The problem of reconstructing and representing the shape of a three-dimensional object from sparse data is considered, with special emphasis on the level of detail of the representation. To this aim, we provide a model that support a multiresolution representation of a shape, which is based on a set of local sculpturing updates on an initial tetrahedral mesh of the convex hull of the given data points. We provide an efficient algorithm for extracting representations of the shape at different levels of detail, possibly variable over different portion of the object, as well as a new sculpturing algorithm for building the multiresolution model from the initial dataset. No limitation on the genus of the reconstructed shape is imposed.