微信服务号

微信订阅号

2025年4月4日 1:50 星期五
首页 > 过刊浏览>2006年第17卷第zk期 >11-20
PDF HTML阅读 XML下载 导出引用 引用提醒
层次隐式张量积B-样条曲面及其在曲面重构中的应用
作者:
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)


Hierarchical Implicit Tensor-Product B-Spline Surface and Its Application in Surface Reconstruction
Author:
  • 摘要
    • | |
  • 访问统计
    • |
  • 参考文献 [29]
    • |
  • 相似文献 [20]
    • | | |
  • 文章评论
    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.

    参考文献
    [1] Clark J. Hierarchical geometric models for visible surface algorithms. Communications of the ACM, 1976,19(10):547-554.
    [2] Schr?der WJ, Zarge JA, Lorensen WE. Decimation of triangle meshes. In: Catmull EE, ed. Proc. of the SIGGRAPH’92. New York: ACM Press, 1992. 65-70.
    [3] Rossignac JR, Borrel P. Multi-Resolution 3D approximations for rendering complex scenes. In: Falcidieno B, Kunii TL, eds. Geometric Modeling in Computer Graphics. Berlin: Springer-Verlag, 1993. 455-465.
    [4] Funkhouser TA, Séquin CH. Adaptive display algorithm for interactive frame rates during visualization of complex virtual environments. In: James TK, ed. Proc. of the SIGGRAPH’93. New York: ACM Press, 1993. 247-254.
    [5] Foresy D, Bartels R. Hierarchical B-spline refinement. In: John D, ed. Proc. of the SIGGRAPH’88. New York: ACM Press, 1988. 205-212.
    [6] Foresy D, Bartels R. Surface fitting with hierarchical splines. ACM Trans. on Graphics, 1995,14(2):134-161.
    [7] Garland M, Heckbert PS. Surface simplification using quadric error metrics. In: Turner W, ed. Proc. of the SIGGRAPH’97. New York: ACM Press, 1997. 209-216.
    [8] Cohen J, Varshney A, Manocha D, Turk G, Weber H, Agarwal P, Brooks F, Wright W. Simplification envelopes. In: Rushmeier H, ed. Proc. of the SIGGRAPH’96. New York: ACM Press, 1996. 119-128.
    [9] Cohen J, Olano M and Manocha D. Appearance-Preserving simplification. In: Rockwood A, ed. Proc. of the SIGGRAPH’98. New York: ACM Press, 1998. 115-122.
    [10] Hoppe H. Progressive meshes. In: Rushmeier H, ed. Proc. of the SIGGRAPH’96. New York: ACM Press, 1996. 99-108.
    [11] Hoppe H. View-Dependent refinement of progressive meshes. In: Turner W, ed. Proc. of the SIGGRAPH’97. New York: ACM Press, 1997. 189-198.
    [12] Losasso F, Hoppe H. Geometry clipmaps: Terrain rendering using nested regular grids. ACM Trans. on Graphics (Proc. of the SIGGRAPH 2004), 2004,23(3):769-776.
    [13] Carr JC, Beatson RK, Cherrle JB, Mitchell TJ, Fright WR, McCallum BC, Evans TR. Reconstruction and representation of 3D objects with radial basis functions. In: Lynn P, ed. Proc. of the SIGGRAPH 2001. New York: ACM Press, 2001. 67-76.
    [14] Zhao H, Osher S. Visualization, analysis and shape reconstruction of unorganized data sets. In: Osher S, Paragios N, eds. Geometric Level Set Methods in Imaging, Vision and Graphics. Berlin: Springer-Verlag, 2002.
    [15] Alexa M, Behr J, Cohen-Or D, Fleishman S, Levin D, Silva C. Point set surfaces. In: Hanspeter P, ed. Proc. of the Conf. on Visualization 2001. New York: IEEE Press, 2001. 21-28.
    [16] Ohtake Y, Belyaev A, Alexa M, Turk G, Seidel HP. Multi-Level partition of unity implicits. ACM Trans. on Graphics (Proc. of the SIGGRAPH 2003), 2003,22(3):463-470.
    [17] Muraki S. Volumetric shape description of range data using “Blobby Model”. In: Sederberg TH, ed. Proc. of the SIGGRAPH’91. New York: ACM Press, 1991. 227-235.
    [18] Jüttler B, Felis A. Least-Squares fitting of algebraic spline surfaces. Advances in Computational Mathematics, 2002,17(1): 135-152.
    [19] Taubin G. Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations, with applications to edge and range image segmentation. IEEE Trans. on Pattern Analysis and Machine Intelligence, 1991,13(11):1115-1138.
    [20] Golub G, Van Loan CF. Matrix Computations. 3rd ed., Baltimore: John Hopkins University Press, 1996.
    [21] Franke R, Nielson G. Smooth interpolation of large sets of scattered data. Int’l Journal for Numerical Methods in Engineering, 1980, 15(11):1691-1704.
    [22] Griebel M, Schweitzer MA. Particle-Partition of unity method for the solution of elliptic, parabolic and hyperbolic PDE. SIAM Journal on Scientific Computing, 2000,22(3):853-890.
    [23] Griebel M, Schweitzer MA. Particle-Partition of unity method-part III: A multilevel solver. SIAM Journal on Scientific Computing, 2002,24(2):377-490.
    [24] Bloomenthal J, Bajaj C, Blinn J, Cani-Gascuel MP, Rockwood A, Wyvill, B, Wyvill G. Introduction to Implicit Surfaces. San Francisco: Morgan Kaufmann Publishers, 1997.
    [25] Bloomenthal J. An implicit surface polygonizer. In: Heckbert P, ed. Graphics Gems IV. San Diego: Academic Press Professional, 1994. 324-349.
    [26] Ju T, Losasso F, Schaefer S, Warren J. Dual contouring of hermite data. ACM Trans. on Graphics (Proc. of the SIGGRAPH 2002), 2002, 21(3):339-346.
    [27] Ohtake Y, Belyaev AG. Dual primal mesh optimization for polygonized implicit surfaces. In: Seidel HP, ed. Proc of the 7th ACM Symp. on Solid Modeling and Applications. New York: ACM Press, 2002.171-178.
    [28] Ronald JB, Kevin GS. Visualization of implicit surfaces. Computers & Graphics, 2001,25(1):89-107.
    [29] Hart JC. Sphere tracing: A geometric method for the antialiased ray tracing of implicit surfaces. The Visual Computer, 1996, 12(10):527-545.
    引证文献
    网友评论
    网友评论
    分享到微博
    发 布
引用本文

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

复制
分享
文章指标
  • 点击次数:3235
  • 下载次数: 5106
  • HTML阅读次数: 0
  • 引用次数: 0
历史
  • 收稿日期:2006-03-15
  • 最后修改日期:2006-09-11
文章二维码
友情链接:中国科学院软件研究所中国计算机学会中国科学院国家自然科学基金委员会CCF数字图书馆Int'l J of Softw Info计算机系统应用
您是第19783552位访问者
版权所有：中国科学院软件研究所 京ICP备05046678号-3
地址：北京市海淀区中关村南四街4号,邮政编码：100190
电话：010-62562563 传真：010-62562533 Email：jos@iscas.ac.cn
技术支持：北京勤云科技发展有限公司

京公网安备 11040202500063号