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COONS PATCH
Steven Anson Coons (19121979): American computer engineer. 
Given four arcs parametrized on [0,1]
such that
The Coons patch is the surface parametrized by where , and so that . 
The Coons patch provides a method to construct a surface supported on a given contour, when the latter is composed of 4 arcs of curves.
Examples:
First ruled surface parametrized by M_{1} joining points P_{1}(t) to points Q_{1}(t). 
Second ruled surface parametrized by M_{2} joining points P_{2}(u) to points Q_{2}(u). 
Bilinear patch parametrized by M_{3} , portion of hyperbolic paraboloid lying on the quadrilateral ABCD. The patch is flat if the 4 vertices are coplanar. 
Final Coons patch M_{1 }+ M_{2 } M_{3} 






Edge formed by 4 arcs of circles of the same radius 
We get a Bohemian dome 




Production of a sphere thanks to Coons patches 
Egg made by assembling Coons patches made by Alexandre Demir, for the best worker in France prize. 
See also the Bezier
surfaces.
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© Robert FERRÉOL 2017