{"title":"伯恩斯坦多项式","authors":"Anandaram Mandyam N","doi":"10.12723/MJS.56.5","DOIUrl":null,"url":null,"abstract":"Bernstein polynomials (aka, B-polys) have excellent properties allowing them to be used as basis functions in many applications of physics. In this paper, a brief tutorial description of their properties is given and then their use in obtaining B-polys, B-splines or Basis spline functions, Bezier curves and ODE solution curves, is computationally demonstrated. An example is also described showing their application to solving a fourth-order BVP relating to the bending at the free end of a cantilever.","PeriodicalId":18050,"journal":{"name":"Mapana Journal of Sciences","volume":"17 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"163","resultStr":"{\"title\":\"Bernstein Polynomials\",\"authors\":\"Anandaram Mandyam N\",\"doi\":\"10.12723/MJS.56.5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Bernstein polynomials (aka, B-polys) have excellent properties allowing them to be used as basis functions in many applications of physics. In this paper, a brief tutorial description of their properties is given and then their use in obtaining B-polys, B-splines or Basis spline functions, Bezier curves and ODE solution curves, is computationally demonstrated. An example is also described showing their application to solving a fourth-order BVP relating to the bending at the free end of a cantilever.\",\"PeriodicalId\":18050,\"journal\":{\"name\":\"Mapana Journal of Sciences\",\"volume\":\"17 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"163\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mapana Journal of Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12723/MJS.56.5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mapana Journal of Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12723/MJS.56.5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Bernstein polynomials (aka, B-polys) have excellent properties allowing them to be used as basis functions in many applications of physics. In this paper, a brief tutorial description of their properties is given and then their use in obtaining B-polys, B-splines or Basis spline functions, Bezier curves and ODE solution curves, is computationally demonstrated. An example is also described showing their application to solving a fourth-order BVP relating to the bending at the free end of a cantilever.
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