# Questions tagged [closest-point]

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### Finding points inside cells of power (generalized Voronoi) diagram

Suppose we have a set of points $p_1,\ldots,p_n\in\mathbb R^d$ as well as a set of weights $w_1,\ldots,w_n\in\mathbb R$. Recall that the power cell associated to the pair $(p_k,w_k)$ is given by: \...
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### Expected runtime complexity of repeated closest Point Pair search

I have to vectors $X_1$ and $X_2$ with 3 dimensional points $p_i$ and $p_j$ contained. As long as $X_1$ is not empty, I want to find the closest pair $p_i$ and $p_j$. The point $p_i$ of this pair I ...
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### Iterative Closest Point Algorithm

I am currently working on an iterative closest point algorithm (in C++, see here). I understand the basic premise of an ICP algorithm. You have two point clouds (a target and a reference) and you ...
I have a 6-sided equilateral polyhedral cone in $R^3$ defined by a symmetric set of equations: $C=\{(X_1,X_2,X_3)\ |\ K X_i\leq X_j \forall i,j\in\{1,2,3\}\}$ Given an point $P=(P_1,P_2,P_3)$, I ...