Coon's patch defines a surface by 4 curve segments that are connected in end-to-end, forming a closed curve chain. For left, right, bottom, top boundary curves denoted by , convex sum (blending) defines two lofting surfaces from to and to .

First patch interpolates and second patch interpolates Adding two patches

and evaluating at boundaries yields

this shows that left boundary curve of , which is sought to be has extra term that can be modelled by Expanding yields

from symmetry, there is no need to perform same procedure for other direction (~ bottom,right). The final form of patch to interpolate all four curves is