Given a set of randomly distributed points in n-dimensional space, I am looking for a way to algorithmically find the optimal simplex (no sharp angles if there are multiple options) surrounding a specific point of interest with favorable time complexity.
Here is an example of what I mean in 2-dimensional space, where the red point is the point of interest. A triangle is then constructed around it using the randomly distributed points. In 3d this would be a tetrahedron, in 4d a 5-cell, and so on.
While researching this problem I quickly came across Delaunay triangulation and Voronoi diagrams. However, triangulating all points if I am only interested in one simplex is not an ideal solution. Additionally, the explanation on how this scales to higher dimensions is very brief and it seems to me that these methods have mainly focused on 2d and 3d triangulation.
Maybe I have been searching in the wrong places, since this should be a common problem in computational geometry. If anyone knows of a method by which this can be achieved for only one simplex and in any dimension, it would be greatly appreciated.