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Regularization of B-Spline Objects.

Guoliang Xu1, Chandrajit Bajaj

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Computer Aided Geometric Design
|January 11, 2011
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Summary
This summary is machine-generated.

This study introduces an efficient regularization method for B-spline objects (curves, surfaces, and volumes). The technique uses L(2)-gradient flows and finite element methods for shape preservation and isometric mapping.

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Area of Science:

  • Computer-Aided Design
  • Geometric Modeling
  • Numerical Analysis

Background:

  • B-spline objects are fundamental in computer graphics and geometric modeling.
  • Regularization is crucial for shape preservation and accurate representation.
  • Existing methods may lack efficiency or robustness for higher dimensions.

Purpose of the Study:

  • To develop an efficient and effective regularization method for d-dimensional B-spline objects (d=1, 2, 3).
  • To ensure shape preservation and approximate isometric mapping of the definition domain.
  • To provide a robust numerical approach for B-spline object manipulation.

Main Methods:

  • Formulation of weak form L(2)-gradient flows based on energy minimization.
  • Integration of these flows using the finite element method (FEM).
  • Application of B-spline basis functions within the FEM framework.

Main Results:

  • Demonstration of an efficient regularization technique for B-spline objects.
  • Successful application across 1D (curves), 2D (surfaces), and 3D (volumes).
  • Experimental validation of the method's effectiveness and shape-preserving capabilities.

Conclusions:

  • The proposed L(2)-gradient flow method offers an effective approach to regularizing B-spline objects.
  • The finite element method with B-spline basis functions provides a suitable numerical integration strategy.
  • This work advances the field of geometric modeling with practical implications for various applications.