Global reflection is considered
for a class of closed Jordan curves Γ : [x(𝜃),y(𝜃)],0 ≦ 𝜃 < 27τ where x(𝜃) and y(𝜃)
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 Γ : [x(𝜃),y(𝜃)] pointwise into [x(𝜃),−y(𝜃)]. This function is defined and
analytic except on a finite set of points inside Γ, and at each of these points it is
continuous.
