Geometric meanings of the parameters on rational conic segments

摘要

Using algebraic and geometric methods, functional relationships between a point on a conic segment and its corresponding parameter are derived when the conic mappings of the mappings represented by the expressions of rational conic segments are given. These formulae relate some triangular areas or some angles, determined by the selected point on the curve and the control points of the curve, as well as by the weights parametric angles of the selected point and two endpoints on the conic segment, as well