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'''Solid Modeling Solutions''' is a company who has an implementation of a mathematical representation of NURBS ([[Non-uniform rational B-spline]]), 3D geometry, and [[Solid modeling]] technology which emerged in the 1980s and 1990's into a commercial implementation known as SMLib (for solid modeling library).<ref>Potts Steves, Michelle and Frechette, Simon. [http://www.nist.gov/manuscript-publication-search.cfm?pub_id=822064 "Viewing Technologies for CAD Models"], NIST, February 2003.</ref> This article will provide the background and history of this implementation into a commercial product line from [http://www.smlib.com Solid Modeling Solutions]™ (SMS). SMS is an independent supplier of source code for a powerful suite of 3D geometry kernels.<ref>Rowe, Jeffrey. [http://www.cadalyst.com/design-visualization/siggraph-evolves-along-with-technology-11232 "SIGGRAPH Evolves Along With Technology"], Cadalyst, August 21, 2008.</ref> 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.<ref>[http://worldcadaccess.typepad.com/blog/2011/12/what-solid-modeling-solutions-plans-for-2012.html "What Solid Modeling Solutions Plans for 2012"], WorldCAD Access, December 20, 2011</ref><ref>Choi, J., Cho,M., Choi, J., Roh, H. [http://lib.hpu.edu.cn/comp_meeting/%CA%C0%BD%E7%B5%DA%C6%DF%BD%EC%BC%C6%CB%E3%C1%A6%D1%A7%B4%F3%BB%E1/data/papers/1727.html "THE INTEGRATION OF SHELL FINITE ELEMENT ANALYSIS WITH GEOMETRIC MODELING"]</ref>
VSLib™ provides deformable modeling as part of a library using the constrained optimization techniques of the calculus of variations. The library supports several very different geometric operations.
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NURBS got started with seminal work at [[Boeing]] and [[SDRC]] (Structural Dynamics Research Corporation), a leading company in mechanical computer-aided engineering in the 1980s and '90's.<ref>[http://isicad.net/articles.php?article_num=14940 "NURBS and CAD: 30 Years Together"], Ushakov, Dmitry, isicad, December 30, 2011.</ref> The history of NURBS at Boeing goes back to 1979 when Boeing began to staff up for the purpose of developing their own comprehensive CAD/CAM system, TIGER, to support the wide variety of applications needed by their various aircraft and aerospace engineering groups. Three basic decisions were critical to establishing an environment conducive to the development of NURBS. The first was Boeing’s need to develop their own in-house geometry capability. Boeing had special, rather sophisticated, surface geometry needs, especially for wing design, that could not be found in any commercially available CAD/CAM system. As a result, the TIGER Geometry Development Group was established in 1979 and strongly supported for many years. The second decision critical to NURBS development was the removal of the constraint of upward geometrical compatibility with the two systems in use at Boeing at that time. One of these systems had evolved as a result of the iterative process inherent to wing design. The other was best suited for adding the constraints imposed by manufacturing such as cylindrical and planar regions. The third decision was simple but crucial and added the ‘R’ to ‘NURBS’. Circles were to be represented exactly: no cubic approximations would be allowed.
By late 1979 there were 5 or 6 well educated mathematicians (PhD’s from Stanford, Harvard, Washington and Minnesota) and some had many years of software experience, but none of them had any industrial, much less CAD, geometry experience. Those were the days of the oversupply of math PhD’s. The task was to choose the representations for the 11 required curve forms, which included everything from lines and circles to Bézier and B-spline curves.
By early 1980, the staff were busy choosing curve representations and developing the geometry algorithms for TIGER. One of the major tasks was curve/curve intersection. It was noticed very quickly that one could solve the general intersection problem if one could solve it for the Bézier/Bézier case, since everything could be represented in Bézier form at the lowest level. It was soon realized that the geometry development task would be substantially simplified if a way could be found to represent all of the curves using a single form.
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There are two reasons why NURBS were so quickly accepted by IGES. The first was that IGES was in great need of a way to represent objects. Up to that point there were, for example, only two surface definitions in IGES and the B-spline form was restricted to cubic splines. The other, surprisingly important, reason for the rapid acceptance was that Boeing, not being a CAD system supplier, was not a threat to any of the major turnkey system vendors. Evidently, IGES easily bogs down when different vendors support their own slightly different representations for the same objects. At this first IGES meeting, it was discovered that the people with the best understanding of the presentation were the SDRC representatives. Evidently SDRC was also active in defining a single representation for the standard CAD curves and was working on a similar definition.
So that’s how NURBS started at Boeing. Boehm’s B-spline refinement paper from CAD ’80 was of primary importance. It enabled the staff to understand non-uniform splines and to appreciate the geometrical nature of the definition so as to use B-splines in solving engineering problems. The first use of the geometrical nature of B-splines was in the curve/curve intersection. The Bezier subdivision process was utilized, and a second use was our curve offset algorithm, which was based on a polygon offset process that was eventually communicated to and used by SDRC and explained by Tiller and Hanson in their offset paper of 1984. The staff also developed an internal NURBS class taught to about 75 Boeing engineers. The class covered Bezier curves, Bezier to B-spline and surfaces. The first public presentation of our NURBS work was at a Seattle CASA/SME seminar in March of 1982. The staff had progressed quite far by then. They could take a rather simple NURBS surface definition of an aircraft and slice it with a plane surface to generate an interesting outline of some of the wing, body and engines. The staff were allowed great freedom in pursuing our ideas and Boeing correctly promoted NURBS, but the task of developing that technology into a useable form was too much for Boeing, which abandoned the TIGER task late in ’84.
For the record, by late 1980, the TIGER Geometry Development Group consisted of Robert Blomgren, Richard Fuhr, George Graf, Peter Kochevar, Eugene Lee, Miriam Lucian and Richard Rice. Robert Blomgren was “lead engineer”.
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