Curve and Surface Modeling with Uncertainties Using Dual Kriging

Abstract

This paper presents a new technique based on dual Kriging interpolation for modeling curves and surfaces in the presence of uncertainties in data points. Uncertainties result from measurement errors; therefore, a direct application of this method is found in curve/surface modeling using discrete sets of digitized points. It focuses on a common problem in geometric modeling, the trade-off between curve/surface smoothness and the approximation errors. The Kriging model filters the noise in the data while controlling the deviation locally at each point. However, the classical least-squares technique minimizes the average deviation, hence allowing only a global control of the model. The presented method generates smoother and more accurate representation of the actual curve or surface. It has potential applications in reverse engineering, NC machining, computer-aided inspection and tolerance analysis and verification. Examples of a computer mouse and a portion of the hood of a scaled-down car are presented for illustration.