  In this paper, we study the following problem. Let $D\geq 2$, $S\subset
\mathbb R^D$ be finite and let $\phi:S\to \mathbb R^D$ with $\phi$ a small
distortion on $S$. We solve the Whitney extension-interpolation-alignment
problem of how to understand when $\phi$ can be extended to a function
$\Phi:\mathbb R^D\to \mathbb R^D$ which is a smooth small distortion on
$\mathbb R^D$. The work in this paper appears in the research memoir [14]
