Shape preserving interpolation by space curves

It is shown that, depending upon the orientation of the end tangents t 0 , t 1 relative to the end point displacement vector p = p 1 − p 0 , the problem of G 1 Hermite interpolation by PH cubic segments may admit zero, one, or two distinct solutions. For cases where two interpolants exist, the bending energy may be used to select among them. In cases where no solution exists, we determine the minimal adjustment of one end tangent that permits a spatial PH cubic Hermite interpolant. The problem of assigning tangents to a sequence of points p 0 , . . . , p n in R 3 , compatible with a G 1 piecewise-PH-cubic spline interpolating those points, is also briefly addressed. The performance of these methods, in terms of overall smoothness and shape-preservation properties of the resulting curves, is illustrated by a selection of computed examples.

show abstract

“…, n according to some established scheme. A typical scheme [16] is to specify s k as a weighted combination of T k and T k+1 ,…”

Section: Interpolating a Sequence Of Pointsmentioning

confidence: 99%

Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics

et al. 2005

View full text Add to dashboard Cite

show abstract

“…As an example, The data in Table 1 is shown in Figure 3 as a curve that can be expressed with the formula in Equation (5): f(x) = 586.6e°009695x +1 .309eOol047 (5) Let df(x)/dx=O, and we obtain the optimal value for x=299. Setting g-299x299, we run the LU application with the same settings as those in Table 1, and we get TfOtaf=58.458(Seconds), which is less than all the sample Ttotai values shown in Table 1.…”

Section: Obtaining G* Through Curve Fittingmentioning

confidence: 99%

“…And then, we evaluate the variation of g* after taking away some CPU power (c) and network bandwidth (b). 5.4.1. The impacts of s and n on g*.…”

Section: Obtaining G* Through Curve Fittingmentioning

confidence: 99%

“…Correspondingly, Figure 5 shows the results of the experiment with 12 work nodes. The curves shown in these two figures are obtained by applying shape-preserving interpolation [5] on the sample data. Both Figures 4 and 5 show that * TC.,p increases with g. The reason is that a larger g causes more cache misses, which leads to more computation time.…”

Section: Obtaining G* Through Curve Fittingmentioning

confidence: 99%

See 1 more Smart Citation

Exploiting the advantages of object-based DSM in a heterogeneous cluster environment

Liu

Jiang

Soh

2005

CCGrid 2005. IEEE International Symposium on Cluster Computing and the Grid, 2005.

View full text Add to dashboard Cite

In recent years, increasing effort has been made by the cluster and grid computing community to build object-based Distributed Shared Memory systems (DSM) in a cluster environment. In most ofthese systems, a shared object is simply used as a data-exchanging unit so as to alleviate the false-sharing problem, and the advantages ofsharing objects remain to be fully exploited. Thus, this paper is motivated to investigate the potential advantages ofobject-based DSM. For example, the performance ofa distributed application may be significantly improved by adaptively andjudiciously setting the size of the sharedobjects, i.e., granularity. This paper, in addition to investigating the advantages of sharing objects, particularly focuses on observing how the performance of a distributed application changes with varied granularity, obtaining the optimal granularity through curvefitting, studying the factors that affect the optimal granularity, and predicting this optimal granularity in a changing runtime environment.

show abstract

“…Interpolation or approximation methods which guarantee the preservation of the shape of the data are of interest in such applications and have received a significant attention in the last decades. They are referred to as shape preserving methods, see [12] and references therein. Usually, a shape preserving method is based on a suitable space of functions (like exponentials, rationals, variable degree polynomials, etc.)…”

Section: Introductionmentioning

confidence: 99%

Shape preserving $$HC^2$$ H C 2 interpolatory subdivision

et al. 2015

View full text Add to dashboard Cite

A subdivision procedure is developed to solve a C 2 Hermite interpolation problem with the further request of preserving the shape of the initial data. We consider a specific non-stationary and non-uniform variant of the Merrien HC 2 subdivision family, and we provide a data dependent strategy to select the related parameters which ensures convergence and shape preservation for any set of initial monotone and/or convex data. Each step of the proposed subdivision procedure can be regarded as the midpoint evaluation of an interpolating function-and of its first and second derivatives-in a suitable space of C 2 functions of dimension 6 which has tension properties. The limit function of the subdivision procedure is a C 2 piecewise quintic polynomial interpolant.

show abstract

Shape preserving interpolation by space curves

Cited by 34 publications

References 9 publications

Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics

Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics

Exploiting the advantages of object-based DSM in a heterogeneous cluster environment

Shape preserving $$HC^2$$ H C 2 interpolatory subdivision

Contact Info

Product

Resources

About