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.