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Summary The paper deals with the general theory of equivalent projection. By specifying the results derived, special cases may be treated. Examples of methods are described which enable free functions to be found in a general solution. A detailed procedure of solving the problem with a numerical example is given, taking into account the optimization according to the global criterton, established for extreme angular distortion.
Dedicated to Professor Frantiek Fiala on the Centenary of his Birthday 相似文献
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Dedicated to Professor Frantiek Fiala on the Centenary of his Birthday 相似文献
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Jozef Minár Marián Jenčo Ian S. Evans Jozef Minár Jr. Martin Kadlec Jozef Krcho 《International journal of geographical information science》2013,27(7):1381-1402
Third-order geomorphometric variables (based on third derivatives of the altitudinal field) have been neglected in geomorphometry, but their application to the delimitation of surface objects will lead to their increasing significance in future. New techniques of computation, presented and evaluated here, facilitate their use. This paper summarizes recent knowledge concerning definition, computation and geomorphologic interpretation of these variables. Formulae defining various third-order variables are unified based on the physical definition of slope gradient. Methods for their computation are compared from the point of view of method error and error generated by digital elevation model (DEM) inaccuracy. For exact mathematical test surfaces, the most natural and simple variant of the method of central differences (CD2) shows a method error 2–3 times smaller than the other methods used recently in geomorphometry. However, success in coping with DEM inaccuracy depends (for a given grid mesh) on the number and weighting of points from which the derivative is computed. This was tested for surfaces with varying degrees of random error. Here least squares-based methods are the most effective for mixed derivatives (especially for finer grids and less accurate DEMs), while a variant of the CD method, that repeats numerical evaluation of first derivatives (CD1), is the most successful for derivatives in cardinal directions. The CD2 method is generally the most successful for coarser grids where the method error is dominant. Utilization of third-order variables is documented from examples of terrain feature (ridge, valley and edge) extraction and from a first statistical test of the hypothesis that real segments of the land surface have a tendency to a constant value of some morphometric variable. For detection of (sharp) ridges and valleys, it is shown that the rate of change of tangential curvature is inadequate: rate of change of normal curvature is also required. A basic confirmation of the constant-value tendency is provided. 相似文献
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