• East Asian mathematical journal
• /
• 제29권1호
• /
• pp.53-68
• /
• 2013

We solve the geometric Hermite interpolation problem with planar Pythagorean-hodograph cubics. For every Hermite data, we determine the exact number of the geometric Hermite interpolants and represent the interpolants explicitly. We also present a simple criterion for determining whether the interpolants have a loop or not.

• Journal of applied mathematics & informatics
• /
• 제28권1_2호
• /
• pp.131-141
• /
• 2010

In this paper, we propose a new method to obtain $C^1$ MPH quartic Hermite interpolants generically for any $C^1$ Hermite data, by using the speed raparametrization method introduced in [16]. We show that, by this method, without extraordinary processes ($C^{\frac{1}{2}}$ Hermite interpolation introduced in [13]) for non-admissible cases, we are always able to find $C^1$ Hermite interpolants for any $C^1$ Hermite data generically, whether it is admissible or not.

• 호남수학학술지
• /
• 제15권1호
• /
• pp.121-127
• /
• 1993

• 대한수학회논문집
• /
• 제9권4호
• /
• pp.809-817
• /
• 1994

• Journal of applied mathematics & informatics
• /
• 제30권3_4호
• /
• pp.381-393
• /
• 2012

In this paper, we show two ways of the time reparametrization of piecewise Pythagorean-hodograph $C^1$ Hermite interpolants. One is the time reparametrization with no shape change, and the other is that with shape change. We show that the first reparametrization does not depend on the boundary data and that it is uniquely determined by the size of parameter domain, up to the general cases. We empirically show that the second parametrization can cause the change of the shape of interpolant.

• 대한수학회지
• /
• 제33권4호
• /
• pp.955-982
• /
• 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]).

• Kyungpook Mathematical Journal
• /
• 제48권4호
• /
• pp.665-684
• /
• 2008

Runge-Kutta-Nystr$\"{o}$m (RKN) methods provide a popular way to solve the initial value problem (IVP) for a system of ordinary differential equations (ODEs). Users of software are typically asked to specify a tolerance ${\delta}$, that indicates in somewhat vague sense, the level of accuracy required. It is clearly important to understand the precise effect of changing ${\delta}$, and to derive the strongest possible results about the behaviour of the global error that will not have regular behaviour unless an appropriate stepsize selection formula and standard error control policy are used. Faced with this situation sufficient conditions on an algorithm that guarantee such behaviour for the global error to be asympotatically linear in ${\delta}$ as ${\delta}{\rightarrow}0$, that were first derived by Stetter. Here we extend the analysis to cover a certain class of ODEs with low-order derivative discontinuities, and the class of ODEs with constant delays. We show that standard error control techniques will be successful if discontinuities are handled correctly and delay terms are calculated with sufficient accurate interpolants. It is perhaps surprising that several delay ODE algorithms that have been proposed do not use sufficiently accurate interpolants to guarantee asymptotic proportionality. Our theoretical results are illustrated numerically.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 1991년도 봄 학술발표회 논문집
• /
• pp.15-19
• /
• 1991

An attempt has been made to generate a cured boundary by using a transfinite interpolation technique. In the following sections, it will be shown how to construct transfinite interpolants both in h-version and in p-version over polygonal and nonpolygonal regions. Numerirical test cases validate the applicability and superior capability with the help of several structural problem.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제1권1호
• /
• pp.1-34
• /
• 1997

In this study, various available meshless methods are briefly reviewed and the connection among them is investigated. The objective of meshless methods is to eliminate some difficulties which are originated from reliance on a mesh by constructing the approximation entirely in terms of nodes. Especially, focusing on Element Free Galerkin Method(EFGM) based on moving least square interpolants(MLSI), a new implementation is developed based on a variational principle with penalty function method were used to enforce the essential boundary condition. In addition, the weighted orthogonal basis functions are constructed to overcome disadvantage of MLSI.

• 대한원격탐사학회:학술대회논문집
• /
• 대한원격탐사학회 1999년도 Proceedings of International Symposium on Remote Sensing
• /
• pp.171-176
• /
• 1999

Intelligent schemes for an automatic generation of DEM (digital elevation model) are implemented. The need for these post-processing schemes is that interpolation alone produces severe blunders, however sophisticated it is. These blunders occur most seriously along the boundaries of a scene, over rivers, and along the coast. Even a state-of-the-art commercial software retains such blunders. The intelligent schemes implemented are (1) center-of-gravity and empty-center-index which quantify how evenly distributed interpolants are within in interpolation radius. (2) a segmentation scheme to discern whether or not an empty segment in stereo-match results should be interpolated, and (3) a segmentation scheme for removing noise-like features, with these methods, in the final DEM, identical coastline and river region to those in the original SPOT scenes are achieved. The DEM exhibits substantial improvements over the products of an existing commercial software.