= Solution
For a regular <parametric surface> $P(u,v)$, form $N=P_u\times P_v$, $n=N/\lVert N\rVert$ and define the offset evaluator
$$
\boxed{P_d(u,v)=P(u,v)+d\,n(u,v).}
$$
It is already a <parametric surface> with the same parameter domain, even if its coordinates no longer belong to the original polynomial or rational patch family. Point interrogation requires evaluations of $P,P_u,P_v$ and one normalization. For tangent or <normal vector> interrogation, differentiate the evaluator. For example,
$$
N_u=P_{uu}\times P_v+P_u\times P_{uv},\qquad n_u=\frac{(I-nn^T)N_u}{\lVert N\rVert},\qquad (P_d)_u=P_u+d n_u,
$$
and similarly for $v$. The offset <normal vector> is the normalized <cross product> $(P_d)_u\times(P_d)_v$ wherever it is nonzero. These derivatives also support intersection, projection and curvature calculations by the usual methods for <parametric surfaces>. For a <variable normal offset>, add $d_u n$ and $d_v n$ to the corresponding tangent derivatives.
With <shape operator> $W=-Dn$, the constant-distance offset differential is $DP_d=(I-dW)DP$. Along a principal direction its factor is $1-d\kappa_i$, where $\kappa_i$ is a <principal curvature>. Consequently regular interrogation fails at $d\kappa_i=1$; on regular pieces the offset principal curvatures are $\kappa_i/(1-d\kappa_i)$ with the continued normal orientation. Global self-intersections can occur even when both local factors are nonzero. \b[Evaluate and differentiate the base surface and its normalized normal; an exact conversion back to the original patch type is unnecessary.]
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