In the Workshop on Mathematical Foundations of CAD (Mathematical Sciences Research Institute, Berkeley, CA. June 4-5, 1999.) the consensus was that: “The single greatest cause of poor reliability of CAD systems is lack of topologically consistent surface intersection algorithms.” Tom Peters, Computer Science and Engineering, The University of Connecticut, estimated the cost to be $1 Billion/year. For more information consult:

Now a decade later these challenges still remain.

Calculation of intersections is not difficult when the surfaces have a regular parameterization and are not near parallel along intersection curves (transversal intersection). However, if the parameterization is not regular, or if the surfaces intersect in regions where the surfaces are parallel or near parallel, intersection calculation gets challenging. One ambition of the GAIA II project has been to provide more accurate solutions for such intersections than what has been available by exploiting teh potential of approximate implcitization.

After the GAIA-project ended we have stabilized he prototype intersection algorithms. However, still the time is little early for industrial use as the approach is computational intensive. However, with the introduction of heterogeneous many core CPUs sufficient computational performance will be available for industrial use. Topics now addressed are:

Another challenge within CAD has been to avoid self-intersections in the shells of the volume described. These self-intersections are of different types:

Isogeometric analysis replaces the boundary structure type CAD-model, by modelling with trivariate rational spline volumes. Consequently the intersection of trivariate spline volumes will have to be handled. The current examples of isogeometric analysis avoid the intersection challenges by directly creating correct models. However, before the isogeometric analysis can be deployed in industry on large scale better approaches for model creation should be devised.

A component of such functionality will be to be able to intersect trivariate volumes and check that the trivariate volumes do not turn back on themselves (self-intersection).

Published December 23, 2009

Example: Transversal intersection.

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Example: Near singular (tangential) intersection.

Example: Open self intersection

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