Approximation of dense scattered data using algebraic surfaces

Describes a new technique for fitting an algebraic surface to dense scattered data. Previous methods for fitting algebraic surfaces yield surfaces that fit the given data accurately. However, the resulting surfaces often exhibit defects such as extra sheets that pass near no data points. This new technique allows for the exclusion of such undesirable surfaces by fitting to auxiliary distance data derived from the original data. The paper concludes with a brief discussion of an extension of this technique to piecewise implicit surfaces. Several examples of this technique applied to medical imaging data are included.>