Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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AN OPTIMAL CONTROL APPROACH TO CONFORMAL FLATTENING OF TRIANGULATED SURFACES

  • PARK, YESOM (DEPARTMENT OF MATHEMATICS, EWHA WOMANS UNIVERSITY) ;
  • LEE, BYUNGJOON (DEPARTMENT OF MATHEMATICS, THE CATHOLIC UNIVERSITY OF KOREA) ;
  • MIN, CHOHONG (DEPARTMENT OF MATHEMATICS, EWHA WOMANS UNIVERSITY)
  • Received : 2019.09.10
  • Accepted : 2019.12.04
  • Published : 2019.12.25
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Abstract

This article presents a new approach for conformal flattening with optimal cone singularity. The algorithm here takes an optimal control for selecting optimal cones and uses the Ricci flow to force the flattening. This work is considered as a modification to the work of Soliman et al. [1] in the sense that they make use of the Yamabe equation for the flattening, which is an approximation of the Ricci flow. We present a numerical algorithm based on the optimal control with the mathematical background. Several numerical results validate that our method is optimal in total cone angle and usage of the Ricci flow ensures the conformal flattening while selecting optimal cones.

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References

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