This paper presents a method for automatically reconstructing accurate and concise piecewise smooth surface models from scattered range data. The method can be used in applications such as reverse engineering, where CAD models are generated from physical objects. The method can model surfaces of arbitrary topological type and recover sharp features like creases and corners. It has been shown to be effective using both simulated and real data. A key contribution is the introduction of a new class of piecewise smooth surface representations based on subdivision. These surfaces are simple to implement, can model sharp features concisely, and can be fit to scattered data using unconstrained optimization. The method consists of three phases: estimation of topological type, mesh optimization, and piecewise smooth surface optimization. The first two phases have been described elsewhere. Phase 1 estimates the topological type of the surface and produces an initial geometry estimate. Phase 2 reduces the number of triangles and improves the fit to the data. Phase 3 fits an accurate, concise piecewise smooth subdivision surface by optimizing an energy function that balances conciseness and fit. The paper also describes the properties of subdivision surfaces, including how to compute surface points and tangent vectors. It introduces a new subdivision scheme that allows modeling of sharp features such as creases, corners, and darts. The method is applied to a wide variety of data, including simulated and real laser scanner data, and is shown to produce accurate and concise surface models. The algorithm for fitting piecewise smooth subdivision surfaces is based on minimizing an energy function that balances conciseness and accuracy. The method is efficient and can be applied to a wide range of data. The paper also discusses related work and future research directions.This paper presents a method for automatically reconstructing accurate and concise piecewise smooth surface models from scattered range data. The method can be used in applications such as reverse engineering, where CAD models are generated from physical objects. The method can model surfaces of arbitrary topological type and recover sharp features like creases and corners. It has been shown to be effective using both simulated and real data. A key contribution is the introduction of a new class of piecewise smooth surface representations based on subdivision. These surfaces are simple to implement, can model sharp features concisely, and can be fit to scattered data using unconstrained optimization. The method consists of three phases: estimation of topological type, mesh optimization, and piecewise smooth surface optimization. The first two phases have been described elsewhere. Phase 1 estimates the topological type of the surface and produces an initial geometry estimate. Phase 2 reduces the number of triangles and improves the fit to the data. Phase 3 fits an accurate, concise piecewise smooth subdivision surface by optimizing an energy function that balances conciseness and fit. The paper also describes the properties of subdivision surfaces, including how to compute surface points and tangent vectors. It introduces a new subdivision scheme that allows modeling of sharp features such as creases, corners, and darts. The method is applied to a wide variety of data, including simulated and real laser scanner data, and is shown to produce accurate and concise surface models. The algorithm for fitting piecewise smooth subdivision surfaces is based on minimizing an energy function that balances conciseness and accuracy. The method is efficient and can be applied to a wide range of data. The paper also discusses related work and future research directions.