Spline Extensions for the MAPLE Plot System

Traditionally computer algebra systems use lines and polygons to represent mathematical func tions graphically While these geometric primitives can easily be rendered on conventional raster graphics hardware a smooth representation using splines would provide a wider range of trade o s between image quality and rendering performance Since modern computer graphics hardware directly supports rendering of spline objects their use becomes more and more interesting In this thesis we examine the possibilities for replacing traditional representations of functions and graphs by spline representations We describe the use of B splines for interpolation and approx imation and discuss several approaches for generating parameterizations for these tasks Finally we present some novel results regarding the use of rational splines for curve and surface tting