Statistical and Visual Analysis of Error In Interpolating Sculptured Surfaces


This paper presents a general method for automatic surface interpolation fromrange data and describes the implementation of high order 2D langrangian methodsfor interpolating surfaces from 3rd to 8th order. It uses a modified 2D lagrangianmethod to interpolating, reconstructing and modeling several surfaces, and due to thisinterpolation there will be an error between interpolated surface and the original one,this paper present an algorithm to detect, represent and analyze these interpolatingerrors and statistical criteria to compare the error in representing the sculpturedsurfaces that interpolated with different order basis functions. The comparison isperformed using a mathematically defined data as real data obtained from theproposed models.The system has been implemented for the design of several sculptured surfaces toillustrate the system flexibility. Then the design results have been implemented formanufacturing two of these surfaces using three axis vertical CNC milling machinetool with ball end mill cutter. The method can be used in a variety of CAD/CAMapplications and it has proven to be effective as demonstrated by a number ofexamples using real data from mathematical functions. By applying the proposedsurface interpolating models the percent error was found to be ranged between0.00001% for some model to 3.5% for some other interpolated models with Lagrangemethod.