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DOI:
Journal of Software:2006.17(zk):11-20

层次隐式张量积B-样条曲面及其在曲面重构中的应用
童伟华,冯玉瑜,陈发来
(中国科学技术大学 数学系,安徽 合肥 230026)
Hierarchical Implicit Tensor-Product B-Spline Surface and Its Application in Surface Reconstruction
TONG Wei-Hua,FENG Yu-Yu,CHEN Fa-Lai
()
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Received:March 15, 2006    Revised:September 11, 2006
> 中文摘要: 提出一类新的隐式曲面表示形式,它具有良好的层次性与自适应性,特别适合于表示层次细节模型.首先给出层次隐式张量积B-样条曲面的定义,回顾曲面重构的一般数学模型,然后提出适于求解该类曲面的最优化模型以及定义域自适应分解的方法.在此基础之上,提出层次逼近算法来逼近采样点数据集.随后,引入单位分解方法,将其用于融合各个子域上的局部逼近函数,使其成为一个具有整体光滑性的函数.最后基于散乱点数据集,给出曲面重构的实例,并作简单的讨论.
Abstract:This paper proposes a hierarchical implicit surface representation which has good adaptability and is very suitable for representing level of detail models. The definition of hierarchical implicit tensor-product B-Spline surface (HITBS) is first given and a mathematical model for surface reconstruction is briefly reviewed. Then an optimization model is proposed based on HITBS and a method is introduced for decomposing the domain in an adaptive fashion. A hierarchical approximation algorithm is proposed to deduce a series of linear equation System. The partition of unity method is introduced to integrate the local approximate functions into a global one. Some examples are given and conclusion remarks are concluded.
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基金项目:Supported by the National Natural Science Foundation of China under Grant Nos.60533060, 60473132 (国家自然科学基金); the the National Grand Fundamental Research 973 Program of China No.2004CB318000 (国家重点基础研究发展规划(973)); the Outstanding Youth Grant of NSF of China under Grant No.60225002 (国家杰出青年基金); the TRAPOYT in Higher Education Institute of MOE of China (教育部高校青年教师奖励计划) Supported by the National Natural Science Foundation of China under Grant Nos.60533060, 60473132 (国家自然科学基金); the the National Grand Fundamental Research 973 Program of China No.2004CB318000 (国家重点基础研究发展规划(973)); the Outstanding Youth Grant of NSF of China under Grant No.60225002 (国家杰出青年基金); the TRAPOYT in Higher Education Institute of MOE of China (教育部高校青年教师奖励计划)
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童伟华,冯玉瑜,陈发来.层次隐式张量积B-样条曲面及其在曲面重构中的应用.软件学报,2006,17(zk):11-20

TONG Wei-Hua,FENG Yu-Yu,CHEN Fa-Lai.Hierarchical Implicit Tensor-Product B-Spline Surface and Its Application in Surface Reconstruction.Journal of Software,2006,17(zk):11-20