Course Unit Code | 460-4023/01 |
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Number of ECTS Credits Allocated | 4 ECTS credits |
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Type of Course Unit * | Choice-compulsory |
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Level of Course Unit * | Second Cycle |
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Year of Study * | First 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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| NEM03 | Ing. Martin Němec, Ph.D. |
Summary |
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The course is designed for students who will also deal with computer graphics, mainly on the modeling of curves and surfaces used in engineering practice. The aim of the course is to deepen the knowledge of chapters of mathematics and geometry in the range of teaching mathematics at technical universities to the needs of modeling curves and surfaces in computer graphics. Instruction in the semester is divided into three parts - chapters. 1st part: This is a selected game on projektivního space. This section is aimed at addressing the general features of given conics methods of projective geometry. 2nd Part: Geometry of curves. Kinematic curves equidistant curves, curves in 3D space.
3rd section. Selected chapters of geometry, which relate to areas used in technical practice (construction, transport, engineering). Equidistant surfaces, packing areas
Implementation of examples will be applied in the environment or Java programming language. C language. |
Learning Outcomes of the Course Unit |
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The course is designed for students who will also deal with computer graphics.
The goal is to deepen knowledge of geometry and mathematics for practical use in computer graphics.
Further extend the knowledge studentůz kinematic geometry and creating technical curves and surfaces. |
Course Contents |
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Fundamental terms
Analytic geometry
Affine space
Projective geometry
Curves, tangent line
Frenet–Serret formulas
Curvature
Surfaces
Curvature of surfaces |
Recommended or Required Reading |
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Required Reading: |
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1. SHIFRIN T.:Differential geometry, University of Georgia. 2014 |
Povinná literatura:
1. SOJKA, E., NĚMEC, M., FABIÁN, T.: Matematické základy počítačové grafiky, VŠB-TU Ostrava, 2012.
2. C. K. Shene: Introduction to Computing with Geometry Notes, Michigan Technological University, http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/notes.html |
Recommended Reading: |
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1. FRANCIS, S. HILL, Jr. Computer Graphics 1990. New York : Macmillian Publishing Company, a division of Macmillian, Inc. ISBN 0-02-354860-6. |
1. JEŽEK F.: Diferenciální geometrie (učební text), Plzeň 2005.
2. KOLAŘ I., POSPÍŠILOVA, R.: Diferenciální geometrie křivek a ploch (elektronické skriptum). Brno 2007
3. FRANCIS, S. HILL, Jr. Computer Graphics 1990. New York : Macmillian Publishing Company, a division of Macmillian, Inc. ISBN 0-02-354860-6. |
Planned learning activities and teaching methods |
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Lectures, Individual consultations, Tutorials |
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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Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |
Exercises evaluation | Credit | 45 (45) | 20 |
Semestrální projekt | Semestral project | 45 | 20 |
Examination | Examination | 55 (55) | 20 |
Písemná zkouška | Written examination | 55 | 20 |