An extended surface fitting algorithm for random data

There are various surface fitting techniques to convert cloud points into surface models in reverse engineering. One type of technique is to reconstruct a surface that can be trimmed with other surfaces. A necessary and sufficient condition for two surfaces to be trimmed is that they should intersect each other. We developed an extended surface fitting to allow the surface boundary to be adjusted freely, while maintaining the accuracy and fairness of the fitted surface. The proposed method determined a base plane from the cloud points, used for the initialization of the parametric values and the determination of the surface boundary. An objective function composed of an error function and an energy function was then proposed. An iterative algorithm incorporating the Gaussian elimination and Newton's method was provided also to optimize the control points and the parametric values. Successful examples were presented to demonstrate the feasibility of the proposed method.