Quadrilateral linear basis functions(generalized barycentric coordinates) are defined as:
What are the steps to calculate the above functions?
Is it possible to obtain basis functions for a 5 sided polygon(pentagon) or in general n-sided polygon?
2026-02-22 19:39:58.1771789198
How to obtain generalized barycentric coordinates for n-sided polygon?
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The key terms are generalized barycentric coordinates and mean value coordinates.
Here are two representative papers on the subject. There are plenty more.
Michael S. Floater, Generalized barycentric coordinates and applications, Acta Numerica, Volume 24, 2015, pp. 161-214 [pdf]
Kai Hormann, Michael S. Floater, Mean value coordinates for arbitrary planar polygons, ACM Transactions on Graphics, Volume 25, 2006, pp. 1424-1441 [pdf]