• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.955-982
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• 1996

In surface compression applications, one of the main issues is how to efficiently store and calculate the computer representation of certain surfaces. This leads us to consider a nonlinear approximation by box splines with free knots since, for instance, the nonlinear method based on wavelet decomposition gives efficient compression and recovery algorithms for such surfaces (cf. [12]).

• Structural Engineering and Mechanics
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• v.12 no.3
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• pp.313-328
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• 2001

A multi-span bridge has the peak value of resultant girder moment or membrane stress at the interior support. In this paper, the spline finite strip method (FSM) is modified to obtain the more appropriate solution at the interior support where the peak values of solution exist. The modification has been achieved by expressing the shape function with non-periodic B-splines which have multiple knots at the boundary. The modified B-splines have the useful feature for interpolating the curve with sudden change in curvature. Moreover, the modified spline FSM is very efficient in analyzing multi-span box girder bridges, since a bridge can be modeled by an assembly of strips extended along the entire bridge length. Numerical examples of the bridge analysis have been performed to verify the efficiency and accuracy of the new spline FSM.

• Journal of the Korea Computer Graphics Society
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• v.21 no.2
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• pp.1-10
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• 2015

In this paper, we propose an improved surface reconstruction method from an oriented point cloud. Our method is a classical least-square scheme, but is based on the 7-direction box-spline and the BCC (Body-Centered Cubic) lattice, which results in surfaces with superior quality and lower computational overhead, compared to other methods based on the B-splines on the Cartesian lattice. Specifically, when compared with two of the most popular techniques our method results in better surfaces but only takes ${\approx}53%$ computation time.

• Journal of the Korea Computer Graphics Society
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• v.18 no.4
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• pp.25-34
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• 2012

This paper presents a real-time GPU (graphics processing unit) ray casting scheme for rendering isosurfaces of BCC (body-centered cubic) volume datasets. A quartic spline field is built using the 7-direction box-spline filter accompanied with a quasi-interpolation prefilter. To obtain an interactive rendering speed on the graphics hardware, the shader code was optimized to avoid lookup table and conditional branches and to minimize data fetch overhead. Compared to previous implementations, our work outperforms the comparable one by more than 20% and the rendering quality is superior than others.

• Journal of the Korea Computer Graphics Society
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• v.19 no.2
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• pp.19-27
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• 2013

This paper presents a real-time GPU (Graphics Processing Unit) isosurface ray-caster that improves the performance by 4-7 folds from our previous method, while keeping the superior visual quality. Such an improvement is achieved by incorporating an efficient empty-space skipping scheme and an analytic normal computation. The empty-space skipping scheme is done by building an min/max octree computed from the BB(Bernslein-B$\acute{e}$zier)-form of spline pieces and the analytic normal Formula provides not only a nice visual quality but also an improved evaluation performance.

• Journal of Ship and Ocean Technology
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• v.10 no.1
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• pp.10-26
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• 2006

The radiation problem for oscillating bodies on the free surface has been formulated by the over-determined Green integral equation, where the boundary condition on the free surface is satisfied by adopting the Kelvin-type Green function and the irregular frequencies are removed by placing additional control points on the free surface surrounded by the body. The B-Spline based higher order panel method is then applied to solve the problem numerically. Because both the body geometry and the potential on the body surface are represented by the B-Splines, that is in polynomials of space parameters, the unknown potential can be determined accurately to the order desired above the constant value. In addition, the potential expressed in B-Spline can be differentiated analytically to get the velocity on the surface without introducing any numerical error. Sample computations are performed for a semispherical body and a rectangular box floating on the free surface for six-degrees of freedom motions. The added mass and damping coefficients are compared with those by the already-validated constant panel method of the same formulation showing strikingly good agreements.