AN OPTIMAL CONTROL APPROACH TO CONFORMAL FLATTENING OF TRIANGULATED SURFACES
- 주제(키워드) Conformal Flattening , Cone Singularity , Discrete Ricci Flow , Optimal Control
- 주제(기타) 자연과학
- 주제(기타) 수학
- 주제(기타) 기하학
- 주제(기타) 응용기하
- 설명문(URI) https://www.kci.go.kr/kciportal/ci/sereArticleSearch/ciSereArtiView.kci?sereArticleSearchBean.artiId=ART002534118
- 관리정보기술 faculty
- 등재 KCI등재
- 발행기관 한국산업응용수학회
- 발행년도 2019
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000169687
- 본문언어 영어
초록/요약
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 flatten-ing, 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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