While a student at MIT, Coons was employed by the Chance
Vought Aircraft Company, in the Master Dimensions Department. He developed a new
conic curve based on the unit square. He published a report entitled
An Analytic Method for Calculations of the Contours of Double Curved Surfaces. The surface was controlled by one through seventh order
polynomials and each curve was expressed as being one unit long and the element plane in a unit square. The polynomials are written: : z=f(d) \text{ where }d = \frac{x-\text{origin}}{\text{range}} and : z = a_0 + ad + a_2d^2 + \cdots + a_7 d^7 This concept allows for the approximate matching of any curve, conic or not. The surface element plane normally a conic curve was expressed as: : c = f(\Phi,u,w,\theta) \text{ all mapped into the unit square.} \, By selecting proper values for Φ (similar to
K in the conic family) in this equation: : \Phi u(w-1) + (w-u)^2 = 0 \, the curve will be fixed. By arbitrarily choosing values of Φ,
u and
w could be solved for: : u = \frac{1}{\sqrt{ \Phi + \sqrt{\theta+(\theta + 1)}}} ,\, w = 1 - \theta(u) During
World War II, he worked on the design of aircraft surfaces, developing the mathematics to describe generalized
surface patches. At
MIT's Electronic Systems Laboratory he investigated the mathematical formulation for these patches, and published one of the most significant contributions to the area of geometric design, a treatise which has become known as
The Little Red Book in 1967. His
Coons patch was a formulation that presented the notation, mathematical foundation, and intuitive interpretation of an idea that would ultimately become the foundation for surface descriptions that are commonly used today, such as
B-spline surfaces,
non-uniform rational B-spline (NURB) surfaces, etc. His technique for describing a surface was to construct it out of collections of adjacent patches, which had continuity constraints that would allow surfaces to have curvature which was expected by the designer. Each patch was defined by four boundary curves, and a set of "
blending functions" that defined how the interior was constructed out of
interpolated values of the boundaries. In 1961, with John Thomas Rule, Coons co-authored a book on mechanical drawing and graphic methods entitled
Graphics. Coons' students included
Ivan Sutherland and
Lawrence Roberts, both of whom went on to make many contributions to computer graphics and (by Roberts) to
computer networks. In a 1964 MIT video, Coons and Roberts explain and demonstrate Sutherland's pioneering computer graphics program
Sketchpad, then hosted on the
MIT Lincoln Laboratory TX-2 computer. Coons also advised
Nicholas Negroponte. == Steven A. Coons Award ==