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Metric-driven RoSy field design and remeshing.

Yu-Kun Lai1, Miao Jin, Xuexiang Xie

  • 1Department of Computer Science and Technology, Tsinghua University, Beijing, PR China. yukun.lai@gmail.com

IEEE Transactions on Visualization and Computer Graphics
|November 14, 2009
PubMed
Summary

This study presents a new method for designing rotational symmetry (N-RoSy) fields on surfaces, offering user control over field topology and singularities. The approach simplifies complex surface geometry for practical applications like remeshing and artistic rendering.

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Area of Science:

  • Computer Graphics
  • Computational Geometry
  • Differential Geometry

Background:

  • Designing rotational symmetry fields (N-RoSy) is crucial for various graphics applications.
  • Existing methods face challenges with arbitrary surfaces and user-defined topologies.

Purpose of the Study:

  • To introduce a rigorous and practical approach for automatic N-RoSy field design on arbitrary surfaces.
  • To provide users with full control over field singularities, topology, and interactive editing.
  • To simplify N-RoSy field construction by flattening Riemannian metrics.

Main Methods:

  • Formulating N-RoSy field construction as designing a Riemannian metric compatible with local symmetry.
  • Proving compatibility conditions using discrete parallel transport.

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  • Simplifying the Riemannian metric to be flat almost everywhere to handle surface curvatures.

    • Main Results:

    • Developed a flexible system for N-RoSy field design with user-defined singularities and topologies.
    • Enabled the design of fields with single singularities and mixed-RoSy fields.
    • Demonstrated applications in pen-and-ink sketching, geometry remeshing, and Celtic knot generation.

    Conclusions:

    • The proposed method offers a simplified and flexible approach to N-RoSy field design on arbitrary surfaces.
    • The technique facilitates advanced graphics applications, including complex remeshing and procedural content generation.
    • The generalization to regular remeshing and direct Celtic knot generation showcases the method's versatility.