Steven Anson Coons
Encyclopedia
Steven Anson Coons was an early pioneer in the field of computer graphical methods. He was a professor at the Massachusetts Institute of Technology
in the Mechanical Engineering Department. Steven Coons had a vision of interactive computer graphics as a design tool to aid the engineer.
z=f(d) where d=(x-origin)/range
and
z=a0 + ad + a2 d2 ... a7 d7
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(Φ,u,w,θ) all mapped into the unit square.
By selecting proper values for Φ (similar to K in the conic family) in this equation:
Φu(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 = 1 / (Sqrt ( Φ + Sqrt ( θ + ( θ + 1)))) and w = 1 - θ(u)
During World War II
, he worked on the design of aircraft surfaces, developing the mathematics to describe generalized "surface patch
es." 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, 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.
Coons's students included Ivan Sutherland
and Lawrence Roberts
, both of whom went on to make numerous contributions to computer graphics and (in Roberts' case) to computer networks. Coons also advised Nicholas Negroponte
.http://archives.obs-us.com/obs/english/books/nn/bd1101bn.htm
Coons co-authored, with John Thomas Rule, a book on mechanical drawing and graphic methods entitled Graphics c. 1961.
SIGGRAPH
has an award named for Coons. The Steven Anson Coons Award for Outstanding Creative Contributions to Computer Graphics is given in odd-numbered years to an individual to honor that person's lifetime contribution to computer graphics and interactive techniques. It is considered the field's most prestigious award.
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
in the Mechanical Engineering Department. Steven Coons had a vision of interactive computer graphics as a design tool to aid the engineer.
Work
While a student at MIT, Steven Anson 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 express as being one unit long and the element plane in a unit square. The polynomials are written:z=f(d) where d=(x-origin)/range
and
z=a0 + ad + a2 d2 ... a7 d7
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(Φ,u,w,θ) all mapped into the unit square.
By selecting proper values for Φ (similar to K in the conic family) in this equation:
Φu(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 = 1 / (Sqrt ( Φ + Sqrt ( θ + ( θ + 1)))) and w = 1 - θ(u)
During World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, he worked on the design of aircraft surfaces, developing the mathematics to describe generalized "surface patch
Bézier surface
Bézier surfaces are a species of mathematical spline used in computer graphics, computer-aided design, and finite element modeling.As with the Bézier curve, a Bézier surface is defined by a set of control points...
es." 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
B-spline
In the mathematical subfield of numerical analysis, a B-spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. B-splines were investigated as early as the nineteenth century by Nikolai Lobachevsky...
surfaces, 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
Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points....
values of the boundaries.
Coons's students included Ivan Sutherland
Ivan Sutherland
Ivan Edward Sutherland is an American computer scientist and Internet pioneer. He received the Turing Award from the Association for Computing Machinery in 1988 for the invention of Sketchpad, an early predecessor to the sort of graphical user interface that has become ubiquitous in personal...
and Lawrence Roberts
Lawrence Roberts (scientist)
Lawrence G. Roberts received the Draper Prize in 2001 and the Principe de Asturias Award in 2002 "for the development of the Internet" along with Leonard Kleinrock, Robert Kahn, and Vinton Cerf....
, both of whom went on to make numerous contributions to computer graphics and (in Roberts' case) to computer networks. Coons also advised Nicholas Negroponte
Nicholas Negroponte
Nicholas Negroponte is an American architect best known as the founder and Chairman Emeritus of Massachusetts Institute of Technology's Media Lab, and also known as the founder of the One Laptop per Child Association ....
.http://archives.obs-us.com/obs/english/books/nn/bd1101bn.htm
Coons co-authored, with John Thomas Rule, a book on mechanical drawing and graphic methods entitled Graphics c. 1961.
Steven A. Coons Award
The Association for Computing MachineryAssociation for Computing Machinery
The Association for Computing Machinery is a learned society for computing. It was founded in 1947 as the world's first scientific and educational computing society. Its membership is more than 92,000 as of 2009...
SIGGRAPH
SIGGRAPH
SIGGRAPH is the name of the annual conference on computer graphics convened by the ACM SIGGRAPH organization. The first SIGGRAPH conference was in 1974. The conference is attended by tens of thousands of computer professionals...
has an award named for Coons. The Steven Anson Coons Award for Outstanding Creative Contributions to Computer Graphics is given in odd-numbered years to an individual to honor that person's lifetime contribution to computer graphics and interactive techniques. It is considered the field's most prestigious award.
Recipients
- Robert L. CookRobert L. CookRobert L. Cook is a computer graphics researcher and developer, and the co-creator of the RenderMan rendering software. Cook was born in Knoxville, Tennessee and educated at Duke University and Cornell University. While at Cornell, Cook worked with Donald P. Greenberg. He is now Vice President of...
(2009) - Nelson Max (2007)
- Tomoyuki NishitaTomoyuki Nishitais a professor at The University of Tokyo. Dr. Nishita received Research Award on Computer Graphics from Information Processing Society of Japan in 1987, and also received The Steven A. Coons Award from ACM SIGGRAPH in 2005....
(2005) - Pat HanrahanPat HanrahanPat Hanrahan is a computer graphics researcher, the Canon USA Professor of Computer Science and Electrical Engineering in the Computer Graphics Laboratory at Stanford University....
(2003) - Lance J. Williams (2001)
- James F. Blinn (1999)
- James D. FoleyJames D. FoleyJames David Foley is a Professor and the Stephen Fleming Chair in Telecommunications in the School of Interactive Computing, and former Dean of the College of Computing at Georgia Institute of Technology from 2008-2010...
(1997) - José Luis Encarnação (1995)
- Edwin CatmullEdwin CatmullDr. Edwin Earl Catmull, Ph.D. is a computer scientist and current president of Walt Disney Animation Studios and Pixar Animation Studios. As a computer scientist, Catmull has contributed to many important developments in computer graphics....
(1993) - Andries van DamAndries van DamAndries "Andy" van Dam is a Dutch-born American professor of computer science and former Vice-President for Research at Brown University in Providence, Rhode Island. Together with Ted Nelson he contributed to the first hypertext system, HES in the late 1960s. He co-authored Computer Graphics:...
(1991) - David C. EvansDavid C. EvansDavid Cannon Evans was the founder of the computer science department at the University of Utah and co-founder of Evans & Sutherland, a computer firm which is known as a pioneer in the domain of computer-generated imagery.-Biography:Evans attended the University of Utah and studied electrical...
(1989) - Donald P. GreenbergDonald P. GreenbergDonald Peter Greenberg is the Jacob Gould Schurman Professor of Computer Graphics at Cornell University.Greenberg earned his undergraduate and Ph.D. degrees from Cornell University, where he played on the tennis and soccer teams and was a member of Tau Delta Phi and the Quill and Dagger society...
(1987) - Pierre BézierPierre BézierPierre Étienne Bézier was a French engineer and one of the founders of the fields of solid, geometric and physical modeling as well as in the field of representing curves, especially in CAD/CAM systems...
(1985) - Ivan E. Sutherland (1983)
Research Papers
- T.B. Sheridan, Steven A. Coons and H.M.Paynter, SOME NOVEL DISPLAY TECHNIQUES FOR DRIVING SIMULATION IEEE TRANSACTIONS ON HUMAN FACTORS IN ENGINEERING vol. HFE5 (1) 29, 1964.
- Steven A. Coons, COMPUTER GRAPHICS AND INNOVATIVE ENGINEERING DESIGN - SUPER-SCULPTOR, DATAMATION 12 (5) 32-34, 1966.
- Steven A. Coons, USES OF COMPUTERS IN TECHNOLOGY, SCIENTIFIC AMERICAN 215 (3) 177, 1966.
- D.V. Ahuja and Steven A. Coons, GEOMETRY FOR CONSTRUCTION AND DISPLAY, IBM SYSTEMS JOURNAL 7 (3-4) 188, 1968.
- Steven A. Coons, MODIFICATION OF SHAPE OF PIECEWISE CURVES, COMPUTER-AIDED DESIGN 9 (3) 178-180, 1977.
- Steven A. Coons, CONSTRAINED LEAST-SQUARES, COMPUTERS & GRAPHICS 3 (1) 43-47, 1978.