I've got n points in d dimensions (typically n is around 30k-60k and d is 5 or 6). I'm using qhull to calculate the Delaunay triangulation and the convex hull of the set of points.
You can assume each point was drawn from the normal multidimensional distribution. I need the triangulation for function interpolation which works quite well once you calculate the simplex/barycentric coordinates of the query point p.
The problem is how to handle points that are outside the convex hull (which occurs fairly infrequently - but does occur)? I need a way to project the point onto the hull's surface and calculate where on the d-1 dimensional face it hit so that I can interpolate this point (essentially clipping the point to the region of the hull).
Is there an efficient algorithm out there that does this? I came across this on the web but am not clear how to apply it across the entire hull efficiently.