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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 1980's 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>
==History==
NURBS got started with seminal work at [[Boeing]] and [[SDRC]] (Structural Dynamics Research Corporation), a leading company in mechanical computer-aided engineering in
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 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 Bezier 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 Bezier/Bezier case, since everything could be represented in Bezier 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.
With this motivation the staff started down the road toward what became NURBS. Consider: the design of a wing demands free-form, C2 continuous, cubic splines to satisfy the needs of aerodynamic analysis, yet the circle and cylinders of manufacturing require at least rational Bezier curves. The properties of Bezier curves and uniform B-splines were well known, but the staff had to gain an understanding of non-uniform B-splines and rational Bezier curves and try to integrate the two. It was necessary to convert circles and other conics to rational Bezier curves for the curve/curve intersection. At that time, none of the staff realized the importance of the work and was considered “too trivial” and “nothing new”. The transition from uniform to non-uniform B-splines was rather straight forward, since the mathematical foundation had been available in the literature for many years. It just had not yet become a part of standard CAD/CAM applied mathematics.
Once there was a reasonably good understanding of rational Bezier and non-uniform splines, we still had to put them together. Up to this point, the staff had not written or seen the form
: <math> P(t) = \frac{\sum_i w_i P_i b_i (t)}{ \sum_i w_i b_i (t) } </math>
<!-- : P(t) = ∑iwiPibi(t) / ∑iwibi(t) -->
for anything more than a conic Bezier segment. Searching for a single form, the group worked together, learning about knots, multiple knots and how nicely Bezier segments, especially the conics, could be imbedded into a B-spline curve with multiple knots. Looking back, it seemed so simple: It is easy to verify that the equation for P(t) is valid for the B-spline basis functions as well as for Bernstein basis functions. By the end of 1980 the staff knew we had a way to present all the required curve forms using a single representation, now know as the NURBS form. But this new representation could easily have died at this point. The staff were already 12 to 18 months down a development path. They had completed a large number of algorithms using the old curve forms. They now had to convince our managers and the other technical groups, such as the database and graphics groups, that they should be allowed to start over using a single representation for all curves. The NURBS surface form did not present a problem since they had not yet developed any surface algorithms. The review of this new TIGER curve form was held on February 13, 1981. The review was successful and the staff were allowed to start over using the new curve form. It was at this time that the NURBS acronym was first used by the other side of the TIGER project, i.e., the TIGER software development groups of Boeing Computer Services. Management was very eager to promote the use of these new curve and surface forms. They had a limited understanding of the mathematics but they were very aware of the need to communicate geometric data between systems. Hence, Boeing very quickly prepared to propose NURBS to the August ’81 [[IGES]] meetings. Richard Fuhr, of our group, was assigned the job of presenting NURBS to IGES. His presentation was very well received and shortly afterwards he put together the Boeing document which was distributed to many IGES members.
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
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”. Richard Smith was our supervisor and the manager of the TIGER project was Robert Barnes. As is written at the end of an obituary, “Peace to the memory of TIGER”.
Robert M. Blomgren subsequently formed Applied Geometry in 1984 to commercialize the technology, and Applied Geometry was subsequently purchased by [[Alias Systems Corporation]]/[[Silicon Graphics]]. Solid Modeling Solutions (SMS) was formed in early 1998 by Robert Blomgren and Jim Presti, founded with a commitment to deliver quality products and services with a strong commitment to responsiveness and partnership with our customers. Alliances were developed with GeomWare and IntegrityWare and the non-manifold topology features led to the initial SMLib product in mid-98. A new alliance was established in 1999 with HarmonyWare driven by close collaboration with our customers. This led to IGES, STEP, and VDAFS data translator products in 1999. In late 2001, Nlib was purchased from GeomWare, and the alliance with IntegrityWare was terminated in 2004. Enhancements and major new features are added twice-yearly. SMS is convinced that a small team of talented and motivated experts create better and more efficient products than large corporate projects.
SMS software is based on years of research and application of NURBS technology. Les Piegl and Wayne Tiller (a partner of Solid Modeling Solutions) wrote the definitive "The NURBS Book" on non-uniform rational B-splines (NURBS) with aids to designing geometry for computer-aided environment applications.<ref>
==
SMLib - fully functional non-manifold topological structure and▼
SMS provides source code to customers in order to enhance and enable their understanding of the underlying technology, provide opportunities for collaboration, improve time to repair, and protect their investment. Product delivery, maintenance, and communication is provided by web-based mechanisms. SMS has established a unique model of technical organization and an adaptive open-source approach. The subscription-based pricing philosophy provides a stable base of technical expertise, and it is cost-effective for its customers when viewed from the perspective of total cost of ownership of complex software.<ref>Greco, Joe. [http://www.highbeam.com/doc/1G1-61298477.html "Kernel Wars - Episode 1"], CADENCE magazine, November 1999</ref>
== SMS Architecture ==
solid modeling functionality.
intersection capabilities.
curves and surfaces.
techniques of the calculus of variations.
provides a set of objects and corresponding methods
to repair, optimize, review and edit triangle mesh
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IGES, STEP, VDAFS, SAT, and OpenNURBS
capabilities.
[http://www.smlib.com/products.html SMS Architecture]
== Functionality ==
Complete descriptions of the SMS product line can be found at the [http://www.smlib.com/products.html SMS Product Page]
==See also==
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==References==
<references/> <references/>
==External links==
* [http://www.smlib.com Solid Modeling Solutions]
* [http://www.springer.com/computer/image+processing/book/978-3-540-61545-3 ''"The NURBS Book"'']
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