Mathematics BSc
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
Strong Weak Prerequisites
Practice class
Strong:
Geometry1L (mm1c1ge2)
Strong:
Algebra2L (mm1c1al2)
Strong:
Calculus2L (mm1c1ka2) or
Analysis2L (mm1c1an2)
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.