Approximation of measured data with interval B-splines

The objective of this paper is to provide an efficient and reliable method for interpolating or approximating a set of measured data with an interval B-spline curve or surface. In general, measured data possess uncertainty, arising from sensor precision and measurement registration, which can be represented as an interval. Both the interpolation and approximation techniques presented in the paper produce interval bounding geometries that strictly enclose the intervals of the original data; in the case of our interpolation method, the achieved fit is extremely tight, and in the case of our approximation technique the achieved fit depends on the number of control points one is willing to allow. Examples using measured data illustrate our method.