The effect of interpolation methods in surface definition: an experimental study

Abstract

Mappings of the earth surface and their representation in 3D (three-dimensional) models are commonly used in most recent research. Modeling research, which starts with classical surveying methods, acquires new dimensions matching the modern technologies. 3D models of any object or earth surface can be used in much visual and scientific research. A digital model of the landscape is an important part within creation of geo-information systems used in the public administration and in the commercial sphere. It is an important tool in applications such as geomorphology, hydrology, geology, cartography, ecology, mining etc.Values of volume in terrains that do not have regular geometric structure can be obtained more accurately by using 3D models of surfaces with respect to developing technology. Basic data of 3D models must indicate 3D coordinates of the surveyed object in the reference frame. Distribution and intensity of points are important factors in modeling earth surfaces. A minimum number of points is desired in defining an object in 3D. Interpolation methods employing different mathematical models are used to obtain 3D models of terrain surfaces. In this study, the effect of interpolation methods in defining a terrain surface is investigated. For this purpose, a uniform surface, hill-shaped artificial object with a known volume is employed. The 3D surface and volume are calculated by using 12 different interpolation methods. Point distribution, point intensity and accuracy of point measurements are not considered. The same data set was used for all the interpolation methods. The interpolation methods are compared and evaluated based on the results.Minimum curvature interpolation was used by Briggs (1974) to interpolate gravity values on the corners of a regular grid using scattered gravity data and finally to produce a contour map. The theory of minimum curvature interpolation, which is a gridding method, is based on minimization of the total curvature at the grid points. The total square curvature of a surface is defined as C z z xThe effect of interpolation methods in surface definition: an experimental study 1351

Credibility of 3D Volume Computation Using GIS for Pit Excavation and Roadway Constructions

“…Polynomial is not really an interpolator because it does not attempt to predict unknown Z values (Yilmaz, 2007). The trend surface changes gradually and captures coarse-scale patterns in the data.…”

Geomorphological reconstruction and morphometric modelling applied to past volcanism

“…), the terrain properties and the purpose of digital modelling (Baldi et al 2006;Szekely and Karatson 2004;Yilmaz 2007). Different interpolation methods can be used to model a regular grid of raster values from data in an input contour map.…”

Regional scale analysis of landform configuration with base-level (isobase) maps

“…Using contours as a source for elevation (resembling the manual method) instead of using all the elevation values along the stream lines might sound as an unnecessary complication, but our experience shows it provides better results. As with any interpolation procedure, one must avoid clusters of data points and use, whenever possible, points with a uniform distribution over the target area in order to prevent interpolation artifacts (Chaplot et al, 2006;Berry, 1997;Yilmaz, 2007;Yue et al, 2007). Extracting the elevation from the intersection of streams and contours yields a smaller number of points to be interpolated, without clusters along streams.…”