Mesh Parameterization: Theory and Practice Mesh Parameterization

Mesh Parameterization: Theory and Practice Mesh Parameterization

Siggraph Course
Mesh Parameterization:
Theory and Practice
Presenters
Kai
Hormann
TU
Clausthal
© Alla Sheffer, 2007
Mathieu
Desbrun
Kun
Zhou
Caltech
Microsoft
Bruno
Lévy
Loria
Alla
Sheffer
UBC
What is Parameterization?
world
atlas
ℝ3
ℝ2
(x,y,z)
(u,v)
parameterization
surface
© Alla Sheffer, 2007
parameter domain
Problem Definition
• Given a surface (mesh) S in R3 and a
domain D find F:D↔S (one-to-one)
© Alla Sheffer, 2007
Why Do We Need It?
© Alla Sheffer, 2007
Why a Course?
© Alla Sheffer, 2007
Course Topics
• Mathematical foundations
• Methods
– Variety of domains: plane, sphere, inter-surface map,
global parameterization
– Atlases & Constraints
• Parameterization applications
– Which methods to choose for which application
• Implementation & numerical tools
© Alla Sheffer, 2007
Syllabus – Part I (2D)
8:30 Introduction [Alla]
8:45 Differential Geometry Primer [Kai]
– Mathematical preliminaries
9:15 Barycentric Mappings [Kai]
– Tutte, conformal, mean-value
9:45 Setting the Boundary Free [Bruno]
– Direct free-boundary methods (UV domain)
© Alla Sheffer, 2007
Syllabus – Part II (2D)
10:30 Indirect methods [Alla]
– ABF, Circle Patterns, etc...
11:00 Segmentation and Constraints [Kun]
– Atlas construction, constrained parameterization
11:45 Comparison & Applications 2D [Kai]
© Alla Sheffer, 2007
Syllabus – Part III (Other Domains)
13:45 Spherical Parameterization [Alla]
– Theory & practice of spherical maps
14:15 Discrete Exterior Calculus [Mathieu]
– Mathematical preliminaries for global methods
14:40 Global Parameterization [Mathieu]
– Simultaneous atlas & parameterization construction
© Alla Sheffer, 2007
Syllabus – Part IV (Extensions)
15:45 X-parameterization/Inter-surface mapping
[Alla]
– Mappings between meshes
16:15 Numerical Aspects [Bruno]
– Numerical solvers for parameterization
16:45 Comparison & Applications of Global
Methods [Bruno]
17:15 Q & A [ALL]
© Alla Sheffer, 2007
External Material
• M. S. Floater and K. Hormann. Surface parameterization: a
tutorial and survey, Advances in Multiresolution for Geometric
Modelling, Mathematics and Visualization, pages 157-186.
Springer, 2005.
• A. Sheffer, E. Praun, and K. Rose. Mesh parameterization
methods and their applications. Foundations and Trends in
Computer Graphics and Vision, 2(2):105-171, 2006.
• B. Lévy. Parameterization and deformation analysis on a
manifold. Technical report, ALICE, 2007.
http://alice.loria.fr/publications
• Source code (Graphite, OpenNL) - http://alice.loria.fr/software.
© Alla Sheffer, 2007