This paper describes a framework for the estimation of shape from sparse or incomplete range data. It uses a shape representation called blending, which allows for the geometric combination of shapes into a unified model— selected regions of the component shapes are cut-out and glued together. Estimation of shape using this representation is realized using a physics-based framework, and also includes a process for deciding how to adapt the structure and topology of the model to improve the fit. The blending representation helps avoid abrupt changes in model geometry during fitting by allowing the smooth evolution of the shape, which improves the robustness of the technique. We demonstrate this framework with a series of experiments showing its ability to automatically extract structured representations from range data given both structurally and topologically complex objects.