Parametric approximation to surfaces

The use of B-splines for the approximation of functions and data is well established. Issues such as parametrization, knot placement and reparametrizaton are important in determining the B-spline representation for the data. Compactness of the B-spline representation also becomes an issue when dealing with complex surfaces.; This thesis discusses these issues in detail and better algorithms for parametrization and reparametrization are presented. Constrained parametrization is used as a technique for approximating features on a surface. A hierarchical approach is used to contain the proliferation of control points every time a knot is added to the tensor-product B-spline representation. This helps keep the representation compact without compromising on the closeness of fit.