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**Thomas W. Sederberg** is the associate dean of the college of physcial and mathematical sciences and professor of Computer Science at Brigham Young University in Provo, Utah. His research involves computer graphics and computer aided design. He helped invent free-form deformation and T-splines.^{ [1] }

**Brigham Young University** is a private, non-profit research university in Provo, Utah, United States completely owned by The Church of Jesus Christ of Latter-day Saints and run under the auspices of its Church Educational System. Approximately 99 percent of the students are members of the LDS Church and one-third of its U.S. students are from Utah. The university's primary focus is on undergraduate education, but it also has 68 master's and 25 doctoral degree programs.

**Provo** is the third-largest city in Utah, United States. It is 43 miles (69 km) south of Salt Lake City along the Wasatch Front. Provo is the largest city and county seat of Utah County.

In computer graphics, **free-form deformation (FFD)** is a geometric technique used to model simple deformations of rigid objects. It is based on the idea of enclosing an object within a cube or another hull object, and transforming the object within the hull as the hull is deformed. Deformation of the hull is based on the concept of so-called *hyper-patches*, which are three-dimensional analogs of parametric curves such as Bézier curves, B-splines, or NURBs. The technique was first described by Thomas W. Sederberg and Scott R. Parry in 1986, and is based on an earlier technique by Alan Barr. It was extended by Coquillart to a technique described as *extended free-form deformation*, which refines the hull object by introducing additional geometry or by using different hull objects such as cylinders and prisms.

Sederberg studied civil engineering at Brigham Young University for both his Bachelor's (1975) and his Master's (1977) degrees.^{ [2] } Sederberg received his PhD from Purdue and joined the civil engineering faculty at BYU in 1983.^{ [1] } His PhD thesis discussed how to compute intersecting Bézier curves.^{ [3] }

He is an associate editor for ACM Transactions on Graphics ^{ [4] } and for Computer Aided Geometric Design.^{ [5] }

* ACM Transactions on Graphics* is a bimonthly peer-reviewed scientific journal that covers the field of computer graphics. It was established in 1982 and is published by the Association for Computing Machinery. Starting in 2003, all papers accepted for presentation at the annual SIGGRAPH conference are printed in a special summer issue of the journal. Beginning in 2008, papers presented at SIGGRAPH Asia are printed in a special November/December issue.

Sederberg co-founded T-Splines, inc. in 2004, which was acquired by Autodesk in 2011.^{ [6] }

**Autodesk, Inc.** is an American multinational software corporation that makes software services for the architecture, engineering, construction, manufacturing, media, and entertainment industries. Autodesk is headquartered in San Rafael, California, and features a gallery of its customers' work in its San Francisco building. The company has offices worldwide, with U.S. locations in Northern California, Oregon, Colorado, Texas, Michigan and in New England in New Hampshire and Massachusetts, and Canada locations in Ontario, Quebec, and Alberta.

SIGGRAPH awarded Sederberg with the Computer Graphics Achievement award in 2006.^{ [7] } In 2013 Sederberg received the Pierre Bézier award for his contributions to solid modeling.^{ [3] }

**SIGGRAPH** is the annual conference on computer graphics (CG) convened by the ACM SIGGRAPH organization. The first SIGGRAPH conference was in 1974. The conference is attended by tens of thousands of computer professionals. Past conferences have been held in Los Angeles, Dallas, New Orleans, Boston, Vancouver, and elsewhere in North America. SIGGRAPH Asia, a second yearly conference, has been held since 2008 in various Asian countries. The strength of SIGGRAPH comes from the chapters set all around the world.

**Pierre Étienne Bézier** was a French engineer and one of the founders of the fields of solid, geometric and physical modelling as well as in the field of representing curves, especially in CAD/CAM systems. As an engineer at Renault, he became a leader in the transformation of design and manufacturing, through mathematics and computing tools, into computer-aided design and three-dimensional modeling.

Purdue gave Sederberg the Outstanding Mechanical Engineer Award in 2014.^{ [2] } Brigham Young University awarded him the Steven V. White University Professorship, the Technology Transfer Award and the Distinguished Faculty Lecturer Award.^{ [8] } His publications are highly cited—in 2014 Thomson Reuters named Sederberg as one of the 108 most-cited professors in computer science.^{ [1] }

Sederberg married Brenda Clark in 1978, and they had eight children. In 1995 Brenda was diagnosed with multiple sclerosis, and she died in 2012.^{ [9] }

A **Bézier curve** is a parametric curve used in computer graphics and related fields. The curve, which is related to the Bernstein polynomial, is named after Pierre Bézier, who used it in the 1960s for designing curves for the bodywork of Renault cars. Other uses include the design of computer fonts and animation. Bézier curves can be combined to form a Bézier spline, or generalized to higher dimensions to form Bézier surfaces. The Bézier triangle is a special case of the latter.

**Computer-aided design** (**CAD**) is the use of computers to aid in the creation, modification, analysis, or optimization of a design. CAD software is used to increase the productivity of the designer, improve the quality of design, improve communications through documentation, and to create a database for manufacturing. CAD output is often in the form of electronic files for print, machining, or other manufacturing operations. The term **CADD** is also used.

**Computational geometry** is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with history stretching back to antiquity.

The **Utah teapot**, or the **Newell teapot**, is a 3D test model that has become a standard reference object and an in-joke within the computer graphics community. It is a mathematical model of an ordinary teapot that appears solid, cylindrical, and partially convex. A teapot primitive is considered the equivalent of a "Hello, World" program, as a way to create an easy 3D scene with a somewhat complex model acting as a basic geometry reference for scene and light setup. Some programming libraries, such as the OpenGL Utility Toolkit, even have functions dedicated to drawing teapots.

**ACM SIGGRAPH** is the international Association for Computing Machinery's Special Interest Group on Computer Graphics and Interactive Techniques based in New York. It was founded in 1969 by Andy van Dam.

**Paul de Casteljau** is a French physicist and mathematician. In 1959, while working at Citroën, he developed an algorithm for evaluating calculations on a certain family of curves, which would later be formalized and popularized by engineer Pierre Bézier, and the curves called De Casteljau curve or Bézier curves. De Casteljau's algorithm is widely used, with some modifications, as it is the most robust and numerically stable method for evaluating polynomials. Other methods, such as Horner's method and forward differencing, are faster for calculating single points but are less robust. De Casteljau's algorithm is still very fast for subdividing a De Casteljau curve or Bézier curve into two curve segments at an arbitrary parametric location.

**Rhinoceros** is a commercial 3D computer graphics and computer-aided design (CAD) application software developed by Robert McNeel & Associates, an American, privately held, employee-owned company founded in 1980. Rhinoceros geometry is based on the NURBS mathematical model, which focuses on producing mathematically precise representation of curves and freeform surfaces in computer graphics.

**Jos Stam** is a researcher in the field of computer graphics, focusing on the simulation of natural physical phenomena for 3D-computer animation. He achieved technical breakthroughs with the simulation of fluids and gases, new rendering algorithms and subdivision surfaces, which are a mix between two previously incompatible worlds of Nurbs- and polygon-modeling in 3D.

In computer-aided geometric design a **control point** is a member of a set of points used to determine the shape of a spline curve or, more generally, a surface or higher-dimensional object.

**Geometric design** (**GD**) is a branch of computational geometry. It deals with the construction and representation of free-form curves, surfaces, or volumes and is closely related to geometric modeling. Core problems are curve and surface modelling and representation. GD studies especially the construction and manipulation of curves and surfaces given by a set of points using polynomial, rational, piecewise polynomial, or piecewise rational methods. The most important instruments here are parametric curves and parametric surfaces, such as Bézier curves, spline curves and surfaces. An important non-parametric approach is the level-set method.

**Chandrajit Bajaj** is an American computer scientist. He is a Professor of Computer science at the University of Texas at Austin holding the Computational Applied Mathematics Chair in Visualization and is the director of the Computational Visualization Center, in the Institute for Computational Engineering and Sciences (ICES).

**Autodesk Inventor** is a computer-aided design application for 3D mechanical design, simulation, visualization, and documentation developed by Autodesk.

A **T-spline** surface can be thought of as a NURBS surface for which a row of control points is allowed to terminate without traversing the entire surface. The control net at a terminated row resembles the letter "T". Modeling surfaces with T-splines can reduce the number of control points in comparison to NURBS surfaces and make pieces easier to merge, but increases the book-keeping effort to keep track of the irregular connectivity. T-splines can be converted into NURBS surfaces, by knot insertion, and NURBS can be represented as T-splines without T's or by removing knots. T-splines can therefore, in theory, do everything that NURBS can do. In practice, enormous amount of programming was required to make NURBS work as well as they do, and creating the equivalent T-Spline functionality would require similar effort. To smoothly join at points where more than three surface pieces meet, T-splines have been combined with geometrically continuous constructions of degree 3 by 3 (bi-cubic) and, more recently, of degree 4 by 4 (bi-quartic).

**Solid Modeling Solutions** is a company who has an implementation of a mathematical representation of NURBS, 3D geometry, and Solid modeling technology which emerged in the 1980s and 1990s into a commercial implementation known as SMLib. This article will provide the background and history of this implementation into a commercial product line from Solid Modeling Solutions™ (SMS). SMS is an independent supplier of source code for a powerful suite of 3D geometry kernels. SMS provides advanced NURBS-based geometry libraries, SMLib™, TSNLib™, GSNLib™, NLib™, SDLib™, VSLib™, and PolyMLib™, that encompass extensive definition and manipulation of NURBS curves and surfaces with the latest fully functional non-manifold topology.

**Shape Data Limited** is a computer software company in Cambridge, England that specializes in developing programs for engineering and manufacturing professionals.

**Ronald Neil Goldman** is a Professor of Computer Science at Rice University in Houston, Texas. Professor Goldman received his B.S. in Mathematics from the Massachusetts Institute of Technology in 1968 and his M.A. and Ph.D. in Mathematics from Johns Hopkins University in 1973.

**Elaine Cohen** is an American researcher in geometric modeling and computer graphics, known for her pioneering research on B-splines. She is a professor in the school of computing at the University of Utah.

Designers have long used computers for their calculations. Digital computers were used in power system analysis or optimization as early as proto-"Whirlwind" in 1949. Circuit design theory, or power network methodology would be algebraic, symbolic, and often vector-based. Examples of problems being solved in the mid-1940s to 50s include: servo motors controlled by generated pulse (1949), a digital computer with built-in computer operations to automatically co-ordinate transforms to compute radar related vectors (1951) and the essentially graphic mathematical process of forming a shape with a digital machine tool (1952). These were accomplished with the use of computer software. The man credited with coining the term CAD, Douglas T. Ross, stated, "As soon as I saw the interactive display equipment," [being used by radar operators 1953] he saw it would be just what his SAGE related data reduction group needed. With the Lincoln Lab people, they were the only ones who used the big, complex display systems put in for the pre-SAGE, Cape Cod system. But "we used it for our own personal workstation.". The designers of these very early computers built utility programs so that programmers could debug programs using flowcharts on a display scope with logical switches that could be opened and closed during the debugging session. They found that they could create electronic symbols and geometric figures to be used to create simple circuit diagrams and flowcharts. And that an object once drawn could be reproduced at will, its orientation, Linkage [ flux, mechanical, lexical scoping ] or scale changed. This suggested numerous possibilities to them. It took ten years of interdisciplinary development work before SKETCHPAD sitting on evolving math libraries emerged from MIT's labs. Additional developments were carried out in the 1960s within the aircraft, automotive, industrial control and electronics industries in the area of 3D surface construction, NC programming, and design analysis, most of it independent of one another and often not publicly published until much later. Some of the mathematical description work on curves was developed in the early 1940s by Robert Issac Newton from Pawtucket, Rhode Island. Robert A. Heinlein in his 1957 novel *The Door into Summer* suggested the possibility of a robotic *Drafting Dan*. However, probably the most important work on polynomial curves and sculptured surface was done by Pierre Bézier, Paul de Casteljau (Citroen), Steven Anson Coons, James Ferguson (Boeing), Carl de Boor (GM), Birkhoff (GM) and Garibedian (GM) in the 1960s and W. Gordon (GM) and R. Riesenfeld in the 1970s.

- 1 2 3 "Dr. Sederberg earns distinction of being "Highly Cited"".
*BYU Computer Science*. BYU. Archived from the original on 2017-11-09. Retrieved 2016-02-22. - 1 2 "Thomas W. Sederberg".
*Purdue University Mechanical Engineering*. Purdue University. 2014. Archived from the original on 2016-03-06. Retrieved 2016-02-24. - 1 2 "Thomas W. Sederberg, the 2013 Pierre Bézier Award Recipient".
*Solid Modeling Association*. Solid Modeling Association. Archived from the original on 2016-03-04. Retrieved 2016-02-24. - ↑ "ACM Graphics Editorial Board".
*ACM Digital Library*. ACM. Archived from the original on 2016-03-03. Retrieved 2016-02-22. - ↑ "Computer Aided Geometric Design Editorial Board". Elsevier. Archived from the original on 2016-03-05. Retrieved 2016-02-22.
- ↑ Hadfield, Joe. "BYU prof's design technology acquired by software giant Autodesk".
*BYU News*. BYU. Archived from the original on 2016-03-10. Retrieved 2016-02-22. - ↑ "Awards".
*ACMSIGGRAPH*. ACMSIGGRAPH. Archived from the original on 2016-03-02. Retrieved 2016-02-24. - ↑ Holligshead, Todd (December 2, 2014). "BYU professors receive prestigious awards from Purdue University". BYU News. Archived from the original on 2016-03-10. Retrieved 2016-02-24.
- ↑ "Brenda Clark Sederberg".
*Deseret News*. September 5, 2012. Archived from the original on 2016-03-03. Retrieved 2016-02-24.

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