Solid Modeling Solutions: Difference between revisions

Revision as of 04:18, 8 January 2025

Revision as of 08:53, 8 February 2025

Line 5:

{{Infobox company

| name = Solid Modeling Solutions

| industry = [[Software]]

| founded = {{Start date and age|1998}} (early)

| defunct = {{Start date and age|2022|05}}

Line 14:

==History==

{{Verification|date=June 2023}}

The development of ''[[non-uniform rational B-spline]]'' (NURBS) originated with seminal work at [[Boeing]] and Structural Dynamics Research Corporation ([[SDRC]]) in the 1980s and 1990s, a company that led in mechanical [[computer-aided engineering]] (CAE) in those years.<ref>[http://isicad.net/articles.php?article_num=14940 "NURBS and CAD: 30 Years Together"], Ushakov, Dmitry, isicad, December 30, 2011.</ref> Boeing's involvement in NURBS dates back to 1979, when they began developing their own comprehensive [[computer-aided design]] (CAD) and [[computer-aided manufacturing]] (CAM), termed CAD/CAM), system, TIGER, to support the diverse needs of their aircraft and aerospace engineering groups. Three basic decisions were critical to establishing an environment conducive to developing NURBS. The first was Boeing's need to develop its own in-house geometry ability. Specifically, Boeing had complex surface geometry needs, especially for wing design, that couldwas then not be found in any commercially available CAD/CAM system. As a resultThus, the TIGER Geometry Development Group was established in 1979 and has received strong support for many years. The second decision critical to NURBS development was the removing the constraint of upward geometricalgeometric compatibility with the two systems used at Boeing at that timethen. One of these systems had evolved due to the iterative process inherent to wing design, while the other was best suited for adding to the constraints imposed by manufacturing, such as cylindrical and planar regions. The third crucial decision was simple but essential: adding the "''R"'' to "''NURBS''." Circles were to be represented precisely, with no cubic approximationsapproximation alloweddisallowed.

By late 1979, there were five or six well-educated mathematicians (PhDs from Stanford, Harvard, Washington, and Minnesota). Some had many years of software experience, but none of them had any industrial, much less CAD, geometry experience. Those were the days of thean oversupply of math PhDs. 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 became evident that if the general intersection problem could be solved for the Bézier/Bézier case, then it could be solved for any case. This is because everything from the lowest level could be represented in Bézier form. 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 singleone form.

With this motivationmotive, the staff startedbegan down the roadwork toward what became NURBS. 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 Bézier curves. The properties of Bézier curves and uniform B-splines were well known, but the staff had to gain an understanding of non-uniform B-splines and rational Bézier curves and try to integrate the two. It was necessary to convert circles and other conics to rational Bézier curves for the curve/curve intersection. At the time, noneNone of the staff realized the importance of the work then, and it 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 justsimply had not yet become a part of standard CAD/CAM applied mathematics. Once there was a reasonably good understanding of rational Bézier and non-uniform splines, they still had to put them together. Up until then, the staff had not written or seen the form.

Once there was a reasonably good understanding of rational Bézier and non-uniform splines, they 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> was used for anything more than a conic Bézier segment.

Line 39 ⟶ 38:

== Philosophy ==

SMS provides [[source code]] to customers 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 are 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 the total cost of ownership of complex software.<ref>Greco, Joe. [https://web.archive.org/web/20160308234121/https://www.highbeam.com/doc/1G1-61298477.html "Kernel Wars - Episode 1"], CADENCECadence magazine, November 1999</ref>

==SMS architecture==

Line 59 ⟶ 58:

*[[Non-uniform rational B-spline]] (NURBS)

*[[Solid modeling]]

*[[Computer-aided design software]]

==References==