A "graphics for vision" approach is proposed to address the problem of reconstruction from a large and imperfect data set: reconstruction on demand by tensor voting, or ROD-TV. ROD-TV simultaneously delivers good efficiency and robustness, by adapting to a continuum of primitive connectivity, view dependence, and levels of detail (LOD). Locally inferred surface elements are robust to noise and better capture local shapes. By inferring per-vertex normals at sub-voxel precision on the fly, we can achieve interpolative shading. Since these missing details can be recovered at the current level of detail, our result is not upper bounded by the scanning resolution. By relaxing the mesh connectivity requirement, we extend ROD-TV and propose a simple but effective multiscale feature extraction algorithm. ROD-TV consists of a hierarchical data structure that encodes different levels of detail. The local reconstruction algorithm is tensor voting. It is applied on demand to the visible subset of data at a desired level of detail, by traversing the data hierarchy and collecting tensorial support in a neighborhood. We compare our approach and present encouraging results.