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The question really boils down to how far two points $x,y$ are from each other in direction $u$. This is easily answered: You need to compute the component of $y-x$ onto $u$, i.e., their (signed) distance in direction $u$ is $\frac{(y-x)\cdot u}{\|u\|}$. For your point cloud, you can then compute for each $i$ the (unsigned) distance $$ d_i = \frac{(\bar x-...


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