Intersection of ellipsoid based on knn search

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Sakshi 2011-6-18

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https://ww2.mathworks.cn/matlabcentral/answers/9797-intersection-of-ellipsoid-based-on-knn-search

I have to determine intersection of 2 ellipsoids. For this, I have created the ellipsoids using the function ellipsoid(0,0,0,xc,yc,zc,10). Then I used knn search to query for points with zero distance for points representing coordinates of the ellipsoids. This method is flawed because the distance is checked only for points of the mesh. (121 points in my case for each ellipsoid, since I have taken mesh size to be 10.) So using knn search if only the points are checked, it is likely that the surface between the points can still intersect and not be detected. Hence one way would be to have a very large meshsize so that the points are close enough to represent the surface of the ellipsoid. This is computationally very expensive and time consuming. Any idea on how do it using knn search ?