Surface modeling - 5MMMS

Goal(s)

Geometric modeling is an area of ??research and computer engineering common to both disciplines, applied mathematics and computer science. It focuses on digital and automated methods for creation, representation, modeling, analysis and acquisition of 3D geometric shapes.

Applications of geometric modeling cover a wide range of areas: CAD / CAM, industrial design, virtual sculpture, surface reconstruction, simulation, animation, video games, scientific visualization, medical imaging, multimedia, 3D content creation.

This course presents a large set of models and algorithms for the representation, modeling and animation of 3D shapes used in geometric design, computer graphics and the applications mentioned above.

he course presents models and algorithms for surface description, which are commonly used in Computer Aided Geometric Design and in Computer Graphics.

Responsible(s)

Stefanie HAHMANN

Content(s)

I. Part 1 (POLYGONAL GEOMETRY PROCESSING)
1. Computational Geometry (Definitions, Triangulations, surface meshes, Delaunay, Voronoi diagrams).
2. Data structures
3. Discrete differential Geometry
4. Smoothing
5. Parametrization, Remeshing
6. Simplification
7. Deformation
8. Reconstruction of surfaces

II. Part 2 (SURFACE MODELS)
1. Differential geometry: parametric curves and surfaces, curvature, geometric invariants, fundamental forms.
2. Triangulations and meshes: Delaunay triangulation, Voronoï diagram, meshes, mesh implication,
B-rep data structures.
3. Spline surfaces: Bezier and B-spline tensor product and triangular patches, algorithms De Casteljau and
De Boor, barycentric coordinates, derivatives, continuity.
4. Coons patches.
5. Subdivision surfaces: Catmul-Clark, Butterfly and Loop's scheme.
6. Surfaces of arbitrary topology: geometric continuity, interpolation of triangular surface meshes.
7. Multiresolution curves and surfaces: B-spline wavelets, multi resolution analysis, level of detail
edition, hierarchical models.

if possible, but not mandatory: Geometric Modeling ENSIMAG 2nd year.

Test

Evaluation : Projet (rendu du code et des résultats) + rapport écrit + soutenance (15 min)

Resit : Projet (rendu du code et des résultats) + rapport écrit (NC)

NORMAL SESSION:
Type of examination: Personal project + written report + defence

No written examination to be organised by the school.
Defences are organised by the teacher.

RE-SIT SESSION:
During the re-sit session, students must complete a full project (similar to that in Session 1). Students must contact the lecturer well in advance to allow sufficient time to complete the project.

Calendar

The course exists in the following branches:

• Curriculum - Math. Modelling, Image & Simulation - Semester 9

Additional Information

Course ID : 5MMMS
Course language(s):

The course is attached to the following structures:

• Team Image Vision Interaction Multimedia Bioinfo

You can find this course among all other courses.

Bibliography

• • M. Botsch, L. Kobbelt, M. Pauly, P. Alliez, B. Lévy: Polygon Mesh Processing, CRC Press, 2010
  • G. Farin: Curves and Surfaces for CAGD, a practical guide, Academic Press, 1997
  • J. Hoschek, D. Lasser: Fundamentals of Computer Aided Geometric Design, AK Peters, 1993
  • E. Cohen, R. Riesenfeld, G. Elber: Geometric Modeling with Splines, AK Peters, 2001
  • JD. Boissonnat, M. Yvinec: Géométrie Algorithmique, Ediscience, 1995
  • M. Do Carmo: Differentiel Geometry of curves and Surfaces, Prentice Hall, 1976
  • SIGGRAPH2000 Course Notes on "Subdivision for Modeling and Animation"
  • SIGGRAPH1997 Course Notes on "Multiresolution Surface Modeling"