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Distance fields on unstructured grids: Stable interpolation, assumed gradients, collision detection and gap function.

Sebastian Wolff1, Christian Bucher

  • 1Forschungsbereich für Baumechanik und Baudynamik, Technische Universität Wien, Karlsplatz 13/E2063, 1040 Wien, Austria ; Aside Vienna University of Technology:Dynardo Austria GmbH, Wagelseilgasse 14, 1120 Wien, Austria.

Computer Methods in Applied Mechanics and Engineering
|July 27, 2013
PubMed
Summary

This study introduces a robust collision detection algorithm using distance fields for complex geometries. It ensures stable distance calculations and conserves momentum for accurate simulations.

Keywords:
ContactContact detectionDistance fieldDynamic explicitFinite elementLevel set

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Area of Science:

  • Computational geometry
  • Numerical analysis
  • Contact mechanics

Background:

  • Collision detection is crucial in simulations.
  • Existing methods struggle with complex geometries and self-contact.
  • Stable distance field interpolation is needed.

Purpose of the Study:

  • To present a novel, robust collision detection algorithm.
  • To improve stability and accuracy for complex geometries.
  • To enable efficient simulations with self-contact.

Main Methods:

  • Utilizes distance fields with novel interpolation for stability.
  • Introduces an assumed gradient formulation for [Formula: see text]-continuous distance functions.
  • Re-expresses the gap function for penalty and Lagrange multiplier methods.

Main Results:

  • The algorithm is fast, simple, and robust for complex geometries and self-contact.
  • Computed tractions conserve linear and angular momentum, even in infeasible contact.
  • Demonstrates effectiveness through 3D numerical examples.

Conclusions:

  • The proposed distance field approach offers a significant advancement in collision detection.
  • The method provides stable and accurate results for challenging contact scenarios.
  • It is suitable for various applications requiring robust contact simulation.