A new class of algorithms for the processing of parametric curves

A new class of algorithms for the processing of parametrically defined curves is presented. All the algorithms are based on the ‘divide and conquer’ (subdivision) paradigm. An important feature which marks out this class of algorithms from earlier subdivision-based algorithms is that the curve is characterized algebraically and not geometrically. Curve shape properties needed for the processing tasks are derived from the algebraic form of the curve. As long as the necessary properties can be derived, any mathematical from of the curve may be used. In particular this paper considers polynominal curves represented in the rational quadratic, cubic or rational cubic form. Shape properties such as linearity and Euclidean bounds are derived and algorithms for drawing and curve-curve intersection are described.