Quote Originally Posted by frankly747 View Post
...what I need now is for someone who knows how to do a tensor product construct of the 4 univariate cases above to produce a multivariate case in 4 dimensions.
That would not be me (though the tensor product is probably just a convenient place to put a lot of indexes). However, I can generalize the linear method above to cubic splines, assuming you can evaluate gamma at lattice points, say (n1, n2, n3, n4) for integer ni's. The general idea is to start by interpolating along each coordinate axis--that is, allow only one of the four variables to vary. This would generate a lot of interpolations--for a 4x4x4x4 lattice, it would generate 4^4 = 256 interpolations, however only a few of these are used. Combine these interpolations by successively creating new interpolations based on intermediate points in these coordinate axis interpolations. After several new interpolations, you'll have your point. I can be more specific if it would help. I would bet that the method I just described is equivalent to an existing method, but I'm not into computer graphics enough to know specifically.