Design for Change

April 12, 2008

Ewald Quak and Jens Gravesen

In the "Forward Looking Session" at the 10th SIAM Conference on Geometric
Design and Computing (San Antonio, Texas, November 2007; http://www.math.vanderbilt.edu/~gdc07/), Kirk Haller from Solidworks explained a requirement of modern engineering design that he termed "Design for Change!" Although some of the changes he was referring to can be achieved manually, many are preferably done automatically, perhaps by some optimization procedure. This is not always easy or even possible in contemporary CAD systems and is one of the challenges presented in the Forward Looking Session.

From its origins about 45 years ago, Computer Aided Design and Manufacturing has grown to play a key part in the product development and production processes in many industries. More than a dozen years ago, with CAD/CAM having reached a fairly mature stage, the technology available at the time was cast into the worldwide ISO 10303 standard STEP (STandard for the Exchange of Product model data). Since then, the CAD industry has undergone an enormous contraction, in the course of which about two-thirds of CAD vendors were eliminated via mergers and buy-outs.

The technology embodied in the current STEP standard dominates the market, and a common misconception is that STEP has solved all the mathematical problems associated with CAD/CAM. In fact, the STEP technology is based on what could be achieved with the commodity workstations available around 1990, which offered computational performance three orders of magnitude below that of current PCs.

Today, the availability of cheap computing power on desktop computers, including high-performance graphics capabilities, and the advent of laser scanners for 3D objects, which are able to digitize even complex geometric models, pose new challenges for CAD/CAM and create additional opportunities. Consequently, geometric models have become both more complex and more prevalent, especially among small and medium-sized enterprises.

In some respects, the STEP standard is not adequate to address many of the mathematical problems that arise today. An example is provided by solid models in which the boundary of a geometric object is described by trimmed NURBS surfaces (Non-Uniform Rational B-Spline patches, the de facto standard for representing sculptured surfaces in CAD systems); these models are almost never watertight, which leads to a seemingly endless sequence of tolerancing and accuracy-related problems. Moreover, the rectangular patches of NURBS technology limit a designer's ability to create arbitrary shapes.

As a consequence, the computer animation, electronic gaming, and 3D digital reconstruction industries, among others, have resorted to simpler geometric representations of objects---namely, triangular meshes as in the STL (Stereo Lithography) standard. This means, in effect, that important new applications in areas as diverse as telecommunications, computer gaming, and medical imaging have been decoupled from the mainstream CAD/CAM world. In the same way, many simulation methods, such as finite element analysis, are based on a discretization of the object's geometry. According to some estimates, up to 80% of the human labor involved in the entire value chain is spent overcoming this rift. It remains open at this point which technology, if any, will ultimately trump the others; given the very real costs of format conversion, many practitioners currently choose to stay put.

Until a few years ago, commodity computers were based almost exclusively on single-core CPUs, and CAD systems were programmed according to that sequential paradigm. Recently, however, thermal considerations have dictated a shift toward additional processors rather than higher processor speeds. With multicore CPUs, considerable reprogramming of CAD systems may be required just to take advantage of the extra processors and data stream accelerators, such as programmable graphics cards. Ongoing experiments (as just one example, see http://www.sintef.no/heterocomp) indicate that data stream accelerators can outperform CPUs by an order of magnitude for a wide variety of computational tasks. This creates opportunities for use of technologies in CAD systems different from those currently in vogue and could lead to the development of novel algorithms. It is inevitable that av-erage users will adopt highly parallelized computing, which will likely lead to a change in CAD design as it is now practiced. Many mathematical and algorithmic challenges will arise as well.

The SIAM Activity Group on Geometric Design (http://www.ifi.uio.no/siag/) is distinguished both for being one of SIAM's smallest activity groups and for having one of the highest percentages of members from industry. The biennial conferences organized by the SIAG for the past 20 years have been among the main general international conferences in geometric modeling and related areas, and they have been well attended by mathematicians and engineers from academia, industry, and government.

The Forward Looking Session, introduced at the San Antonio conference and organized by the authors of this report, featured seven speakers from industry who challenged conference participants with academically interesting problems of practical industrial relevance. We see it as "a chance for people from industry to tell those academics what they really should be looking into."

The problems described by the industrialists ranged from very focused, practical problems, such as surface feature detection, to broad, sweeping challenges, such as harnessing the power of today's workstations. The audience appreciated the speakers' candor in admitting what they are currently unable to do, or at least cannot do sufficiently well. In the lively panel discussion that concluded the session, the contributors fielded questions from the audience as to where things are heading in our field.

The Forward Looking Session, centered on the presentation of industrial problems, is meant to be a regular feature of the conference series. The next conference, in two years, will be a time for taking stock of the activity and progress achieved on the suggested problems. To facilitate this, the contributors agreed to prepare Web presentations of their problems for future reference; they will be posted as they become available at http://www.ifi.uio.no/siag/problems, which is part of our new SIAG portal. We welcome input from nonspecialists outside the SIAG concerning important practical problems related to geometric design and computing needs, and our problem section on the Web portal stands ready as an open discussion forum.

Ewald Quak divides his time between Estonia (Center for Nonlinear Studies at Tallinn University of Technology) and Norway (Center of Mathematics for Applications at the University of Oslo, and the SINTEF Department of Applied Mathematics). Jens Gravesen is a member of the Department of Mathematics at the Technical University of Denmark.


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