Course No.：S070104ZJ007
Course Category：Professional Basic Course
Period/Credits：40/2
Prerequisites：Calculus, linear algebra, differential geometry.
Aims & Requirements：
Computer Aided Geometric Design is the basic course for computer graphics, computer aided design, and computer aided manufacture, etc. The course will introduce the definition and mathematics theory including curves, surfaces, solids and their geometric properties. Some special modeling techniques are introduced including Bezier, B-spline and so on. The application algorithms are also studied such as degree increase and decrease, blending, approximation, intersection of the geometric models. Some advanced results are encouraged to be known.
Primary Coverage：
Chapter 1 Basis of curves and surfaces
The concepts of parametric and implicit representation, interpolation, approximation, fitting etc.
Chapter 2 Parametric curves
Spline curves, Bezier curves, B-spline curves, rational parametric curves, degree reduction, blending, geometric continuity.
Chapter 3 Parametric surfaces
Rational Bezier surfaces, B-spline surfaces, Coons and Gordon surfaces, blending, geometric continuity, subdivision methods.
Chapter 4 Triangular surface
Triangular B-B surfaces, blending conditions, interpolation for scatter dates.
Chapter 5 Geometric modeling
Intersection of surfaces, deformation of surfaces, reconstructions, simplification, offset and its approximation.
References：
[1] Yuan Li,Kaifu Zhang,Jianfeng Yu, Computer aided geometric design and its application. Press of West-north University, 2007.
[2] Fazhong Shi, Computer aided geometric design and non-uniform rational B-spline, Press of high education, 2001.
[3] Josef Hosche K, Dieter Lasser , Fundamentals of Computer Aided Geometric Design, Translated by Larry L Schumaker, A.K peters Ltd. 1993.
[4] Geral Farin, Curves and surfaces for CAGD, A practical Guide. 3rd Academic Press 1993.
Author：Liyong Shen (School of Mathematical Sciences, GUCAS)
Date：June, 2009
