Global reflection for a class of simple closed curves

Abstract

Global reflection is considered for a class of closed Jordan curves : [x(6), y()], 0 ^ < 2 where x() and y() are trigonometric polynomials. Every curve of this form is algebraic and global reflection across it reduces to investigating an algebraic function and its critical points. The reflection function is picked to be that solution of the algebraic equation that maps : [x(), y()] pointwise into [x(), -y()]. This function is defined and analytic except on a finite set of points inside , and at each of these points it is continuous.