Special Topics in Computer Science:
Geometric Design of Curves and Surfaces
This course focuses on the preparation for creation, representation and manipulation of
geometric objects using computers. Besides the basic topics of the classical differential
geometry of curves and surfaces, the investigations of polynomial curves and surfaces,
which are determined by the Bézier method and by the B-splines, are also covered.
Prof. Dr. Mancho Manev
University of Plovdiv
||15:30 - 18:00
||15:30 - 18:00
||13:45 - 17:00
- Parametric Curves
Parametric Curves: A Review; Tangent Vector and Tangent Line; Normal Vector
and Curvature; Continuity Issues; Rational Curves
- Bézier Curves
An Introduction; Construction; Moving Control Points; De Casteljau's Algorithm;
De-rivatives of a Bézier Curve; Subdividing a Bézier Curve; Degree Elevation
of a Bézier Curve
- B-spline Curves
Motivation; B-spline Basis Functions (Definition, Important Properties,
Computation Examples); B-spline Curves (Definition -- Open and Closed Curves,
Important Properties, Computing the Coefficients, A Special Case, Moving
Control Points, Modifying Knots, Derivatives of a B-spline Curve); Important
Algorithms for B-spline Curves Knot Insertion (Single Insertion,
Inserting a Knot Multiple Times, De Boor's Algo-rithm, De Casteljau's and
de Boor's Algorithms, Subdividing a B-spline Curve)
Basic Concepts; Bézier Surfaces (Construction, Important Properties,
De Casteljau's Algorithm); B-spline Surfaces (Construction, Important Properties,
De Boor's Algorithm)
The marks for this course will be based on a project, which the students have to deliver
to the lecturer. The project specification can be downloaded from
- Theodore Shifrin. Differential Geometry: A First Course in Curves and Surfaces. 2008,
available freely online at
- Wolfgang Boehm and Hartmut Prautzsch, Geometric Concepts for Geometric Design, AK Peters, Wellesley, MA, 1994.
- Gerald Farin. Curves and Surfaces for Computer Aided Geometric Design. Morgan-Kaufmann, 2001. Fifth edition.
- Gerald Farin, Curves and Surfaces for CAGD: A Practical Guide, fifth edition, Academic Press, 2002.
- Gerald Farin and Dianne Hansford, The Essentials of CAGD, A K Peters, 2000.
- Josef Hoschek and Dieter Lasser, Fundamentals of Computer Aided Geometric Design, translated from the
German 1989 edition by Larry L. Schumaker, A K Peters, 1993.
- Les Piegl and Wayne Tiller, The NURBS Book, second edition, Springer-Verlag, 1997.
- David F. Rogers, An Introduction to NURBS with Historical Perspective, Academic Press, 2001.