Two closely related problems 1) adaptive curve fitting and 2) suboptimization can be solved by using the generalized maximum principle. A given curve is approximated by a sequence of arcs in such a way that the duration covered by an arc is automatically shortened at places where the curve is more curly. For the suboptimization problem, a discrete version of the Euler-Lagrange equation is obtained.
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Sheng Chang (1968) studied this question.
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