Converting a CAD model into a non-uniform subdivision surface

Shen, Jingjing; Kosinka, Jiří; Sabin, Malcolm; Dodgson, Neil A.

doi:10.1016/j.cagd.2016.07.003

Cited by 20 publications

(16 citation statements)

References 40 publications

(67 reference statements)

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“…Example 2. In the study of Shen et al [13], they address a method that converts multiple NURBS (non-uniform rational B-splines) patches to a single untrimmed NURBS-compatible subdivision surface in order to avoid a gap between a pair of adjacent NURBS patches, which are usually trimmed and stitched by the standard CAD tools. In their method, they adopt quadrangle patches and bivariate parameterization (i.e.…”

Section: Application Examples Of Surface Continuitiesmentioning

confidence: 99%

“…In the procedure of Shen et al [13], a coarse quadrilateral mesh is created first from the trimmed bi-cubic NURBS patches. Then, this coarse mesh is refined to form a non-uniform subdivision mesh that is maintained to retain the boundary geometry property of each NURBS patch through boundary curve spacing and surface fitting.…”

Section: Application Examples Of Surface Continuitiesmentioning

confidence: 99%

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Study of Second-Order Continuities of a Composite Surface

Liu¹,

Yue²

2020

APM

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There are two classes of continuities, parametric continuities and geometric continuities, which are used to illuminate the smoothness of a composite surface in surface construction and reconstruction in computer graphics (CG) and computer aided design (CAD). A parametric continuity is more stiff than its corresponding geometric continuity of the same order. This paper uncovers the geometric properties of parametric and geometric continuities less than and equal to second order and presents the proofs for the corresponding propositions. These propositions can be applied to the existent or promising schemes of surface construction or reconstruction, which can provide a convincing theory for researchers to establish their schemes in surface construction. Three examples are used in this paper to show the applications of these propositions.

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Section: Application Examples Of Surface Continuitiesmentioning

confidence: 99%

Section: Application Examples Of Surface Continuitiesmentioning

confidence: 99%

Study of Second-Order Continuities of a Composite Surface

Liu¹,

Yue²

2020

APM

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“…To merge two surfaces across their trimming curve further modifications are made using their proposed NU-NURBS. Another approach uses subdivision surfaces [15,16], although the parameterization is modified and the geometry is approximated in at least a region of adjacent patches near the trim. These methods take advantage of the topological flexibility of these respective techniques and generate a unified control mesh/surface representation of the output model.…”

Section: Related Workmentioning

confidence: 99%

Refinement for a Hybrid Boundary Representation and its Hybrid Volume Completion

Song¹,

Cohen²

2019

The SMAI Journal of Computational Mathematics

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With the increasing need for volumetric B-spline representations and the lack of methodologies for creating semi-structured volumetric B-spline representations from B-spline Boundary Representations (B-Rep), hybrid approaches combining semi-structured volumetric B-splines and unstructured Bézier tetrahedra have been introduced, including one that transforms a trimmed B-spline B-Rep first to an untrimmed Hybrid B-Rep (HB-Rep) and then to a Hybrid Volume Representation (HV-Rep). Generally, the effect of h-refinement has not been considered over B-spline hybrid representations. Standard refinement approches to tensor product B-splines and subdivision of Bézier triangles and tetrahedra must be adapted to this representation. In this paper, we analyze possible types of h-refinement of the HV-Rep. The revised and trim basis functions for HB-and HV-rep depend on a partition of knot intervals. Therefore, a naive h-refinement can change basis functions in unexpected ways. This paper analyzes the the effect of h-refinement in reducing error as well. Different h-refinement strategies are discussed. We demonstrate their differences and compare their respective consequential trade-offs. Recommendations are also made for different use cases.2010 Mathematics Subject Classification. 65D17.

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“…For the case n � 0, the desired scheme reproducing EP ΓΛ 0 is actually the scheme (4). From Section 3.1.1, by setting ω k � − (α k 0 − (1/4(1 + v k+1 ))), it reduces to the D-D 2-point scheme reproducing EP ΓΛ 0 when ω k � 0 and becomes the cubic exponential B-spline scheme (1) generating EP ΓΛ 1 and reproducing k+1 ), the corresponding k-level symbol can be rewritten as a k ΓΛ 0 ,ω k (z) � (1 − θ k )e ΓΛ 0 ,1 (z) + θ k e k ΓΛ 0 ,2 (z), where e ΓΛ 0 ,1 (z) denotes the symbol of the D-D 2-point scheme and e k ΓΛ 0 ,2 (z) denotes the k-level symbol of the cubic exponential B-spline scheme (1).…”

Section: Remarkmentioning

confidence: 99%

“…Subdivision schemes are efficient tools to generate smooth curves/surfaces from a given set of discrete control points. Over the last decades, they are shown to be important tools in many fields like CAD/CAM [1,2], wavelets [3,4], biomedical imaging [5], and isogeometric analysis [6]. According to whether the refinement rules depend on the recursion level, subdivision schemes can be divided into stationary and nonstationary schemes.…”

Section: Introductionmentioning

confidence: 99%

A Family of Binary Univariate Nonstationary Quasi‐Interpolatory Subdivision Reproducing Exponential Polynomials

Zhang

Zheng

Pan

et al. 2019

Mathematical Problems in Engineering

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In this paper, by suitably using the so-called push-back operation, a connection between the approximating and interpolatory subdivision, a new family of nonstationary subdivision schemes is presented. Each scheme of this family is a quasi-interpolatory scheme and reproduces a certain space of exponential polynomials. This new family of schemes unifies and extends quite a number of the existing interpolatory schemes reproducing exponential polynomials and noninterpolatory schemes like the cubic exponential B-spline scheme. For these new schemes, we investigate their convergence, smoothness, and accuracy and show that they can reach higher smoothness orders than the interpolatory schemes with the same reproduction property and better accuracy than the exponential B-spline schemes. Several examples are given to illustrate the performance of these new schemes.

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Converting a CAD model into a non-uniform subdivision surface

Cited by 20 publications

References 40 publications

Study of Second-Order Continuities of a Composite Surface

Study of Second-Order Continuities of a Composite Surface

Refinement for a Hybrid Boundary Representation and its Hybrid Volume Completion

A Family of Binary Univariate Nonstationary Quasi‐Interpolatory Subdivision Reproducing Exponential Polynomials

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