A Proposal for the Automatic Computation of Envelopes of Families of Plane Curves

作     者：BOTANA Francisco RECIO Tomás 

作者机构：Depto. de Matemática Aplicada I Universidad de Vigo Campus A Xunqueira Depto. de Matemáticas Estad'?stica y Computación Universidad de Cantabria 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2019年第32卷第1期

页      面：150-157页

核心收录：

学科分类：0810[工学-信息与通信工程] 1205[管理学-图书情报与档案管理] 07[理学] 0811[工学-控制科学与工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：supported by the Spanish Ministerio de Economía y Competitividad the European Regional Development Fund(ERDF)under Grant No.MTM2017-88796-P 

主　　题：Automated deduction in geometry dynamic geometry envelopes parametric polynomial systems symbolic computation 

摘      要：The idea of envelope of a family of plane curves is an elementary notion in differential geometry. As such, its implementation in dynamic geometry environments is quite universal(Cabri,The Geometer s Sketchpad, Cinderella, Geo Gebra,...). Nevertheless, most of these programs return,when computing certain envelopes, both some spurious solutions and the curves that truly ?t in the intuitive de?nition of envelope. The precise distinction between spurious and genuine parts has not been made before: This paper proposes such distinction in an algorithmic way, ready for its implementation in interactive geometry systems, allowing a ?ner classi?cation of the different parts resulting from the current, advanced approach to envelope computation and, thus, yielding a more precise output, free from extraneous components.