The paper presents a method for automatic reconstruction of accurate and concise piecewise smooth surface models from scattered range data. The method is applicable in various fields, including reverse engineering, where it can generate CAD models from physical objects. Key contributions include a new class of piecewise smooth surface representations based on subdivision, which can model surfaces of arbitrary topological type and sharp features such as creases and corners. The method consists of three phases: estimating the topological type, optimizing the mesh, and fitting an accurate piecewise smooth subdivision surface. The optimization problem is formulated as minimizing an energy function that balances conciseness and fit to the data. The paper also discusses the background on subdivision surfaces, the development of new subdivision rules for modeling sharp features, and the algorithm for fitting piecewise smooth subdivision surfaces. Experimental results demonstrate the effectiveness of the method in various applications, including real and simulated data. Future work includes extending the method to model more complex sharp features, improving optimization algorithms, and enhancing real-time data capture capabilities.The paper presents a method for automatic reconstruction of accurate and concise piecewise smooth surface models from scattered range data. The method is applicable in various fields, including reverse engineering, where it can generate CAD models from physical objects. Key contributions include a new class of piecewise smooth surface representations based on subdivision, which can model surfaces of arbitrary topological type and sharp features such as creases and corners. The method consists of three phases: estimating the topological type, optimizing the mesh, and fitting an accurate piecewise smooth subdivision surface. The optimization problem is formulated as minimizing an energy function that balances conciseness and fit to the data. The paper also discusses the background on subdivision surfaces, the development of new subdivision rules for modeling sharp features, and the algorithm for fitting piecewise smooth subdivision surfaces. Experimental results demonstrate the effectiveness of the method in various applications, including real and simulated data. Future work includes extending the method to model more complex sharp features, improving optimization algorithms, and enhancing real-time data capture capabilities.