Constrained Visualization Using the Shepard Interpolation Family

Brodlie, Ken; Asim, Muhammed Rafiq; Unsworth, K.

doi:10.1111/j.1467-8659.2005.00903.x

Cited by 43 publications

(31 citation statements)

References 13 publications

(11 reference statements)

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“…In cases where these methods are applied on an island, they do not perform an interpolation and the whole island takes exactly the same elevation. This is known as the flat-problem (Floater & Iske 1996;Maisuradze & Thompson 2003;Brodlie & Asim 2005).…”

Section: Inverse Distance Weighted (Idw) Methodsmentioning

confidence: 99%

The Inverse Distance Weighted interpolation method and error propagation mechanism – creating a DEM from an analogue topographical map

Achilleos

2011

Journal of Spatial Science

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Interpolation procedures are widely used in science, especially in sciences that involve spatial data and continuous phenomena that can be depicted on a continuous spatial surface. Interpolation makes use of accurate and qualitative sampling data in order to produce a continuous representation of the phenomenon in question. The accuracy of the data used for interpolation directly affects the results. This research examines error propagation within the Inverse Distance Weighted (IDW) method, applied as a means of representing the earth's relief. Interpolation of a DEM within contours on a topographical map is considered to be a three-stage procedure. The first stage is the digitising of the contours depicted on the analogue map. Errors involved in this stage are propagated to the second stage, the geometric transformation of coordinates of these digitised contours. Additional errors due to the application of the transformation model are embedded within the results thus obtained. Finally, the errors are propagated to the third stage. Errors are magnified due to the application of an interpolation method, in our case, the IDW method. Any stage of the procedure can be considered separately. The procedure aims to cover the situation where a DEM is created using an analogue topographical map in conjunction with the IDW interpolation method.

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Section: Inverse Distance Weighted (Idw) Methodsmentioning

confidence: 99%

The Inverse Distance Weighted interpolation method and error propagation mechanism – creating a DEM from an analogue topographical map

Achilleos

2011

Journal of Spatial Science

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“…This paper examines the problem of shape preservation of positive data sets. In recent years, various authors have worked in the area of shape preservation [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In this paper, the shape preserving interpolation has been discussed for positive data, using rational cubic spline.…”

Section: Introductionmentioning

confidence: 99%

Visualization of Positive Data by Rational Cubic Spline Interpolant

Sarfraz

Hussain

Shaikh

2010

2010 14th International Conference Information Visualisation

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This paper discusses the problem of constructing positive cubic spline interpolation. To obtain smooth curve for positive data, piecewise rational cubic function has been used. In the description of rational interpolant, two families of parameters have been constrained to preserve positive shape of the data, the rational spline scheme has a unique representation. In addition, to preserve the shape of positive data sets, the degree of smoothness attained is 2 C .

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“…Xiao and Woodbury [7] look at several meshless methods for constrained scattered data interpolation for 3D data. For Shepard, Brodile et al [8] discussed the modified quadratic Shepard method, which interpolates scattered data of any dimensionality, can be constrained to preserve positivity.…”

Section: Introductionmentioning

confidence: 99%

A new approach for shape preserving interpolating curves

2011

Computers & Mathematics with Applications

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a b s t r a c tIn this paper, we present an new approach to construct the so-called shape preserving interpolation curves. The basic idea is first to approximate the set of interpolated points with a class of MQ quasi-interpolation operators and then pass through the set with the use of multivariate interpolation by using compactly supported radial basis functions. This approach possesses the advantages of certain shape preserving and good approximation behaviors. The proposed algorithm is easy to implement.

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Constrained Visualization Using the Shepard Interpolation Family

Abstract: Abstract

Cited by 43 publications

References 13 publications

The Inverse Distance Weighted interpolation method and error propagation mechanism – creating a DEM from an analogue topographical map

The Inverse Distance Weighted interpolation method and error propagation mechanism – creating a DEM from an analogue topographical map

Visualization of Positive Data by Rational Cubic Spline Interpolant

A new approach for shape preserving interpolating curves

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