We describe an algorithm for fitting a Catmull-Clark subdivision surface model to an unstructured, incomplete and noisy data set. We complete the large missing data regions with the a-priori shape information and produce a smooth, compact and structured data description. The result can be used for further data manipulation, compression, or visualisation. Our fitting algorithm uses a quasi-interpolation technique which manipulates the base mesh of the subdivision model to achieve better approximation. We extend the approach designed for scientific visualisation and animation to deal with incomplete and noisy data and preserve prior shape constraints where data is missing. We illustrate the algorithm on range and stereo data with a set of different subdivision models and demonstrate the applicability of the method to the problem of novel view synthesis from incomplete stereo data. © Springer-Verlag Berlin Heidelberg 2007.