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Geometry for Computer Graphics

Class at Faculty of Mathematics and Physics |
NPGR020

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

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.