Splines and geometric modeling

Abstract

Piecewise polynomials of some xed degree and continuously di erentiable upto some order are known as splines or nite elements. Splines are used in applications ranging from image processing, computer aided design, to the solution of partial di erential equations via nite element analysis. The spline tting problem of constructing a mesh of nite elements that interpolate or approximate multivariate data is by far the primary research problem in geometric modeling. Parametric splines are vectors of multivariate polynomial (or rational) functions while implicit splines are zero contours of multivariate polynomials. This survey shall dwell mainly on spline surface tting methods in IR Tensor product splines in (Section xx.1,...), triangular basis splines (Section xx.7,...). The following criteria may be used in evaluating these spline methods: