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Lecturer(s)
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Bastl Bohumír, Doc. Ing. Ph.D.
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Course content
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1. Lecture: Applications of geometric modeling. Analytic geometry - Projective extension of homogeneous coordinates. Matrix form for transformation and projection. Exercise: Repeat analytical and differential geometry. 2. Lecture: Differential geometry - Equations of curves, tangent, parameterization, first and second curvature. Frenet formula. Ferguson cubic. Practice: Entering projects. Properties of Ferguson cubic. 3. Lecture: Spline function. Cubic spline curve. Splines of higher degrees. Spline under tension, nonlinear spline. Exercise: Introduction to the use geometric features of mathematical software. 4. Lecture: Bézier curve - Bernstein polynomials, de Casteljau algorithm, a description of spline curves. Exercise: Spline curve. 5. Lecture: B-spline bases, de Boor algorithm, features of B-spline curves. Rational Bezier curves and NURBS (non-uniform rational B-spline). $\beta$ - spline. Exercise: Bezier curves, B-spline. 6. Lecture: Differential geometry - curvature on surfaces. Exercise: Introduction to work with the geometric modeler. 7. Lecture: the tensor product surfaces - spline surfaces and Bézier surfaces. Exercise: NURBS modeling, consultation exercises. 8. Lecture: Coons interpolation - bilinear, bicubic and Ferguson patch, patching. Exercise: Coons patches. 9. Lecture: the tensor product surfaces - B-spline and NURBS surfaces. Exercise: Bezier surfaces and NURBS surfaces 10. Lecture: barycentric coordinates, interpolation on a triangle. Subdivision techniques. Exercise: barycentric calculus, subdivision techniques. 11. Lecture: The geometric model in CAD - edge, surface and volume model. Decomposition, CSG and B-representation. Topological characteristics of solids. Euler characteristics. Exercise: Presentation of student projects. 12. Lecture: Parameterization of the model - parameterization methods, graph algorithms, test for good parameterization, methods of artificial intelligence. Exercise: Presentation of student projects. 13. Lecture: Overview of CA systems, methods of geometric modeling. Basic trends in geometric modeling. Exercise: Presentation of student projects.
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Learning activities and teaching methods
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Project-based instruction, Students' portfolio, Lecture, Practicum
- Contact hours
- 65 hours per semester
- Preparation for an examination (30-60)
- 45 hours per semester
- Team project (50/number of students)
- 30 hours per semester
- Presentation preparation (report in a foreign language) (10-15)
- 20 hours per semester
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| prerequisite |
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| Knowledge |
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| orientovat se v základních pojmech analytické geometrie v rovině a v prostoru, výhodou je také zvládnutí základních vlastností křivek a ploch metodami diferenciální geometrie |
| orientovat se v základních pojmech lineární algebry |
| Skills |
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| používat metody diferenciálního počtu |
| pracovat s maticemi a vektory |
| Competences |
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| N/A |
| learning outcomes |
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| Knowledge |
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| rozumět teoretickým základům reprezentace křivek a ploch v moderních CAx, GIS a dalších graficky orientovaných systémech |
| definovat interpolační spline křivku a umět ji použít |
| definovat Bézierovy, B-spline a NURBS křivky a plochy a umět je použít |
| definovat Coonsovy pláty a spline plochy a umět je použít |
| Skills |
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| umět sestavit geometrický model pro složité jevy v souladu s moderními požadavky CAGD (Computer Aided Geometric Design) |
| používat matematický software pro práci s objekty moderního geometrického modelování, pro tvorbu geometrických modelů a pro odvozování jejich důležitých vlastností |
| připravit referát na odborné téma s problematikou geometrického modelování na základě odborné literatury |
| Competences |
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| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Lecture |
| Lecture supplemented with a discussion |
| Interactive lecture |
| Practicum |
| Project-based instruction |
| Task-based study method |
| Students' portfolio |
| Skills |
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| Practicum |
| Task-based study method |
| Students' portfolio |
| Competences |
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| Practicum |
| Students' portfolio |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Seminar work |
| Individual presentation at a seminar |
| Skills |
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| Seminar work |
| Individual presentation at a seminar |
| Competences |
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| Seminar work |
| Individual presentation at a seminar |
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Recommended literature
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Farin, Gerald; Kim, Myung-Soo; Hoschek, Josef. Handbook of computer aided geometric design. 1st ed. Amsterdam : Elsevier, 2002. ISBN 0-444-51104-0.
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Ježek, František. Geometrické a počítačové modelování. ZČU, 2009.
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