Tin Plate Spline (TPS) firstly introduced by j. Duchon (1976). These days TPS have been found so many uses, as an example, geophysical applications in aeromagnetic & gravimetric surveying, modelling of fingerprints, medical researches, converting elevation contours to a grid. In this paper, we used TPS for constructing digital elevation model.
Thin plate spline is a physically based 2D interpolation witch represents a thin metal sheet that is constrained not to move at grid points and free from any external force relied upon control points from this sight it should have minimum bending energy in control points. This bending energy function is show as follow:
That represents a height in 3D model. This equation is invariant under translation, rotation, or scaling of either set of control points, support second norm of surface and when it is minima it means that bending of surface in control point got to be minimized and slope variation in tangential plates reduced to minimum.
From another point of view Thin Plate Splines as an approximation of a real surface of control point must cross this points as near as possible. Therefore a constraint of distance between control points and the surface also must have been minimized. We showed that the TPS as density independence method can be used for construction of surfaces in new brand geomatics because of miscellaneous of data sources and difference in their density’s, note that weights is always of concern of surveys. From other side using TPS, without Voronoi algorithms whereby produced limitations in number of control points and reduce speed of operation, one can create a surface in contrary to other surface simulation methods such as BSplines all at once. Because of density independence mathematical form of straigh method, one can use it in CAD/CAM softwares.
It is certain that independency of density must to be of specifications of thin plate spline thus purpose other research on other solutions of TPS. Because at least one can prove that in dense and bare zones it can be used with comparable error results. By results of this article we purpose using of TPS for mountainous-flat areas because variations of one zone don’t affect other zones so much.
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