- course no.
- 263-5907-00
- semester
- Fall 2024
- lecturer
- Helmut Pottmann
- assistant
- Olga Sorkine-Hornung
(contact via adress below only, please) - contact
- lecture
- Tue 10-12; CAB, G 57
- ECTS credits
- 1 credit
announcements
- 17.09.24
- Welcome to the fall semester! Note that the first lecture of the course will start on October 8, 2024.
overview
Assuming some basic knowledge of elementary differential geometry of curves and surfaces in 3-dimensional Euclidean space, we will discuss concepts of classical constructive differential geometry and their discrete versions, with a focus on quadrilateral nets. Topics to be addressed include mappings between surfaces, conjugate parameterizations, principal parameterizations, developable surfaces and their applications in architectural structures, design of mechanical metamaterials and fabrication processes based on bending of material. Another focus is on geometric optimization problems, discussing mainly geometric ideas on initialization, regularization and the formulation of frequently appearing objective functions. A further topic is given by transformations which preserve important structures. This reaches into the sphere geometries of Möbius and Laguerre and transformations of nets. Finally, we present the basics of kinematical geometry, such as velocity fields and their use in registration algorithms, infinitesimal flexibility and the closely related static equilibrium of shells.
Course objectives
The main intention of the course is to present geometric concepts that turned out to simplify the solution of problems in computational design and fabrication and hold promise to provide useful methodology for future research in this area.
Course work and performance assessment
Ungraded semester performance.
schedule and course notes
Note: Course notes are only accessible within the ETH network (addresses 129.132.*). Use VPN to access from outside.
The course schedule is tentative and might be adjusted along the way.
- 01.10.24
- No class.
- 08.10.24
-
Motions in the plane and in 3D; envelopes; Frenet frames and rotation-minimizing frames.
Lecture slides, notes on velocities, notes on rotation-minimizing frames. - 15.10.24
-
Kinematic surface reconstruction.
Lecture slides - 22.10.24
-
Distance functions and registration; Optimization and mappting between surfaces.
Lecture slides (part 01), lecture slides (part 02), notes on registration with known correspondences, notes on generalized eigenvalue problem. - 29.10.24
-
Quad mesh based mappings between surfaces and applications.
Lecture slides, notes on developable surface. - 05.11.24
-
Quad mesh with planar faces and freeform architecture from planar panels; developable quad meshes and contact element nets.
Lecture slides (part 01), lecture slides (part 02), related paper ("developable quad meshes"). - 12.11.24
-
Principal meshes, mesh parallelisum and nodes, offset meshes, mesh with offset edges.
Lecture slides - 19.11.24
-
Asymptotic nets (A-nets), Tchebychev A-nets (K-nets), principal symmetric quad meshes (S-nets), sphere geometric concepts
Lecture slides (part 01), Lecture slides (part 02). - 26.11.24
-
Geometry and computational design of equilibrium structures, isotropic geometry and its applications
Lecture slides (part 01), Lecture slides (part 02), related paper ("Quad meshes as optimized architectural freeform structures").
books and references
- Architectural geometry, H. Pottmann, A. Asperl, M. Hofer and A. Kilian. Bentley Institute Press (2007), ISBN 978-1-934493-04-5.
- Applied geometry notes, H. Pottmann
- Computational line geometry, H. Pottmann and J. Wallner
- Industrial geometry, H. Pottmann