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Geometry for Computer Graphics

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code460-4023/01
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Choice-compulsory
Level of Course Unit *Second Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
NEM03Ing. Martin Němec, Ph.D.
Summary
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
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
Fundamental terms
Analytic geometry
Affine space
Projective geometry
Curves, tangent line
Frenet–Serret formulas
Curvature
Surfaces
Curvature of surfaces
Recommended or Required Reading
Required Reading:
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:
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
Lectures, Individual consultations, Tutorials
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Exercises evaluation and ExaminationCredit and Examination100 (100)51
        Exercises evaluationCredit45 (45)20
                Semestrální projektSemestral project45 20
        ExaminationExamination55 (55)20
                Písemná zkouškaWritten examination55 20