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Informatique et Mathématiques appliquées
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> Formation > Cursus ingénieur

Surface modeling - 5MMMS

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  • Number of hours

    • Lectures : 30.0
    • Tutorials : 6.0
    ECTS : 3.0

Goals

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.

Contact Stefanie HAHMANN

Content

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.



Prerequisites

Geometric Modeling ENSIMAG 2nd year.

Tests

Personal work on computer and written report and 2 exercices.

the same personal work has to be performed for the SESSION NORMALE and for the SECOND SESSION of exams.



N1=P1
N2=P2

Additional Information

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

Bibliography

    • 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
    • SIGGRAPH2000 Course Notes on "Subdivision for Modeling and Animation"
    • SIGGRAPH1997 Course Notes on "Multiresolution Surface Modeling"

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Date of update January 15, 2017

Grenoble INP Institut d'ingénierie Univ. Grenoble Alpes