Smooth Surface Fitting and Finite Element Mesh Generation for Irregularly Distributed Data Points

Abstract This paper presents two computational methods for geometric modeling of curved surfaces represented by irregularly distributed data points. The study emphasizes irregularly distributed data points since this represents the most general case in geometric data interpretation. The first method is a direct mesh mapping procedure, which projects an relatively regular mesh to the complicated real surface. The second method is a surface fitting technique that reconstructs the mathematical surface model using piecewise bi-cubic parametric functions or B-spline functions. This data reconstruction method uses a normal-distance least-squares concept to generate the best fit. Recursive subdivision algorithm and quad tree data structure are applied to optimize the number of patches needed within the desired precision and thus minimize the computing time in the further processing of the surface model. A computer program based on the two computational methods in surface modeling has been developed and demonstrated by its engineering application. Its development provides an automated tool for design engineers and structure analysts to interpret and model complex surfaces derived from data points.