1. A method of generating a finer volumetric abstraction for viewing by a human viewer, the finer volumetric abstraction corresponding to a digital three-dimensional (3D) input model, the method comprising: digitally acquiring a coarser volumetric abstraction corresponding to the digital 3D input model; digitally performing subvolume extraction to determine one or more subvolumes to add to or subtract from the coarser volumetric abstraction; for each subvolume of the one or more subvolumes: digitally determining, as a function of the digital 3D input model, whether to 1) add the subvolume to the coarser volumetric abstraction or 2) subtract the subvolume from the coarser volumetric abstraction; and depending on said digitally determining, either 1) digitally adding the subvolume to the coarser volumetric abstraction or 2) digitally subtracting the subvolume from the coarser volumetric abstraction in generating the finer volumetric abstraction; outputting the finer volumetric abstraction for viewing by the human viewer; wherein: said digitally performing subvolume extraction includes, for each subvolume of the one or more subvolumes: digitally fitting a volume primitive to the coarser volumetric abstraction; and digitally geometrically beautifying the volume primitive as a function of the digital 3D input model to create the subvolume; and the coarser volumetric abstraction includes surfaces and the method further comprises segmenting the surfaces into clusters of matched or unmatched subregions as a function of the digital 3D input model; and determining where on the coarser volumetric abstraction to fit the volume primitive as a function of said segmenting.