline, Ferguson spline, parametrization |
| 3 | Bézier curve: de Castaljau-algorithm, Bernstein polynomials, properties of the curve, derivatives, half cutting, continuity |
| 4 | B-spline: normalized B-spline base function, definition, properties, derivatives, linear independence, Definition of the B-spline curve, properties, de Boor algorithm, derivatives, continuity, inserting new point, interpolation |
| 5 | Description of surfaces, modeling systems, line surfaces, Coons-patches (bilinear, bicubic, Hermite patch) |
| 6 | Surfaces as tensor products, derivation, Bézier surfaces (definition and properties), B-spline surfaces (definition and properties) |
| 7 | Solid modeling: wireframe models, volumetric models, cell-based methods, modifiers |
| 8 | Image formats Color spaces, histograms, noise filtering, convolutional filters, edge highlighting and detection, segmentation, thresholding. Overview of Python, Jupyter, OpenCV, matplotlib. Some examples of object detection |
| 9 | Break (Easter) |
| 10 | Calculation of feature vectors, Segmentation problem by using convolutional classifier. Usage of clustering methods. Usage of Artificial Neural Networks |
| 11 | Modeling by using a CAD system |
| 12 | Modeling by using a CAD system |
| 13 | Modeling by using a CAD system |
| 14 | Final consultation and evaluation of the semester projects |
Downloading and installing Creo Parametric