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Intersections of two offset parametric surfaces based on topology analysis.

Ying-Xiu Ouyang1, Mi Tang, Jun-Cheng Lin

  • 1State Key Laboratory of CAD & CG, AI Institute, Zhejiang University, Hangzhou 310027, China. oyyx_zju@sohu.com

Journal of Zhejiang University. Science
|January 17, 2004
PubMed
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This study introduces a novel algorithm for calculating surface-surface intersections (SSI) of offset parametric surfaces. It leverages topological relationships between intersection loops for robust and efficient computation, overcoming limitations of conventional methods.

Area of Science:

  • Computer-Aided Design (CAD)
  • Geometric Modeling
  • Computational Geometry

Background:

  • Conventional surface-surface intersection (SSI) algorithms are computationally intensive.
  • Existing methods often fail to utilize topological relationships between offset surfaces.
  • Degenerate conditions like loop and singularity leaking are common issues.

Purpose of the Study:

  • To develop a robust and efficient algorithm for calculating intersections between offset parametric surfaces.
  • To leverage topological relations between intersection curves of surfaces with varying offset distances.
  • To overcome limitations and improve upon conventional SSI algorithms.

Main Methods:

  • Pre-processing parametric surfaces to identify topology transition points (TTPs).

Related Experiment Videos

  • Categorizing TTPs to determine optimal initial point searching strategies.
  • Employing a tracing algorithm to march intersection curves from identified initial points.
  • Utilizing previously computed intersection loops to inform new calculations.

    • Main Results:

    • The proposed algorithm effectively calculates intersection curves by exploiting topological relations.
    • It demonstrates robustness in handling complex geometric configurations.
    • Successfully overcomes degenerate conditions frequently encountered in traditional SSI methods.

    Conclusions:

    • The novel algorithm offers a significant improvement in efficiency and robustness for offset parametric surface intersections.
    • Leveraging topological information provides a more reliable approach compared to conventional iterative methods.
    • The method is capable of handling challenging cases, enhancing practical applications in geometric modeling.