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基于近似几何误差的动态隐式曲线重构
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Supported by the National Natural Science Foundaton of China under Grant NO.10201030(国家自然科学基金)；the National Science Fund for Distinguished Young Scholars under Grant No 60225002 (国家杰出青年基金)；the National Research Foundation for the Doctoral Program of Higher Education of China under Grant No．20010358003(国家教育部博士点基金)；the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE,China(国家教育部高校优秀青年教师教学科研奖励计划)：the Research Foundation for Young Scholars in University of Science and Technology of China under Grant No．kb0122(中国科学技术大学青年基金)


Dynamic Implicit Curve ReconstructiOn Based On Approximate Geometric Distance
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    摘要:

    提出一种以代数张量积样条曲线作为几何表示形式,基于近似几何误差和薄板能量极小化的隐式重构模型.同时结合最优化理论中的信赖域思想，给出自适应的迭代求解算法及其实现．这种方法采取无代价初始化技术，通过迭代能稳定地达到目标点集的高质量重构，特别是对复杂形状的目标，具有很强的处理能力．

    Abstract:

    An implicit Curve reconstruction method is proposed which represents the curve with all algebraic tensor-product B-spline，and minimizes the tension ofthe B-spline and the approximate geometric distance between the curve and the point set．The method is dynamic and self-adaptive based on trust-region algorithm in optimization theory．The specification of the initial shape is priceless，and the high-quality reconstruction corvc is obtained in a robust way．Some examples are implemented．

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杨周旺,邓建松,陈发来.基于近似几何误差的动态隐式曲线重构.软件学报,2004,15(zk):264-272

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