Minimal Distance between One Geoset and Another Obtained by Transforming the Coordinates of the First

Eliminating Influences of Position and Dimensions from Minimal Distance


In this chapter we deal briefly with several problems, related in part to those discussed in Chapter 12: (a) Given a geoset gG, we transform the coordinates of its elements by parallel translation, dilatation of deviations from the center, rotation, reflection, or other changes of position and dimensions and thus obtain a new geoset gJ; we then investigate the minimal distance between gG and gJ. (b) Considering a pair of geosets gG and gJ we study how m\( \bar D \)(G, J) and m\( \ddot D \)2(G, J) change when we transform the coordinates of both geosets in the same way.


Minimal Distance Arithmetic Average Parallel Translation Optimal Transportation Standard Distance 
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© Kluwer Academic / Plenum Publishers 1999

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