Geometry for Computer Graphics - NMMB433
Title: Geometrie pro počítačovou grafiku
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
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
Is provided by: NPGR020
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: doc. RNDr. Zbyněk Šír, Ph.D.
Class: M Mgr. MMIB
M Mgr. MMIB > Povinně volitelné
Classification: Informatics > Computer Graphics and Geometry
Mathematics > Geometry
Incompatibility : NPGR020
Interchangeability : NPGR020
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Annotation -
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.
Last update: Voráčová Šárka, Mgr., Ph.D. (06.04.2006)
Course completion requirements - Czech

Je možno se přímo přihlásit na zkoušku.

Last update: Šír Zbyněk, doc. RNDr., Ph.D. (06.02.2018)
Literature - Czech

•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,

Last update: Voráčová Šárka, Mgr., Ph.D. (06.04.2006)
Requirements to the exam - Czech

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

Last update: Šír Zbyněk, doc. RNDr., Ph.D. (06.02.2018)
Syllabus -

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

Last update: G_I (12.06.2007)