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Course, academic year 2023/2024
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Geometry for Computer Graphics - NPGR020
Title: Geometrie pro počítačovou grafiku
Guaranteed by: Department of Software and Computer Science Education (32-KSVI)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Additional information:
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: doc. RNDr. Zbyněk Šír, Ph.D.
Class: DS, softwarové systémy
DS, obecné otázky matematiky a informatiky
Informatika Bc.
Informatika Mgr. - Softwarové systémy
Classification: Informatics > Computer Graphics and Geometry
Is incompatible with: NMMB433
Is interchangeable with: NMMB433
Annotation -
Last update: Mgr. Šárka Voráčová, Ph.D. (06.04.2006)
In this course, we will investigate some of the geometry behind computer graphics and needed to generate computer images. This will involve a brief introduction to several areas in geometry, including analytic geometry in affine and euclidean space, kinematics and differential geometry and how these areas can be used in solving problems arising in geometric modelling.
Course completion requirements - Czech
Last update: doc. RNDr. Zbyněk Šír, Ph.D. (06.02.2018)

Je možno se přímo přihlásit na zkoušku.

Literature - Czech
Last update: Mgr. Šárka Voráčová, Ph.D. (06.04.2006)

•J. Janyška, A. Sekaninová: Analytická teorie kuželoseček a kvadrik, skriptum Masarykovy univerzity v Brně, 2001

•M. Sekanina, L. Boček, M. Kočandrle, J. Šedivý: Geometrie II, SPNP,1988

•B. Budinský: Analytická a diferenciální geometrie, SNTL,1983

•G. Farin, J. Hoschek, M. Kim : Handbook of Computer Aided Geometric Design, Elsevier, 2002

•M. Lávička: KMA/G2 Geometrie 2, pomocný učební text, ZČU Plzeň, 2006,

Requirements to the exam - Czech
Last update: doc. RNDr. Zbyněk Šír, Ph.D. (06.02.2018)

Zkouška probíhá jednak formou diskuze nad třemi samoztatně vytvořenými implementacemi geometrických problémů a dále ústního zkoušení předem určených témat.

Syllabus -
Last update: G_I (12.06.2007)

1. Definition of affine and Euclidean space, affine system, linear Cartesian coordinates, dependence of vectors

2. Barycentric coordinates, convex sets, affine combinations and it's application - algorithm de Casteljau

3. Affine subspaces, parallelism

4. Affine maps, axonometric images, cavalier and military projection

5. Euclidean motions and orthogonal projections

6. Projective space, homogenous coordinates, projective combinations

7. Projective maps, perspective projection

8. Reconstruction of the scene - epipolar geometry, fundamental and essential matrix

9. Conic section and quadrics in projective space

10. Fundamentals of differential geometry-curve, surface and it's parameterization

11. Arc length, osculating plane

12. Frenet frame, curvature and torsion of the curve

13. Representation of surface, curve on surface, first and second fundamental form. Gauss curvature

14. Special surfaces - minimal surfaces, Developable surface

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