Constrained variational refinement (Q2378274)

From the introduction: We consider a non-uniform, variational method for refining curves subject to convex set constraints that is a generalization of the uniform, interpolatory refinement scheme in [\textit{L. Kobbelt}, Comput. Aided Geom. Des. 13, No. 8, 743--761 (1996; Zbl 0875.68878)]. We derive optimality conditions, including conditions for optimal free knots, and we use these and simpler methods of parametrization (such as centripetal parametrizations) to develop computational algorithms [see \textit{E. T. Y. Lee}, Comput.-Aided Des. 21, No. 6, 363--370 (1989; Zbl 0675.65002)]. We generalize ``uniform interpolation'' to ``non-uniform near-interpolation''. In particular, we assume that the near-interpolatory constraints are convex. The algorithm given here is easy to program, and good for computing approximate solutions.