Surface Quality

Last Updated: July 14, 1997
One of the results of the past ten year of research is the importance of surface quality. Essentially, humans can recognize surfaces having good shape when we see them. Unfortunately, this idea of "good shape" is hard to define mathematically. What is clear is that it is a metric of the entire surface patch (and probably the entire surface). This is why tangent plane continuous techniques fail to produce surfaces of good shape: they are only a metric applied to a differential area along the boundaries between adjacent patches.

Variational methods try to minimize energy functions over an entire surface patch (or patches). These techniques are slow because it is expensive to evaluate these functionals, and since you have to vary parameters to minimize this value, you have to evaluate your functional many times.

One of the many questions of shape is how to test the quality of surface patches. Commonly used techniques include shaded images, curvature plots, reflections lines, and isophotes. But it is unclear what metrics should be used, and indeed, different applications probably require different metrics.

Thus, there are several areas of research here:

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