A survey on the local refinable splines

Li, Xin; Chen, FaLai; Kang, Hongmei; Deng, Jiansong

doi:10.1007/s11425-015-5063-8

Cited by 25 publications

(11 citation statements)

References 80 publications

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“…Note that the same property holds between bases Q 0 and A 1 in the test T 0 , which implies that the solution in T 0 Q0,A1 is expressed by Eq. (28), and by adding the property of degree elevation Eq. (29), we can conclude that the solution in T 0 Q0,A2 is given by Eq.…”

Section: Results and Discussion Of Patch Testsmentioning

confidence: 99%

Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub‐ and super‐geometric analysis to Geometry‐Independent Field approximaTion (GIFT)

Atroshchenko

Tomar

et al. 2018

Numerical Meth Engineering

106

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This paper presents an approach to generalize the concept of isogeometric analysis by allowing different spaces for the parameterization of the computational domain and for the approximation of the solution field. The method inherits the main advantage of isogeometric analysis, ie, preserves the original exact computer-aided design geometry (for example, given by nonuniform rational B-splines), but allows pairing it with an approximation space, which is more suitable/flexible for analysis, for example, T-splines, LR-splines, (truncated) hierarchical B-splines, and PHT-splines. This generalization offers the advantage of adaptive local refinement without the need to reparameterize the domain, and therefore without weakening the link with the computer-aided design model. We demonstrate the use of the method with different choices of geometry and field spaces and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for nonnested spaces.

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Section: Results and Discussion Of Patch Testsmentioning

confidence: 99%

Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub‐ and super‐geometric analysis to Geometry‐Independent Field approximaTion (GIFT)

Atroshchenko

Tomar

et al. 2018

Numerical Meth Engineering

106

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“…An extraordinary control point and its corresponding extraordinary region are show in the figure. To evaluate the surface in extraordinary region, special treatment has to be applied [25]. In the very first definition of T-splines, a subdivision rule is applied to evaluate the surface in extraordinary region.…”

Section: T-spline Surface With Extraordinary Control Pointsmentioning

confidence: 99%

Five-Axis Tool Path Generation of Injection Mold Represented by T-Spline Surface

Shang

Shen

et al. 2020

Advances in Polymer Technology

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Injection molding is widely used in industries to produce polymeric products. At present, compound NURBS surfaces are commonly used to represent freeform surfaces in mold models. This work uses T-spline surface with extraordinary control points instead of NURBS to represent freeform surfaces in mold models. Compared with NURBS, T-splines’ higher-order continuity facilitates the mold quality control especially at the patch boundary. And, its patch layout information can be utilized for tool path planning. We propose an algorithm to determine the patch processing order and generate nonretraction tool path for T-spline surface models. The tool paths are generated patch by patch using isoparametric strategy. Actual machining and injection molding experiments have been conducted. The result shows the feasibility of the proposed method, and the final product is in good quality.

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“…C 1 ‐ or C 2 ‐continuous local refinable splines defined on hierarchical data structures are often used for isogeometric analysis [DCL∗08, BLE∗14, LCKD16]. Fuchs et al [FBHD17] use them for volume rendering and report runtimes of 38 milliseconds for around 256000 cells.…”

Section: Related Workmentioning

confidence: 99%

Interactive Visualization of Flood and Heavy Rain Simulations

Cornel

Buttinger‐Kreuzhuber

Konev

et al. 2019

Computer Graphics Forum

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In this paper, we present a real‐time technique to visualize large‐scale adaptive height fields with C ‐continuous surface reconstruction. Grid‐based shallow water simulation is an indispensable tool for interactive flood management applications. Height fields defined on adaptive grids are often the only viable option to store and process the massive simulation data. Their visualization requires the reconstruction of a continuous surface from the spatially discrete simulation data. For regular grids, fast linear and cubic interpolation are commonly used for surface reconstruction. For adaptive grids, however, there exists no higher‐order interpolation technique fast enough for interactive applications. Our proposed technique bridges the gap between fast linear and expensive higher‐order interpolation for adaptive surface reconstruction. During reconstruction, no matter if regular or adaptive, discretization and interpolation artifacts can occur, which domain experts consider misleading and unaesthetic. We take into account boundary conditions to eliminate these artifacts, which include water climbing uphill, diving towards walls, and leaking through thin objects. We apply realistic water shading with visual cues for depth perception and add waves and foam synthesized from the simulation data to emphasize flow directions. The versatility and performance of our technique are demonstrated in various real‐world scenarios. A survey conducted with domain experts of different backgrounds and concerned citizens proves the usefulness and effectiveness of our technique.

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A survey on the local refinable splines

Cited by 25 publications

References 80 publications

Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub‐ and super‐geometric analysis to Geometry‐Independent Field approximaTion (GIFT)

Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub‐ and super‐geometric analysis to Geometry‐Independent Field approximaTion (GIFT)

Five-Axis Tool Path Generation of Injection Mold Represented by T-Spline Surface

Interactive Visualization of Flood and Heavy Rain Simulations

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