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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 smalldistortion on $S$. We solve the Whitney extension-interpolation-alignmentproblem 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$\mathbb R^D$.

On the Whitney Extension-Interpolation-Alignment problem for almost isometries with small distortion in $\Bbb R^D$