= Shadow tracing for a subdivision curve
{title2=$S(u,v)=L+\lambda(C(t)-L),\quad\lambda>1$}
For a point light at $L$, the shadow of a curve point is the first surface intersection on its ray beyond that point. Certified patch bounds and subdivision isolate intersections; regular hits are corrected with a three-variable <Newton method> solve. Differentiating the displayed equation gives $[S_u,S_v,-(C-L)](u',v',\lambda')^T=\lambda C'$, a predictor for continuation along the shadow. Surface boundaries and grazing rays require clipping and reseeding; every visible component must be isolated, rather than assumed detectable from a fixed sample of the casting curve.
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