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A quick algorithm for evaluation of minimum zone circles from polar coordinate data.

Xiuming Li1, Yuwei Liu1

  • 1School of Mechanical Electronic & Information Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China.

The Review of Scientific Instruments
|January 3, 2020
PubMed
Summary
This summary is machine-generated.

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Selecting initial points for minimum zone circles improves efficiency. New algorithms evaluate these circles using lower envelope lines, a four-point intersection principle, and bisection, with applications to maximum inscribed circles.

Area of Science:

  • Computational geometry
  • Metrology
  • Geometric tolerancing

Background:

  • Accurate determination of minimum zone circles is crucial for geometric tolerancing.
  • Existing methods for evaluating minimum zone circles can be computationally intensive.

Purpose of the Study:

  • To enhance the computational efficiency of minimum zone circle determination.
  • To propose novel algorithms for evaluating minimum zone circles and related geometric features.

Main Methods:

  • Selection of four initial candidate points for minimum zone circles.
  • Development of three error evaluation models based on lower envelope lines, the four-point intersection principle, and the bisection method.
  • Algorithm design for evaluating minimum zone circles and maximum inscribed circles.

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Main Results:

  • Improved computational efficiency through strategic selection of initial points.
  • Validated algorithms for minimum zone circle evaluation using diverse methods.
  • Demonstrated applicability of lower envelope line points for maximum inscribed circle evaluation.

Conclusions:

  • The proposed methods significantly improve the efficiency of minimum zone circle calculations.
  • The developed algorithms provide robust solutions for evaluating geometric tolerances.
  • The study offers practical tools for metrology and computational geometry applications.