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Lecturer(s)
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Krauz Lukáš, doc. Ing. Ph.D.
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Pařez Klaus, doc. RNDr. Ph.D.
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Breitfelder Ondřej, Mgr.
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Kovaříková Freya, RNDr. Ph.D.
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Course content
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1. Transformations (coordinates and objects) in E2 and E3 2. Differential geometry of curves - matematical reprezentation, tangent vector, curvature 3. Curves - plane curves, helix 4. Differential geometry of surfaces - matematical reprezentation, tangent plane, curvatures (Gauss curvature) 5.Interpolation - Lagrange polynomial, spline functions. Approximation - method of least squares. 6. Surfaces - classification, problems for surfaces 7. Rotational and helix surfaces - equation, meridian, tangent plane, cuts, common curve 8. Envelope surfaces - characteristic, equation, methods of tanget sphere and plane. 9. Developable surface - classification, development 10. Quadrics - equation, signature, classification, split of common curve
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Learning activities and teaching methods
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Individual study, Lecture, Practicum
- Contact hours
- 39 hours per semester
- Individual project (40)
- 20 hours per semester
- Preparation for an examination (30-60)
- 40 hours per semester
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| prerequisite |
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| Knowledge |
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| General prerequisity is basic knowledge in differential calculus (one and more variables), linear algebra, analytical geometry, and projection methods (content is given by subjects MS1, MS2, and GS1). |
| learning outcomes |
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| Student is able to describe curves and surfaces which are used in mechanical engineering and he/she is able to construct orthogonal projection of this objects and to solve geometric problems on surfaces (tangets, curvatures, cuts, common curve, development). Student uses graphics and computational methods. |
| teaching methods |
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| Lecture |
| Practicum |
| Individual study |
| assessment methods |
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| Combined exam |
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Recommended literature
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Budinský, B. Analytická a diferenciální geometrie. 1. vyd. Praha : SNTL, 1983.
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Ježek, František; Míková, Marta. Maticová algebra a analytická geometrie. 2., přeprac. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7082-996-6.
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Štauberová, Zuzana. Axonometrie, křivky, plochy. 1. vyd. V Plzni : Západočeská univerzita, 2004. ISBN 80-7043-322-1.
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Urban, Alois. Deskriptivní geometrie. II.. Praha : SNTL, 1979.
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Urban, Alois. Deskriptivní geometrie. I.. Praha : SNTL, 1977.
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