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    “Algorithms for Degree-Raising of Splines”中的问题及其解决办法

    SOLUTIONS TO THE PROBLEM IN “ALGORITHMS FOR DEGREE RAISING OF SPLINES”

    • 摘要: 研究表明,Cohen,Lyche和Schumaker于1985年在ACMTransactionsonGraphics杂志上所发表的论文“AlgorithmsforDegree-RaisingofSplines”中存在着严重问题.文中给出了解决B样条曲线升阶的经典理论中的这些问题的三个算法,同时也给出了计算实例.

       

      Abstract: A Chinese author argues that there are some mistakes in the paper entitled “Algorithms for Degree Raising of Splines” by Cohen,Lyche,and Schumaker .The associated algorithms may fail when used for degree raising of uniform B spline curves.For instance,when the equations (2 1) and (2 2) and theorem 2 1 in reference 1 are used for degree raising of B spline curves,the associated algorithm 3 1 in reference 1 will fail if the spacing between the knots is equal.The Chinese author proposes three algorithms for the above problem. Additional results for uniform B spline curves are obtained.

       

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