 Transversal surface intersection tracing

For a parametric surface $F(u,v)$ and a scalar implicit equation $f(P)=0$, set $g=f\circ F$. At a regular transversal intersection, $\nabla g\ne 0$, and $(-g_v,g_u)$ is a parameter tangent vector. Normalize its image under $DF$ to choose physical arc length steps. A predictor followed by Newton method correction of $g=0$ and a transverse plane equation gives a local continuation method. Certified patch bounds are useful for finding seeds; corner signs alone do not detect a closed intersection entirely inside a patch.