Approximate Merging of Two Adjacent B-Spline Surfaces Using Least Square Approximation

The approximate merging of two adjacent B-spline surfaces into a B-spline surface is the core problem in data communication. A novel algorithm is presented in this paper to solve this problem. In this algorithm, we compute the merging error using L2 norm instead of the Euclidean norm, the process of merging is minimizing the approximate error and we only need solve a system of linear equations to get the final merging surface. In order to reduce the merging error, we add a weighed function on objective function to start the next merger; this function adds greater weight on where error is larger. After the next merger, the merging error will be significantly reduced. Finally, some examples are given to demonstrate the effectiveness and validity of the proposed algorithm.

Approximate Merging B-Spline Curves via Least Square Approximation

An algorithm of B-spline curve approximate merging of two adjacent B-spline curves is presented in this paper. In this algorithm, the approximation error between two curves is computed using norm which is known as best least square approximation. We develop a method based on weighed and constrained least squares approximation, which adds a weight function in object function to reduce error of merging. The knot insertion algorithm is also developed to meet the error tolerance.