An influence-knot set based new local refinement algorithm for T-spline surfaces

Wang, Aizeng; Zhao, Gang

doi:10.1016/j.eswa.2013.12.032

Cited by 9 publications

(3 citation statements)

References 10 publications

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“…Using the initial mesh of B-spline and local knot refinement method in Sederberg et al (2004), Wang et al (2014), all of the T-spline can be extended to a standard T-spline or semi-standard T-spline. Thus, T-spline surface representation can be defined by:…”

Section: Traditional Least-square T-spline Fitting Methodsmentioning

confidence: 99%

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A fast T-spline fitting method based on efficient region segmentation

Jiang

Huo

et al. 2020

Comp. Appl. Math.

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T-spline has been recently developed to represent objects of arbitrary shapes in computeraided design, computer graphics, and reverse engineering. In fact, fitting a T-spline over a point cloud is usually ineffective by using traditional iterative fit-and-refine paradigm. In traditional T-spline least-square fitting method, all control points are recomputed in each iteration, which costs large amount of calculations. In this paper, we propose a fast T-spline fitting method based on T-mesh segmentation. The segmentation technology is introduced to identify the inactive and active region of T-mesh. Computational costs can be largely reduced since only the control points in the active part need to be recalculated in the upcoming process, while those in inactive part are kept invariant once the fitting accuracy is achieved. Classical datasets are used to validate the proposed fast fitting method, and the experimental results yield that a total running time is reduced to 34% of the traditional T-spline fitting method. We argue this method is particularly useful in the reconstruction of scanned scatter data of which the parameter distribution is not uniform.

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Section: Traditional Least-square T-spline Fitting Methodsmentioning

confidence: 99%

“…T-spline refinement technology is used in the inserting step which can be found in Sederberg et al 2004, Wang et al (2014). The above algorithms are designed to insert as few nodes as possible.…”

Section: Efficient Region Segmentation Technologymentioning

confidence: 99%

A fast T-spline fitting method based on efficient region segmentation

Jiang

Huo

et al. 2020

Comp. Appl. Math.

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“…To overcome those drawbacks, Sederberg et al put forth T-splines [4,5], which have T-junctions in their control meshes and so can achieve flexible local refinement. Subsequently, research was done to complete the T-spline theory, including the linear independence of blending functions [6][7][8], local refinement algorithm [9][10][11][12], and other fundamental theories of T-splines [13][14][15]. It also extended the applications of NURBS and T-splines in CAD and CAE such as the isogeometric analysis [16] based integration of NURBS or T-splines with finite element analysis [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Unified Representation of Curves and Surfaces

Wang

Zhao

2021

Mathematics

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In conventional modeling, shared control points can be employed to realize a unified representation for an object consisting of only curves or only surfaces touching one another. However, this method fails in treating the following two cases: (a) a system consisting of detached curves or surfaces; (b) a system having both curves and surfaces. The purpose of the present paper is to develop a new theoretical tool to solve such problems. By introducing the definitions of naked knot and I-mesh, the concept of I-spline is put forth, which is, in essence, an expanded B-spline or T-spline. It is verified by examples that the naked knots make I-splines flexible and effective in transforming different surfaces and/or curves into a unified one, especially in the above two cases.

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