Detecting similarity of rational plane curves

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• 作者：Juan Gerardo Alcá ; zar^a ; ^{juange.alcazar@uah.es" class="auth_mail} ; Carlos Hermoso^a ; ^{carlos.hermoso@uah.es" class="auth_mail} ; Georg Muntingh^b ; ^c ; ^{georgmu@math.uio.no" class="auth_mail}
• 关键词：Similarity of planar algebraic curves ; Similarity detection ; Pattern Recognition ; Rational planar curves
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：15 October 2014
• 年：2014
• 卷：269
• 期：Complete
• 页码：1-13
• 全文大小：585 K

文摘

A novel and deterministic algorithm is presented to detect whether two given rational plane curves are related by means of a similarity, which is a central question in Pattern Recognition. As a by-product it finds all such similarities, and the particular case of equal curves yields all symmetries. A complete theoretical description of the method is provided, and the method has been implemented and tested in the Sage system for curves of moderate degrees.