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Special Topics in Computer Science:
Geometric Design of Curves and Surfaces
339.013 
1KV 
Manev 
Block 
Begin: 6.5.2009 
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 Bsplines, are also covered.
Lecturer
Prof. Dr. Mancho Manev
University of Plovdiv
mmanev@uniplovdiv.bg
Dates
Date 
Time 
Room 
We 6.5.2009 
15:30  18:00 
T 041

Th 7.5.2009 
15:30  18:00 
KG 712

Fr 8.5.2009 
13:45  17:00 
UC 5

Contents
 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;
Derivatives of a Bézier Curve; Subdividing a Bézier Curve; Degree Elevation
of a Bézier Curve
 Bspline Curves
Motivation; Bspline Basis Functions (Definition, Important Properties,
Computation Examples); Bspline Curves (Definition  Open and Closed Curves,
Important Properties, Computing the Coefficients, A Special Case, Moving
Control Points, Modifying Knots, Derivatives of a Bspline Curve); Important
Algorithms for Bspline Curves Knot Insertion (Single Insertion,
Inserting a Knot Multiple Times, De Boor's Algorithm, De Casteljau's and
de Boor's Algorithms, Subdividing a Bspline Curve)
 Surfaces
Basic Concepts; Bézier Surfaces (Construction, Important Properties,
De Casteljau's Algorithm); Bspline Surfaces (Construction, Important Properties,
De Boor's Algorithm)
Exam
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
here.
Literature
 Theodore Shifrin. Differential Geometry: A First Course in Curves and Surfaces. 2008,
available freely online at
www.math.uga.edu/_shifrin/ShifrinDiffGeo.pdf
 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. MorganKaufmann, 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, SpringerVerlag, 1997.
 David F. Rogers, An Introduction to NURBS with Historical Perspective, Academic Press, 2001.
