Summary: In reverse engineering, laser scanners are commonly used since 3D data is sampled fast and accurately relative to other systems. However, they provide an enormous amount of irregular data that requires intensive reconstruction processing, based on the parameterization and surface fitting stages. Selection of an appropriate parameterization is essential for topology reconstruction as well as surface fitness. Current parameterization methods have topological problems, leading to undesired noisy self-intersecting surfaces. In this paper, a new adaptive parameterization PDE (Partial Differential Equation) method is proposed for sculptured objects that were scanned from a single direction. The method is based on calculating a PDE non-self-intersecting parametric grid, and then fitting the base surface using CMA (Control Mesh Approximation) and adaptive GDA (Gradient Descent Approximation) methods.