Parallel surface ($P_d=P+dn$)

A parallel surface is a constant-distance normal displacement $P_d=P+dn$ of a regular surface with unit normal vector $n$. With shape operator $W=-Dn$, its differential is $(I-dW)DP$; it can become singular where $1-d{\kappa }_i=0$ for a principal curvature ${\kappa }_i$.

// Target: geometry-and-topology.bigb

A variable normal offset displaces a parametric surface along its unit normal vector by a scalar field $d(u,v)$. Unlike a constant-distance parallel surface, its derivatives also contain $d_{u}n$ and $d_{v}n$.

// Target: analysis.bigb