Mathematics BSc
Course description
2013.
Course description
2013.
Applied geometry
Hours lect+pc |
Credits lect+pc |
Assessment | Specialization | Course code lect/pc |
Semester | Status |
---|---|---|---|---|---|---|
2 + 2 | 2 + 3 | exam + term grade |
applied math. | mm1c1ag5e mm1c2ag5e |
5 | recommended |
Course coordinator
Strong | Weak | Prerequisites | |
---|---|---|---|
Practice class | |||
Strong:
Geometry1L
(mm1c1ge2)
| |||
Strong:
Algebra2L
(mm1c1al2)
| |||
Strong:
| |||
Lecture | |||
Weak:
practice class
|
Literature
- Gerald Farin: Curves and surfaces for CAGD: A Practical Guide. 5th ed. Morgan Kaufmann, San Francisco, CA, 2002.
Syllabus
- Affine systems of coordinates. Analytic treatment of affine maps, congruences, and rigid motions.
- Elements of projective geometry, homogeneous coordinates, projective equations of curves.
- Curves defined by quadratic equations. Elementary properties of conics. Quadric surfaces. Conjugacy, poles and polars.
- Parametric curves and surfaces.
- Differential geometry and modelling of curves: curvature and torsion. Polynomial curves, Bernstein polynomials, Bézier curves, splines.
- Differential geometry and modelling of surfaces: normals, tangent planes, principal curvatures, Gauss curvature, Minkowski curvature. Bézier surfaces.
- Classical methods of mapping the space into the plane. Fundamentals of computer aided graphical design.
- Simple geometric algorithms.