Adaptive Approximation of Shapes

We consider scalar-valued shape functionals on sets of shapes which are small perturbations of a reference shape. The shapes are described by parameterizations and their closeness is induced by a Hilbert space structure on the parameter domain. We justify a heuristic for finding the best low-dimensional parameter subspace with respect to uniformly approximating a given shape functional. We also propose an adaptive algorithm for achieving a prescribed accuracy when representing the shape functional with a small number of shape parameters.

Automated summary

The study examines scalar-valued shape functionals on sets of shapes that are small perturbations of a reference shape. The shapes are described by parameterizations and their closeness is measured by a Hilbert space structure on the parameter domain. The study justifies a heuristic for finding the best low-dimensional parameter subspace and proposes an adaptive algorithm for achieving a prescribed accuracy when representing the shape functional with a small number of shape parameters.