Plugging the ray equation \(r: \mathbb {R} \rightarrow \mathbb {R}^n\) into the function \(f: \mathbb {R}^n \rightarrow \mathbb {R}\) that defines the implicit surface produces the composite real function \(F: \mathbb {R} \rightarrow \mathbb {R}\) where \(F=f \circ \boldsymbol {r}\) such that the solutions to
\[
F(t)=0
\]
correspond to ray intersections with the implicit surface. Theses solutions are also called the roots of the function \(F\).