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In this study, some stochastic and deterministic models have been proposed for the assessment of the regularity and isotropy of geodetic point patterns. These models utilized realized point configurations within a rectangular window, leaning on stochastic geometry. As an illustrative example, the geographical extent of the Egyptian Territory was selected as a test window. The proposed models have agreed with the visual and qualitative characteristics of the investigated patterns. Also, it has been found that the stochastic and deterministic models for regularity and isotropy have very strong mutual correlation coefficients. Furthermore, the proposed models were applied to some geoid interpolation algorithms. In particular, the relationships among the data/check point distributions and the geoid interpolation accuracies, were investigated. Finally, a closed expression was proposed, which efficiently describes the relations among such features. So, it is recommended to use such approach for the pre-analysis and planning of the geographic distributions of point patterns in similar and other geodetic applications.

Models for assessing the spatial distribution of geodetic point patterns: application to geoid prediction quality