| Course Unit Code | 230-0442/01 |
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| Number of ECTS Credits Allocated | 5 ECTS credits |
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| Type of Course Unit * | Optional |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | Third Year |
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| Semester when the Course Unit is delivered | Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| DLO44 | Mgr. Dagmar Dlouhá, Ph.D. |
| Summary |
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The course combines geometric and computer disciplines - planimetry, stereometry, analytic geometry, 3D modeling, computer graphics and programming.
In the exercise there is used free software GeoGebra and POV-Ray. |
| Learning Outcomes of the Course Unit |
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• to solve planimetric and stereometric tasks with the help of computer
• to know how to characterize geometric curves and surfaces by synthetic and also analytic way
• to acquaint with geometric and physical principles of 3D modeling |
| Course Contents |
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Program of lectures
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Week Lecture content
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1 Basic geometric objects (point, line, plane), concepts and constructions
2 Planimetry - properties of triangles, construction of basic triangles (height, center of gravity, angles)
3 Planimetry - construction of triangles advanced, uniformity (tangent of two circles, triangle inscribed in squares)
4 Conic sections - derivation from a rotational conical surface, definition and construction of an ellipse
5 Conics - definition and construction of a hyperbola
6 Conic sections - definition and construction of a dish
7 Kinematic geometry - elliptic and cardioid motion, conchoidal and cyclic movements
8 Stereometry - cube sections, slices of other bodies
9 Modeling and 3D Printing - Introduction to 3D Modeling and 3D Printing (Technology, Materials)
10 Modeling and 3D Printing - Basic Bodies (Spheres, Cylinders, Cones, Blocks)
11 Modeling and 3D Printing - Transform (Shift, Rotate, Scale)
12 Modeling and 3D Printing - Set Operations (Unification, Intersection, Difference)
13 Modeling and 3D Printing - Visual Programming (Mathematical Functions, Cycles)
14 Reserve
Exercise and seminar program + individual student work
================================================== ======
Week Content of seminars and seminars
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1 Basic geometric objects (point, line, plane), concepts and constructions
2 Planimetry - properties of triangles, construction of basic triangles (height, center of gravity, angles)
3 Planimetry - construction of triangles advanced, uniformity (tangent of two circles, triangle inscribed in squares)
4 Conic sections - derivation from a rotational conical surface, definition and construction of an ellipse
5 Conics - definition and construction of a hyperbola
6 Conic sections - definition and construction of a dish
7 Kinematic geometry - elliptic and cardioid motion, conchoidal and cyclic movements
8 Stereometry - cube sections, slices of other bodies
9 Modeling and 3D Printing - Introduction to 3D Modeling and 3D Printing (Technology, Materials)
10 Modeling and 3D Printing - Basic Bodies (Spheres, Cylinders, Cones, Blocks)
11 Modeling and 3D Printing - Transform (Shift, Rotate, Scale)
12 Modeling and 3D Printing - Set Operations (Unification, Intersection, Difference)
13 Modeling and 3D Printing - Visual Programming (Mathematical Functions, Cycles)
14 Reserve |
| Recommended or Required Reading |
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| Required Reading: |
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Černý, J.: Geometry. Praha: Vydavatelství ČVUT, 1996. ISBN 80-01-01535-1.
Vavříková, Eva: Descriptive Geometry, VŠB – TUO, Ostrava 2005.
Foley, J., van Dam, A., Feiner, S., Hughes, J.: Computer Graphics-Principles and Practise. 2nd ed., Addison-Wesley, Reading, Massachusetts, 1990.
Stillwell, J.: Geometry of surfaces. New York: Springer, 1992. ISBN 0-387-97743-0. |
http://mdg.vsb.cz/portal/gp/Dlouha_cervenka-geometrie_na_pocitaci.pdf
Burda, P., Havelek, R. a Hradecká, R.: Algebra a analytická geometrie: matematika I. Ostrava: VŠB - Technická univerzita Ostrava, 1997. ISBN 80-7078-479-2.
Žára, J.: Moderní počítačová grafika. 2. přeprac. a rozš. vyd. Brno: Computer Press, 2004. ISBN 80-251-0454-0.
Černý, J.: Geometry. Praha: Vydavatelství ČVUT, 1996. ISBN 80-01-01535-1. |
| Recommended Reading: |
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Kreyszig, E.: Differential geometry. New York: Dover Publications, 1991. ISBN 0-486-66721-9.
Kobayashi, S.: Transformation groups in differential geometry. Berlin: Springer, 1972. Classics in mathematics. ISBN 3-540-05848-6.
Umehara, M. and Yamada, K.: Differential geometry of curves and surfaces. Kaiteiban. Translate Rossman, W.. Singapore: World Scientific, 2017. ISBN 978-981-4740-23-4.
Falconer, K. J. Fractal geometry: mathematical foundations and applications. 3rd ed. Chichester: Wiley, 2014. ISBN 978-1-119-94239-9. |
Budinský, B. a Kepr, B. Základy diferenciální geometrie s technickými aplikacemi. Praha: SNTL - Nakladatelství technické literatury, 1970.
Žára J., Beneš B., Felkel P.: Moderní počítačová grafika. Computer Press, Praha 1998.
Kohout, V.: Diferenciální geometrie. Praha: SNTL - Nakladatelství technické literatury, 1971. Matematický seminář SNTL.
Stillwell, J.: Geometry of surfaces. New York: Springer, 1992. ISBN 0-387-97743-0. |
| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Tutorials, Project work, Other activities |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 20 | 5 |
| Examination | Examination | 80 (80) | 30 |
| Písemná zkouška | Written examination | 60 | 25 |
| Ústní zkouška | Oral examination | 20 | 5 |