In this paper we present a new physically motivated curve descriptor based on the solution of Helmholtz's equation. The descriptor satisfies the six principles set by MPEG-7: it has a good retrieval accuracy, it is compact, it can be applied in general contexts, it has a reasonable computational complexity, it is robust and provides an hierarchical representation of the curve from coarse to fine. Moreover this descriptor generalizes straightforwardly to three dimensional surfaces. We tested the performance of the descriptor in the context of affine invariant curve matching using the multiview curve dataset (MCD), which consists of 40 curves (extracted from the MPEG-7 shape dataset) imaged under 14 different points of view. The results we obtained show that the proposed descriptor satisfies the MPEG-7 requirements and presents some advantages over some of the commonly used curve descriptors.