Application of the method of sorting Schwartzian transform in the computational geometry

The article discusses the use of Schwartzian transform sorting applied to computational geometry objects. In computer science, the Schwartzian transform is a Perl programming idiom used to improve the efficiency of sorting a list of items. This idiom is appropriate for comparison-based sorting when the ordering is actually based on the ordering of a certain value of the elements of array, where computing this value is an intensive operation that should be performed a minimal number of times. The Schwartzian Transform for Perl language is notable in that it does not use named temporary arrays. We consider the question how to use Schwartzian transform for some computational geometry problems such that construct convex hull and orientation planar graph. The results is illustrated by tables with fulfilment time of sorting. The gain in time is approximately $3.3$ times. Also, we give implementation of Schwarzian transform for Python programming language.