Coons surfaces were first defined by and named for mathematician Stephen A. Coons. Coons surfaces are useful for filling in the area bounded by curves. In general, you use four curves and the curves each must be open, but together form a closed loop. To use three curves, set the Three curve Coons checkbox and the fourth curve field is disabled. If the corners don’t match, you receive an error message, “unable to construct surface with these inputs.”
You must have four curves whose endpoints meet to construct a Coons surface
Use the Surface wizard or select Coons in the surface toolbar flyout.
Name the surface for future reference.
Pick the curve on one bounding edge of the surface, corner one.
Pick curve two so that it matches corner one and sets up for corner two of the surface.
Pick curve three so that it matches with corner two and corner four.
Pick curve four so it matches with corner three and links to curve one on its open corner.
Specify an acceptable Tolerance. Tolerance means that the resulting surface may deviate from the exact offset by no more than value you enter.
Decide whether to set Reparameterize curves.
Click Preview to see how the current settings affect the surface. Make adjustments as necessary until the surface is how you want it.
Click Finish or OK to create the surface.
An example of a Coons surface.