Polynomial Curves and Surfaces

This lecture is an introduction to the topic of Polynomial Curves and Surfaces. It covers parts of the former Geometric Modeling 1 & 2 lectures, concentrating on the polynomial representation of curves and surfaces. The subject of Subdivision Curves and Surfaces will be the topic of a forthcoming lecture.

 

More information will follow shortly.

 

Lecturer:	Prof. Dr. Leif Kobbelt
Contact:	David Bommes
	Henrik Zimmer

 

 

News:
From now on, both exercises are held in our seminar room 6317!

 

Prerequisites:
Basic knowledge of linear algebra is recommended.

 

Lecture type:
ECTS 6  (V3/Ü2)

 

Lecture:
Tuesday,  15:00h-16:30, AH V   (starting at 20.10.2009 )

Friday, 10:00h-11:30, AH VI      (starting at 23.10.2009, only every second week)

 

Exercise course:
Thursday, 10:00 - 11:30, 6317,  (starting at 15.10.2009)
Thursday, 15:00 - 16:30, 6317    (starting at 15.10.2009)

Contents:

• Foundations of geometry: affine spaces, parametric curves and surfaces
• Bezier-curves: Bernstein-polynomials, algorithm of de Casteljau, derivatives, integration, conversion, polar form
• Bspline-curves: definition, algorithm of de Boor, derivatives, knot insertion, interpolation and approximation of scattered data
• Tensor product surfaces: definition, polar form, evaluation,derivatives
• Bezier surface patches: multivariate Bernstein-polynomials, multivariate algorithm of de Casteljau, polar form, derivatives degree elevation
• Construction of smooth surfaces: Clough-Tocher interpolant, analytic and geometric continuity

 

Exercises:

• Introduction (15.10.2009)
• Assignment 1 (till 29.10.2009) [Maple worksheet .mw and .pdf]
• Assignment 2 (till 5.11.2009)   [Maple worksheet .mw and .pdf]
• Assignment 3 (till 12.11.2009) [Maple worksheet .mw and .pdf]
• Assignment 4 (till 19.11.2009) [Maple worksheet .mw and .pdf]
• Assignment 5 (till 26.11.2009) [Maple worksheet .mw and .pdf]

 

 

Literature:

• G. Farin: Curves and surfaces for computer aided geometric design
• H.Prautzsch, W.Boehm, M.Paluszny: Bezier and B-Spline Techniques
• L.Piegl, W.Tiller: The NURBS Book
• Very preliminary lecture notes from the lecture Geometric Modeling I are also available.