UNDER CONSTRUCTION for the next few days

The Need for Robustness

Robustness refers to the ability of a system to handle a wide variety of inputs without failure. In addition, it is usually assumed that we would like to have correctness and consistency in a system - i.e. the results that we get are right and the results will be the same for the same input.

Practical experience has shown us that robustness is an important aspect of a solid modeling system. Many times, model designers will create models which are full of degenerate cases (such as surface/surface overlap). In addition, there may be many nearly degenerate cases which will also cause problems.

Exact Computing

Exact Computing appears to be the only way to deal effectively with the problems of degeneracies and near-degeneracies. By exact computing we do not mean that each number and position must be stored

Our Current Approach

Future Work

Two key areas we need to look at in order to have a truly robust system are:

• Handling Degeneracies (using Perturbations) - it has been shown that perturbation schemes can deal with degeneracies. Often, these methods will require a symbolic or exact arithmetic for their use, and our approach has been designed to work well in such a scheme
• Singularities - Currently, we assume that there are no singularities in our surfaces and curves. We will have to modify our current approach to handle these cases

There are other areas which will be helpful to explore further in order to improve the usefulness of this system. These include:

• Higher Degree Surfaces - Our current approach seems to be acceptable for lower degree surfaces, but higher degree surfaces may take too much time to deal with. It would be useful to allow somewhat higher degree surfaces.
• Using Floating Point Artithmetic for Speedup - It has been shown that a combination of floating point and exact arithmetic can perform much faster (without loss of accuracy) than pure exact arithmetic
• Non-manifold Cases - Some people have presented methods for handling non-manifold geometries, and it might be useful to see whether we could adapt our approach to do likewise.
• Non-Parametric/Algebraic Surfaces - It might be useful to allow surfaces other than our current rational parametric surfaces.

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