456-0312/01 – Geometry for Computer Graphics (GPG)

Gurantor departmentDepartment of Computer ScienceCredits4
Subject guarantorDr.RNDr. Arnošt ŠarmanSubject version guarantorDr.RNDr. Arnošt Šarman
Study levelundergraduate or graduateRequirementChoice-compulsory
YearSemestersummer
Study languageCzech
Year of introduction2003/2004Year of cancellation2009/2010
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
S1A60 Dr.RNDr. Arnošt Šarman
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 5+5

Subject aims expressed by acquired skills and competences

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.

Teaching methods

Lectures
Tutorials
Project work

Summary

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.

Compulsory literature:

FRANCIS, S. HILL, Jr. Computer Graphics 1990. New York : Macmillian Publishing Company, a division of Macmillian, Inc. ISBN 0-02-354860-6.

Recommended literature:

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Přednášky: Základní pojmy. Homogenní souřadnice, dělící poměr, dvojpoměr (věta Pappova). Geometrické příbuznosti. Afinní prostor (podprostor). Afinní transformace. Afinita. (Stejnolehlost.) Kolineace. Projektivní prostor. Kolineace. Korelace. Projektivní geometrie. Definice kuželoseček (bodová, tečnová), Pascalova a Brianchonova věta. Involuce. Polární vlastnosti kuželoseček. Kuželosečky. Definice, základní (fokální) vlastnosti, hyperoskulační kružnice, konstrukce tečny a průsečíků. Kolineace v prostoru 3D. Vektorový prostor. Euklidovský prostor. Metrické vlastnosti (rovnoběžnost, kolmost, identita,...). Transformace 3D 2D. Příklad na kolineaci kuželoseček. Příklad na prostorový úkol. Řešení rovinných a prostorových úloh metodou analytické geometrie. Křivky. Vyjádření křivky, délka oblouku a tečna křivky. Průvodní trojhran křivky a Frenetovy vzorce. První a druhá křivost, přirozené rovnice křivky. Styk křivek a oskulační kružnice. Asymptoty. Singulární body křivek. Obalové křivky, rovnoběžné, spádové, evoluty a evolventy. Plochy. Definice a vyjádření plochy. Křivka na ploše. Tečná rovina a normála plochy. 1. základní forma plochy. 2. základní forma plochy. Křivost plochy. Gausova křivost. Klasifikace bodů na ploše. Cvičení: Počítačové laboratoře: Příklad na afinní transformaci. Příklad na kolineaci. Příklad na kresbu kuželoseček. Příklad na řešení v prostoru 3D. (Řez na jehlanu, válci, a pod., afinita resp. kolineace.) Příklad na kolineaci kuželoseček. Příklad na prostorový úkol. Příklad v 3D. (Řez na jehlanu, hranolu, kužely, válci a pod.) Příklad zobrazení prostorové křivky. Příklad na průvodní trojhran v bodě křivky. Příklad na hyperoskulační kružnice. (Elipsa pomocí kruhových oblouků.) Příklad na evolventu křivky 2. stupně. Příklad plochy zadané explicitně, implicitně, parametricky. Příklad aplikace normály plochy při zvýraznění plochy ( rendering ). Programování v jazyce Autolisp.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2009/2010 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P Czech Ostrava 1 Optional study plan
2009/2010 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K Czech Ostrava 1 Optional study plan
2008/2009 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P Czech Ostrava 1 Optional study plan
2008/2009 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K Czech Ostrava 1 Optional study plan
2008/2009 (N2646) Information Technology (2612T025) Computer Science and Technology K Czech Ostrava 2 Choice-compulsory study plan
2007/2008 (N2646) Information Technology (2612T025) Computer Science and Technology P Czech Ostrava 2 Choice-compulsory study plan
2007/2008 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2007/2008 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
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2007/2008 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2007/2008 (N2646) Information Technology (2612T025) Computer Science and Technology K Czech Ostrava 2 Choice-compulsory study plan
2007/2008 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P Czech Ostrava 1 Optional study plan
2007/2008 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K Czech Ostrava 1 Optional study plan
2006/2007 (N2646) Information Technology (2612T025) Computer Science and Technology P Czech Ostrava 2 Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
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2006/2007 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2006/2007 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2006/2007 (N2646) Information Technology (2612T025) Computer Science and Technology K Czech Ostrava 2 Choice-compulsory study plan
2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2006/2007 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology P Czech Ostrava 1 Optional study plan
2006/2007 (N2647) Information and Communication Technology (2612T025) Computer Science and Technology K Czech Ostrava 1 Optional study plan
2005/2006 (N2646) Information Technology (2612T025) Computer Science and Technology P Czech Ostrava 2 Choice-compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2005/2006 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2005/2006 (N2646) Information Technology (2612T025) Computer Science and Technology K Czech Ostrava 2 Choice-compulsory study plan
2005/2006 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 4 Choice-compulsory study plan
2004/2005 (N2646) Information Technology (2612T025) Computer Science and Technology P Czech Ostrava 2 Choice-compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2004/2005 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2004/2005 (N2646) Information Technology (2612T025) Computer Science and Technology K Czech Ostrava 2 Choice-compulsory study plan
2004/2005 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava 4 Choice-compulsory study plan
2003/2004 (N2646) Information Technology (2612T025) Computer Science and Technology P Czech Ostrava 2 Choice-compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics P Czech Ostrava 2 Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2601T004) Measurement and Control Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2612T018) Electronics and Communication Technology P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (10) Elektrické stroje a přístroje P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (2642T004) Electrical Machines, Apparatus and Drives (20) Elektrické pohony a výkonová elektronika P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (3902T023) Computer Science P Czech Ostrava Choice-compulsory study plan
2003/2004 (M2612) Electrical Engineering and Computer Science (3907T001) Electrical Power Engineering P Czech Ostrava Choice-compulsory study plan
2003/2004 (N2646) Information Technology (2612T025) Computer Science and Technology K Czech Ostrava 2 Choice-compulsory study plan
2003/2004 (N2646) Information Technology (1103T021) Computational Mathematics K Czech Ostrava 2 Choice-compulsory study plan
2003/2004 (B2612) Electrical Engineering and Computer Science (1801R001) Computer Science P Czech Ostrava 4 Choice-compulsory study plan

Occurrence in special blocks

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