= 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, $\nabla g\ne0$, 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.
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