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7.3 More about stationary points

If it is only necessary to determine the absolute maximum or absolute minimum of the squared distance function between two geometric objects, then simply computing the maximum or minimum of the set of distances at the stationary points is sufficient, provided that this set is finite. However, it is often necessary to classify each stationary point as a local maximum, local minimum, or saddle point. Furthermore, the set of stationary points may not be finite (for example, consider the distance function between two concentric circles) and it may be required to trace out these infinite point sets. In this section we examine these questions.



Subsections

December 2009