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Related Experiment Videos

Geometry-aware bases for shape approximation.

Olga Sorkine1, Daniel Cohen-Or, Dror Irony

  • 1The authors are with the School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel. sorkine@tau.ac.il

IEEE Transactions on Visualization and Computer Graphics
|March 8, 2005
PubMed
Summary

We developed a novel shape approximation method for irregular triangular meshes. This geometry-aware technique efficiently reconstructs and refines mesh shapes using anchor vertices and sparse linear algebra.

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Area of Science:

  • Computer Graphics
  • Geometric Modeling
  • Numerical Analysis

Background:

  • Irregular triangular meshes are widely used in computer graphics and simulations.
  • Existing shape approximation methods often lack geometry-awareness or computational efficiency.

Purpose of the Study:

  • To introduce a new class of geometry-aware shape approximation techniques for irregular triangular meshes.
  • To develop an efficient and incrementally updatable method for mesh geometry approximation and refinement.

Main Methods:

  • Approximating mesh geometry using a linear combination of geometry-aware basis vectors.
  • Defining basis vectors based on mesh connectivity and geometrically important anchor vertices.
  • Solving the reconstruction problem via a sparse linear least-squares problem using matrix factorization.

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Main Results:

  • The proposed method generates geometry-aware bases, unlike geometry-oblivious spectral methods.
  • Reconstruction is achieved by solving a single sparse linear least-squares problem efficiently.
  • An incremental update scheme allows for fast, online refinement of mesh geometry.

Conclusions:

  • The new technique offers an effective approach for shape approximation and progressive mesh refinement.
  • The method's computational efficiency enables real-time applications and interactive geometry editing.
  • Geometry-aware basis functions provide a more accurate and compact representation of mesh shapes.