A universal parametrization in B-spline curve and surface interpolation

Lim, Choong-Gyoo

doi:10.1016/s0167-8396(99)00010-2

Cited by 58 publications

(27 citation statements)

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“…Several methods are available to perform such interpolation but each comes at an expense of accuracy or the inability to handle large-scale datasets. Shene *** compares the performance of various interpolation methods, and from all the sampled methods, the Universal Method 16 was chosen to be a very convenient approach for B-Spline Interpolation. As opposed to a traditional approach of B-Spline interpolation where parameters are first determined, then followed by the computation of knot vectors, the Universal method prescribes the use of uniformly spaced knots for the computation of the parameters.…”

Section: B Non-linear Discretizationmentioning

confidence: 99%

An Approach to Convert Vertex-Based 3D Representations to Combinatorial B-Splines for Real-Time Visual Collaboration

Kalivarapu

Winer

2005

43rd AIAA Aerospace Sciences Meeting and Exhibit

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approach to convert vertex-based 3D representations to combinatorial B-splines for realtime visual collaboration" (2005). Mechanical Engineering Conference Presentations, Papers, and Proceedings. 160. http://lib.dr.iastate.edu/me_conf/160 An approach to convert vertex-based 3D representations to combinatorial B-splines for real-time visual collaboration Abstract Scientific Visualization and Virtual Reality are increasingly being used for the design of complex systems. These technologies offer powerful capabilities to make decisions that are cost and time effective. The next logical extension is to collaborate with these visual models in real-time, where parts of a design team are geographically separated. Specifically, visual collaboration enables ideas and proposed changes to be discussed exactly on a virtual model of a product. However, high-end visualization hardware and Internet technologies impede widespread use of real-time visual collaboration due to the large amount of data from which these representations are created. These data are typically in the form of 3D vertex-based models, which offer a high degree of realism when displayed, but at a price of storage, rendering speeds and processing efficiency. The more realistic the representation desired, the larger the number of vertices required and hence the higher the file size. In this paper, we propose a new data modeling and handling technique where traditional vertex-based models are converted into combinatorial B-Spline based wire-frame models that allow realtime visual collaboration in the context of typical virtual reality systems. Using appropriate filtering methods, parametric equations are computed for each curved segment in a vertexbased representation and bundled together with sampled linear segments of the model. The computed parametric equation based models occupy only a fraction of the size when compared to the original vertex-based models. These lightweight models can easily be transmitted over the Internet, in real-time, for viewing with a platform independent visual client program. The proposed methods were tested on several example data files to prove the method's effectiveness. KeywordsVirtual Reality Applications Center, data modeling, vertex-based models, virtual reality Scientific Visualization and Virtual Reality are increasingly being used for the design of complex systems. These technologies offer powerful capabilities to make decisions that are cost and time effective. The next logical extension is to collaborate with these visual models in real-time, where parts of a design team are geographically separated. Specifically, visual collaboration enables ideas and proposed changes to be discussed exactly on a virtual model of a product. However, high-end visualization hardware and Internet technologies impede widespread use of real-time visual collaboration due to the large amount of data from which these representations are created. These data are typically in the form of 3D vertex-based models, which offer a high degree of re...

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Section: B Non-linear Discretizationmentioning

confidence: 99%

An Approach to Convert Vertex-Based 3D Representations to Combinatorial B-Splines for Real-Time Visual Collaboration

Kalivarapu

Winer

2005

43rd AIAA Aerospace Sciences Meeting and Exhibit

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“…Therefore, two parametric values are redundant and the knot vector selection can be arbitrary. Lim [15] indicated through his experimentations that knot vector selection similar to parameter values provides more natural looking curves. In this study, the same concept is adopted for the evaluation of spline curves and the knot vectors T i 's are selected as follows:…”

Section: Unequally Spaced Knot Vectorsmentioning

confidence: 99%

Unequally spaced non‐periodic B‐spline finite strip method

Choi

Hong

Kim

2003

Numerical Meth Engineering

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SUMMARYThe unequally spaced non-periodic B-spline ÿnite strip method (FSM) is presented. The motivation to investigate the irregularly spaced interior nodes in the longitudinal direction of strip is to generalize the concept of non-periodic B-spline FSM and to improve the general accuracy of the stress evaluation in the region of high stress gradients. In the present paper, the unequally spaced non-periodic B3-spline series with multiple knots at the boundary are introduced for the interpolation of displacement and description of geometry in the formulation of isoparametric spline FSM. The use of multiple knots at the boundary makes the shape function satisfy the Kronecker delta properties at the boundary. The unequally spaced B-spline FSM is applied to the stress-reduced shell problem with six degrees of freedom per node. The main purpose of this study is to ÿnd a way of ensuring that the geometry of strip is appropriately approximated when the interior nodes of the strip are not regularly spaced along the longitudinal direction. Some numerical results have been compared with those of the previous studies to evaluate the accuracy and e ciency of this method.

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“…This situation arises due to the inevitable process of progressive merging of different knot vectors to make the B-spline curves compatible. The novelty of the present approach lies in its use of universal parameterization, allowing the knots to be selected freely (Jung, 1998;Lim, 1999;Jung et al, 2000). Since the universal parameterization permits that the number of control points in v-direction is equal to the number of contours, the proposed approach can realize efficient data reduction and provide a compact representation of B-spline surface, retaining the desired surface shape.…”

Section: Introductionmentioning

confidence: 99%

An interpolation method of b-spline surface for hull form design

Jung¹

2010

International Journal of Naval Architecture and Ocean Engineeri

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A universal parametrization in B-spline curve and surface interpolation

Cited by 58 publications

References 0 publications

An Approach to Convert Vertex-Based 3D Representations to Combinatorial B-Splines for Real-Time Visual Collaboration

An Approach to Convert Vertex-Based 3D Representations to Combinatorial B-Splines for Real-Time Visual Collaboration

Unequally spaced non‐periodic B‐spline finite strip method

An interpolation method of b-spline surface for hull form design

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