SIAM Activity Group on Geometric Design

Problem Section

This section is an outcome of the Forward Looking Session at the 10th SIAM conference on Geometric Design and Computing in San Antonio, Texas, November 2007.

The session's goal was to suggest topics for future research, which are both academically challenging and of practical industrial relevance. Call it a chance for people from industry to tell those academics what they really should be looking into.

We are very happy that representatives for various segments of industrial applications (such as aircraft design, CAD/CAM companies, medicine) accepted to contribute to this session, describing a problem, the setting it arises in and why it is important to tackle it.

As it turned out, the problem descriptions ranged from very practical issues one can immediately get ones hands dirty with (such as surface feature detection), to broad, more-policy like statements about future directions (such as how to harness the power of today's workstations).

The contributors have been asked to prepare web presentations of their problems for future reference, which can be found below: click on the titles to get the full web presentations. As organizers of the session, we are very grateful to the people involved, since going through all the necessary approval processes within a company is no small task.

Jens Gravesen (Technical University of Denmark)
Ewald Quak (Tallinn University of Technology)

Geometric Modeling Problems in Industrial CAD/CAM/CAE

George Allen,
Siemens PLM Software
Summary: This paper is a broad discussion of some of the geometric problems that arise in the real-world use of commercial CAD/CAM/CAE systems. The goal is to help the research community understand what problems exist in commercial environments today, which ones are important, and how they can help address them via future work. The focus will be on the design and manufacturing of mechanical devices (as opposed to electrical devices, buildings, or other types of products). First we briefly survey some of the business problems faced by companies who design and manufacture mechanical products, so that we can try to relate these business problems to possible future innovations. Next we describe some necessary technology background, and then three sample problems. One problem (filleting) is fairly narrow and specific, while the other two (history-based modeling and performance) are broader and more general. For comparison, we classify research papers from a recent conference, to assess their alignment with the needs and interests of the CAD/CAM/CAE business.

Medical image registration

Solveig Bruvoll, Knut Mørken, and Eigil Samset,
University of Oslo and Rikshospitalet
Summary: The challenge presented here is not a well defined problem that can be solved within a reasonable amount of time. It is a whole research area with many subproblems and is challenging both mathematically and computationally. Although researchers from other fields are already working actively on these problems, we believe that experts with a background from geometric modelling can contribute both methods and insights to the area.

Surface Modeling for Composite Materials

Thomas A. Grandine,
The Boeing Company
Summary: Prior to the 787, most composite parts were manufactured so that the finished side of the part was closest to the tooling surface. With fuselage sections constructed out of one piece barrel sections, outer surface tooling and the need for an enormous autoclave were deemed too impractical for the 787, and a decision was made to use inner surface tooling instead. While this achieved great savings in terms of tooling and manufacturing costs, it also introduced the problem of determining the final outer mold line. In a nutshell, the problem is to compute the shape of the post-cure surface given the pre-cure ply distribution, stack up, and orientation, successfully accounting for resin flow and autoclave pressure to determine the final surface.

Spherical curves for the design of conical Moineau pumps

Jens Gravesen
Technical University of Denmark
Summary: The problem presented here is concerned with curves on the sphere. The challenge is to find a pair of closed curves on the sphere, one inside the other, such that they touches each other in a finite number of points and thereby form a series of closed chambers. Furthermore, if the inner curve is moved by the motion generated by letting two circles roll on each other, then the curves stay in contact and the chambers open and close during the motion.

Surface Feature Redetection

Wolfgang Klemm
Cocreate Software GmbH
Summary: This presentation will focus on sketch interpolation techniques. Typically a shape consists of several surfaces that are created by sweep, loft or skin interpolation methods, using planar cross-sections and guide curves. Planar sections and guide curves usually are interpolated to a given accuracy. Sections become isoparametric curves of the resulting surface. The planar sections and guide curves often consist of a sequence of straight lines, circular arcs, elliptical arcs or other conical section curves. Modification of shape is often done by changing curve parameters (like radii, distances, ) of the sections or guide curves and then recreating the surface. This can be easily achieved, as long as all the information about sections and guide curves is available (like in a parametric or feature based CAD system).
However this information is typically lost during data exchange between different CAD applications. In order to modify shapes by the desired methods, it is important to detect and extract section and guideline information from such pure (imported) NURBS surface.