Least Squares Approximation of Scattered Data

Abstract

Surface reconstruction from scattered data in applications like reverse engineering, geographic information systems and geological modeling usually involves huge amount of data. Creating surface triangulations with vertices in every given data point may be too memory demanding and time consuming, and is usually not required in such cases. Data acquired with scanning devices or data from seismic surveys may also contain considerable noise. Therefore a “good” approximation to the measured data is often sought instead of exact interpolation. Approximation by least squares is a common approach to constructing surfaces from measured data and in this chapter least squares approximation is applied to fit surface triangulations to data.