Geometric Modeling

Lecturer	Teaching Assistants
Michael Wand	Silke Jansen Ruxandra Lasowski Art Tevs

Email addresses are available through the links on the homepages.

Lecture:

• Tue, 14-16h (c.t.), building E1 4, room 021
• Thu, 16-18h (s.t.), building E1 4, room 024

Exercise Course:

• Wed 14-16h, Fri 14-16h, Building E1 4, Room 021

Final Exam:

• Tue, July 31st, 14-16h
• Building E1 3, Lecture Hall 001

Re-Exam:

• Fri, September 21st, 14-16h
• Building E1 3, Lecture Hall 001

List of topics (tentative):

• Mathematical background for geometric modeling

• Modeling Techniques:
  • Splines, curves and surfaces
  • Bezier splines, B-Splines, NURBS, implicits functions
  • Variational Modeling
• Geometry Processing:
  • Processing of 3D scanner data
  • Registration, reconstruction, data fitting
• Practical Skills: Programming assignments & tutorials

Remark: Some slides are password protected out of formal reasons, a public version is provided that is mostly identical to the classroom version.

Lecture#1: April 17th 2012

• Formalities (pub-version)
• Literature (pub-version)
• Introduction (pub-version)

Lecture#2: April 20th 2012
Lecture#3: April 24th 2012

• Linear Algebra and Function Spaces (pub-version) [updated: April 24th 2012]
  (update April 26th: see recommended Literature below)

Lecture #4,#5,#6: April 24th, May 3rd, 8th 2012

• Differential Geometry (pub-version) (updated May 22nd)
  

Lecture#7: May 10th 2012

• Interpolation and Approximation (pub-version)
  

Lecture#8: May 15th 2012

• Intrinsic Geometry (pub-version) (Avinash)
  

Lecture#9,#11: May 22nd 2012, May 31st 2012

• Differential Geometry (pub-version) updated May 22nd (summary intrinsic geometry; same link as above)
• Spline Curves (pub-version)
  

Lecture#10: May 29th 2012

• Triangle Meshes and Multiresoluton (pub-version)
  

Lecture#13: June 5th 2012

• Blossoming and Polar Forms (pub-version) (latest updated: June 26st - last two slides, added geometric construction of deriviatives)
  

Lecture#14: June 19th 2012

• Point-Based Modeling (pub-version)
  

Lecture#15: June 21st/ 2012

• Rational Splines (pub-version)
  

Lecture#21: July 5th 2012

• Spline Surfaces (pub-version)
  

Lecture#22/23: July 10/12th 2012

• Implicit Surfaces (pub-version)
  

Lecture#24: July 17th 2012

• Subdivision Surfaces (pub-version)
  

Lecture#25/26: July 19th/24th 2012

• Variational Modelling (pub-version) (minor changes, July 26th, 18.00h, also renumbered slide set consistently)
  

Lecture#27: July 26th 2012

• Summary (pub-version)
  

For your orientation, you can find old slides from the previous lecture over here.

Main textbooks, on shelf in the CS-library ("Semesterapparat")

• Gerald Farin: Curves and Surfaces for Computer Aided Geometric Design (Fifth Edition), Morgan Kaufmann, 2002.
• Alfred Gray: Modern Differential Geometry of Curves and Surfaces with Mathematica® (Second Edition), CRC, 1997.
• Additional textbooks on shelf in the CS-library

Recommended additional reads:

• Richard O. Duda, Peter E. Hart, David G. Stork: Pattern Classification (Second Edition), Wiley & Sons, 2000.
  Relevant Topics: Statistical techniques, least-squares, total-least-squares (PCA)
• James D. Foley, Andries VanDam und Steven K. Feiner: Computer Graphics: Principles and Practice, Addison-Wesley, 1992.
  Relevant Topics: Computer Graphcis, Fourier Transform & Signal Theory (Chapter 14.10).

Assignment sheets:

• Assignment sheet #0 (practice): Introduction to GeoX (Art Tevs, no due date)
  This assignment is meant as an introduction to our framework (see download below) and to refresh your C++ skills. We will discuss it in the first tutorial course on May 2nd/4th. If you have any questions, feel free to contact us any time
• Assignment sheet #1 (theory): Math Recap (Silke Jansen, due: May 8th 2012, before the lecture)
• Assignment sheet #2 (practice): Interpolation and Approximation (Art Tevs, due: May 16/18th 2012, during the interviews)
• Assignment sheet #3 (theory): Curvature and Approximation (Silke Jansen, due: May 22nd 2012, before the lecture)
• Assignment sheet #4 (practice): PCA & Splines (Art Tevs, due: May 30th/June 1st 2012, during the interviews: Art's office room 219)
• Assignment sheet #5 (theory):Basis Functions (Silke Jansen, due: June 4th 2012, before the lecture)
• Assignment sheet #6 (practice): Bezier & kd-tree (Art Tevs, due: June 13th/15th 2012, during the interviews: Art's office room 219)
• Assignment sheet #7 (theory):Blossoming and Polar Forms (Silke Jansen, due: June 18th 2012, before the lecture)
• Assignment sheet #8 (practice): Bezier & MLS (Art Tevs, due: June 27th/29th 2012, during the interviews: Art's office room 219)
• Assignment sheet #9 (theory):(Rational) Spline Curves (Silke Jansen, due: July 3rd 2012, before the lecture)
• Assignment sheet #10 (practice): Projection and Rational Bezier Curve, patch, image.bmp (Art Tevs, due: July 11th/13th 2012, during the interviews: Art's office room 219)
• Assignment sheet #11 (theory): Splines & Differential Geometry (includes Bonus exercises) (Silke Jansen, due: July 17th 2012, before the lecture)
• Assignment sheet #12 (practice): Marching Cubes/Squares, sor.cpp, image.bmp (Art Tevs, due: July 25th/27th 2012, during the interviews: Art's office room 219)


• Preparatory Exam (no due date)

GeoX Framework:

• GeoX is our (optional) programing framework for the practical tutorials.
• You can download the sources here.
• An introduction to the GeoX framework can be found here.
• Additional hints for the compilation under Unix/Linux are given here.
• Please note that the software is open source (GPL2)
• Patch from 21.05.2012 - can be downloaded here
• Patch from 02.07.2012 - can be downloaded here

• If you have any questions about the lecture: mail to Michael Wand.
  • Office hours: In principle, you can drop by any time; to make sure that I am around and have time for you, drop me a short email for an appointment, if possible.

• If you have any questions about the current assignments, please mail to the responsible teaching assistant (indicated for each assignment sheet above). We are not able to give advice on how to solve the problems, only on questions of factual understanding.