Algebraic Methods for Sectioning Parametric Surfaces

This paper is devoted to show how the already widely used Scientific Computing Systems (in our case Maple) integrating symbolic and numeric capabilities can be used to develop Problem Solving Environments very useful to solve problems into a CAD/CAM framework before they are integrated into a concrete CAD/CAM system. It is shown and motivated how algebraic techniques and Scientific Computing Systems can be very useful in Computer Aided Geometric Design by presenting how generic implicitation can be used to solve problems arising when computing the planar section of a parametric surface and to the computation (topologically exact) of a revolution surface sectioning.