Dyadic T-mesh subdivision

Kovacs, Denis; Bisceglio, Justin; Zorin, Denis

doi:10.1145/2766972

Cited by 19 publications

(14 citation statements)

References 36 publications

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“…One common approach to define a non‐uniform subdivision scheme is to use a heuristic way to generalize non‐uniform bi‐cubic B‐spline refinement rules to arbitrary valences, such as [SZSS98, KBZ15]. However, the subdivision matrices by these approaches cannot ensure the second and third eigenvalues to be identical, which is the necessary condition for the surface to be G 1 [PR08].…”

Section: Eigen‐polyhedramentioning

confidence: 99%

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Non‐Uniform Subdivision Surfaces with Sharp Features

Tian

Chen

2020

Computer Graphics Forum

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Sharp features are important characteristics in surface modelling. However, it is still a significantly difficult task to create complex sharp features for Non‐Uniform Rational B‐Splines compatible subdivision surfaces. Current non‐uniform subdivision methods produce sharp features generally by setting zero knot intervals, and these sharp features may have unpleasant visual effects. In this paper, we construct a non‐uniform subdivision scheme to create complex sharp features by extending the eigen‐polyhedron technique. The new scheme allows arbitrarily specifying sharp edges in the initial mesh and generates non‐uniform cubic B‐spline curves to represent the sharp features. Experimental results demonstrate that the present method can generate visually more pleasant sharp features than other existing approaches.

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Section: Eigen‐polyhedramentioning

confidence: 99%

“…For this purpose, [SZSS98] introduced the first NURBS‐compatible non‐uniform subdivision scheme. And later this scheme was improved by many researchers [MRF06, Urs09, MFR*10, KBZ15, LFS16]. In order to create non‐uniform sharp features, a general approach is to set some knot intervals to be zeros [SZSS98, KSD14b, ZML15].…”

Section: Introductionmentioning

confidence: 99%

Non‐Uniform Subdivision Surfaces with Sharp Features

Tian

Chen

2020

Computer Graphics Forum

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“…The importance of this aspect for prominent use cases of quad layouts is well known [LRL06, ACSD*03, CSAD04, CIE*16]. Depending on the application, it serves maximizing surface approximation quality [D'A00], minimizing normal noise and aliasing artefacts [BK01], optimizing element planarity [LXW*11] or achieving smooth curvature distribution (due to their tensor‐product nature common spline surface representations are prone to ripples (curvature oscillations) if aligned badly [KBZ15]). Besides, principal direction alignment can also be of interest for aesthetic reasons.…”

Section: Foundationsmentioning

confidence: 99%

Partitioning Surfaces Into Quadrilateral Patches: A Survey

Campen

2017

Computer Graphics Forum

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The efficient and practical representation and processing of geometrically or topologically complex shapes often demands a partitioning into simpler patches. Possibilities range from unstructured arrangements of arbitrarily shaped patches on the one end, to highly structured conforming networks of all‐quadrilateral patches on the other end of the spectrum. Due to its regularity, this latter extreme of conforming partitions with quadrilateral patches, called quad layouts, is most beneficial in many application scenarios, for instance enabling the use of tensor‐product representations based on splines or Bézier patches, grid‐based multi‐resolution techniques and discrete pixel‐based map representations. However, this type of partition is also most complicated to create due to the strict inherent structural restrictions. Traditionally often performed manually in a tedious and demanding process, research in computer graphics and geometry processing has led to a number of computer‐assisted, semi‐automatic, as well as fully automatic approaches to address this problem more efficiently. This survey provides a detailed discussion of this range of methods, treats their strengths and weaknesses and outlines open problems in this field of research.

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“…To construct a global parametric spline mesh for arbitrary topology, the local refinement of T-splines was investigated in Sederberg et al (2004), Scott et al (2012). Kovacs et al (2015), Campen and Zorin (2017) presented efficient algorithms for building discrete conformal similarity maps and developed an algorithm to build a global T-mesh. Ying et al (2006) developed the manifold T-spline, using global conformal parameterizations.…”

Section: Introductionmentioning

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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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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Dyadic T-mesh subdivision

Cited by 19 publications

References 36 publications

Non‐Uniform Subdivision Surfaces with Sharp Features

Non‐Uniform Subdivision Surfaces with Sharp Features

Partitioning Surfaces Into Quadrilateral Patches: A Survey

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

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