Curve interpolation with constrained length
We consider the problem of finding a curve which interpolates at given points such that (approximately) the length of the curve between each two subsequent interpolation points is equal to some given number. We only consider the functional case. We give an algorithm which yields an interpolating cubic polynomial spline. In case the data is taken from a (smooth enough) function this spline function converges at least quadratically in the mesh size to the original one. If the mesh is `regular enough' it is even third order accurate. We also give an extension to the bivariate case. For the univariate case it will be shown that the length on each interval of this constructed spline at most differs quadratically in the mesh size from the actual lengths. Assuming regularity on the partition this estimate can also be improved by one order.
scientific article; zbMATH DE number 714644
scientific article