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Related Experiment Videos

Boolean operations with implicit and parametric representation of primitives using R-functions.

Yohan D Fougerolle1, Andrei Gribok, Sebti Foufou

  • 1University of Tennessee, Knoxville, TN 37996-2100, USA. yfougero@utk.edu

IEEE Transactions on Visualization and Computer Graphics
|September 8, 2005
PubMed
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This study introduces an efficient algorithm for polygonizing complex implicit surfaces formed by Boolean operations. The method accurately generates both implicit equations and surface meshes for advanced shape modeling.

Area of Science:

  • Computer Graphics
  • Geometric Modeling
  • Computational Geometry

Background:

  • Implicit surfaces offer advantages in representing complex shapes but often lack efficient polygonization methods.
  • Constructive Solid Geometry (CSG) is a powerful modeling paradigm, but integrating deformations and ensuring accurate surface representation remains challenging.

Purpose of the Study:

  • To develop a novel and efficient algorithm for the accurate polygonization of implicit surfaces generated by Boolean operations on deformed primitives.
  • To handle objects with both implicit and parametric representations, including superquadrics, supershapes, and Dupin cyclides.

Main Methods:

  • Utilizes a Constructive Solid Geometry (CSG) tree incorporating Boolean operations, primitive parameters, and global deformations.
  • Employs implicit formulations for subtree evaluation and parametric definitions for refining meshes around intersection curves.

Related Experiment Videos

  • Applies R-functions to combine primitive implicit equations, ensuring guaranteed differential properties for the resulting implicit equation.

    • Main Results:

    • The algorithm produces both a mathematically sound implicit equation and a precise mesh representation of the solution.
    • Achieves accurate polygonization by generating vertices that lie exactly on the zero-set of the implicit equation.
    • Demonstrates the generation of complex objects with guaranteed continuity and differentiability.

    Conclusions:

    • The proposed algorithm offers an efficient and accurate method for polygonizing complex implicit surfaces derived from Boolean operations.
    • The approach effectively integrates implicit and parametric representations, enabling precise shape modeling.
    • Potential applications span mechanical engineering, shape recognition, and data compression.