Interpolation pdf

Error of spline sine function interpolation. Error ofNN arbitrary curve interpolation. Error of spline arbitrary The encountered values are shown in Table 2. Experiment two To test the algorithm, a patch of a sphere was used. To train the net, a series of equally spaced points was used as input vector. Point spacing was 1. Tests were performed with a non-homogeneous grid with.

The resulting error is shown in fig. Elapsed processor time for each case. Tests were made using Matlab v 4. Comparisons were made against spline interpolation of functions, because it is a well established industry procedure, used widely in the auto and die-cast shops. The shape of error is relevant. Both types of approximation show similar features: Peak error occurs in the extremes of the interval and periodic behaviour is present.

Peak error can be due to the fact that the algorithms used did not take into account the functions first derivative value at interval ends. The NN approach shows longer periods than splines with better peak values. The time needed for completing a whole mesh is considerable smaller using NNs, because of their two-dimensional interpolation capability. These properties make NN approximation of functions interesting from the shop floor point of view.

This approach lends itself to better finished pieces because of smoother error behaviour. A set of programs was developed for an environment suitable for CNC shop. They are intended for all the process. The set is already running and suits superbly in a networked shop, where the fmal DIN language programs are relatively a minor part of overall traffic. Mathematics and Applications" J. Bose, N. York, Coons, S. Hagan, M.

Orr, M. Edinburgh University, Related Papers Adaptable geometric patterns for five-axis machining: a survey By Dr. Stanislav S. Introduction 1. Method: In this paper, we propose an edge-directed interpolation EDI method and apply it on a group of fetal spine MR images to evaluate its feasibility and perfo. Join Co-production practitioners network. Sign Up or Sign In. Powered by. Badges Report an Issue Terms of Service. Co-production practitioners network A network for co-production practitioners.

Blogs Forum. Co-production Email Dige. New edge directed interpolation pdf writer. Add a Comment You need to be a member of Co-production practitioners network to add comments! Kriging is most appropriate when you know there is a spatially correlated distance or directional bias in the data. It is often used in soil science and geology.

The predicted values are derived from the measure of relationship in samples using sophisticated weighted average technique. It uses a search radius that can be fixed or variable.

The generated cell values can exceed value range of samples, and the surface does not pass through samples. Kriging is similar to IDW in that it weights the surrounding measured values to derive a prediction for an unmeasured location. The general formula for both interpolators is formed as a weighted sum of the data:.

However, with the kriging method, the weights are based not only on the distance between the measured points and the prediction location but also on the overall spatial arrangement of the measured points.

To use the spatial arrangement in the weights, the spatial autocorrelation must be quantified. The following sections discuss how the general kriging formula is used to create a map of the prediction surface and a map of the accuracy of the predictions.

Ordinary kriging assumes the model. One of the main issues concerning ordinary kriging is whether the assumption of a constant mean is reasonable. Sometimes there are good scientific reasons to reject this assumption. However, as a simple prediction method, it has remarkable flexibility. Ordinary kriging can use either semivariograms or covariances , use transformations and remove trends , and allow for measurement error.

Simple kriging assumes the model. Simple kriging can use either semivariograms or covariances , use transformations , and allow for measurement error.

Universal kriging assumes the model. Universal kriging can use either semivariograms or covariances, use transformations , and allow for measurement error. Indicator kriging assumes the model.

The creation of binary data may be through the use of a threshold for continuous data, or it may be that the observed data is 0 or 1. For example, you might have a sample that consists of information on whether or not a point is forest or nonforest habitat, where the binary variable indicates class membership. Using binary variables, indicator kriging proceeds the same as ordinary kriging. Indicator kriging can use either semivariograms or covariances.

Probability kriging assumes the model. Probability kriging strives to do the same thing as indicator kriging, but it uses cokriging in an attempt to do a better job.

Probability kriging can use either semivariograms or covariances , cross-covariances , and transformations , but it cannot allow for measurement error.

Disjunctive kriging assumes the model. In Geostatistical Analyst, you can predict either the value itself or an indicator with disjunctive kriging. In general, disjunctive kriging tries to do more than ordinary kriging. While the rewards may be greater, so are the costs. Disjunctive kriging requires the bivariate normality assumption and approximations to the functions f i Z s i ; the assumptions are difficult to verify, and the solutions are mathematically and computationally complicated.

Disjunctive kriging can use either semivariograms or covariances and transformations , but it cannot allow for measurement error. A method that is similar to IDW, the PointInterp function allows more control over the sampling neighborhood. Points outside the neighborhood have no influence.

The weighted value of points inside the neighborhood is calculated using an inverse distance weighted interpolation or inverse exponential distance interpolation. This method interpolates a raster using point features but allows for different types of neighborhoods. Neighborhoods can have shapes such as circles, rectangles, irregular polygons, annuluses, or wedges.

Trend is a statistical method that finds the surface that fits the sample points using a least-square regression fit. It fits one polynomial equation to the entire surface.