A Generalized Form of Parametric Equations for Planar Second-order Curves

A mathematical model for shading analysis developed for purposes of solar engineering is described. Closed form expressions giving the position of the shadow as a function of time for an isolated point are derived. It was found that these expressions define second-order planar curves. Furthermore, the developed equations can be expressed in generalized parametric form enabling a smooth transition between different curves of the same class. Feasibility of these expressions for computer graphics should be further investigated.