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Course, academic year 2016/2017
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Geometry for Computer Graphics - NPGR020
Czech title: Geometrie pro počítačovou grafiku
Guaranteed by: Department of Software and Computer Science Education (32-KSVI)
Faculty: Faculty of Mathematics and Physics
Actual: from 2013
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Additional information:
Note: předmět je možno zapsat mimo plán
povolen pro zápis po webu
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.
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,

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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