2D Piecewise Algebraic Splines for Implicit Modeling

	2D Piecewise Algebraic Splines for Implicit Modeling
	Li, Qingde 1; Tian, Jie 2
发表期刊	ACM TRANSACTIONS ON GRAPHICS
	2009-04-01
卷号	28 期号:2 页码:-
文章类型	Article
摘要	2D splines are a powerful tool for shape modeling, either parametrically or implicitly. However, compared with regular grid-based tensor-product splines, most of the high-dimensional spline techniques based on nonregular 2D polygons, such as box spline and simplex spline, are generally very expensive to evaluate. Though they have many desirable mathematical properties and have been proved theoretically to be powerful in graphics modeling, they are not a convenient graphics modeling technique in terms of practical implementation. In shape modeling practice, we still lack a simple and practical procedure in creating a set of bivariate spline basis functions from an arbitrarily specified 2D polygonal mesh. Solving this problem is of particular importance in using 2D algebraic splines for implicit modeling, as in this situation underlying implicit equations need to be solved quickly and accurately. In this article, a new type of bivariate spline function is introduced. This newly proposed type of bivariate spline function can be created from any given set of 2D polygons that partitions the 2D plane with any required degree of smoothness. In addition, the spline basis functions created with the proposed procedure are piecewise polynomials and can be described explicitly in analytical form. As a result, they can be evaluated efficiently and accurately. Furthermore, they have all the good properties of conventional 2D tensor-product-based B-spline basis functions, such as non-negativity, partition of unit, and convex-hull property. Apart from their obvious use in designing freeform parametric geometric shapes, the proposed 2D splines have been shown a powerful tool for implicit shape modeling.
关键词	Algorithm Design Algebraic Splines Csg Isosurface Level Set Function-based Shape Modeling Implicit Curve Implicit Modeling Implicit Surface
WOS标题词	Science & Technology ; Technology
关键词[WOS]	APPROXIMATION ; INTERPOLATION ; SURFACES ; CURVES
收录类别	SCI
语种	英语
WOS研究方向	Computer Science
WOS类目	Computer Science, Software Engineering
WOS记录号	WOS:000266818600002
引用统计	被引频次：22[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.ia.ac.cn/handle/173211/3896
专题	中国科学院分子影像重点实验室
通讯作者	Tian, Jie
作者单位	1.Univ Hull, Dept Comp Sci, Kingston Upon Hull HU6 7RX, N Humberside, England 2.Chinese Acad Sci, Inst Automat, Beijing 100080, Peoples R China
通讯作者单位	中国科学院自动化研究所
推荐引用方式 GB/T 7714	Li, Qingde,Tian, Jie. 2D Piecewise Algebraic Splines for Implicit Modeling[J]. ACM TRANSACTIONS ON GRAPHICS,2009,28(2):-.
APA	Li, Qingde,&Tian, Jie.(2009).2D Piecewise Algebraic Splines for Implicit Modeling.ACM TRANSACTIONS ON GRAPHICS,28(2),-.
MLA	Li, Qingde,et al."2D Piecewise Algebraic Splines for Implicit Modeling".ACM TRANSACTIONS ON GRAPHICS 28.2(2009):-.

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