Made another commit which generalizes the Base.in method above to embedded affine simplices in a higher dimensional manifold. This allows checking whether a 4 dimensional point is contained inside an embedded affine triangle in only 150ns compared to checking whether a point is inside a full dimensional simplex of the manifold with only 50ns. Would like to challenge other developers to try and make a faster method for determining if a 4 dimensional point is inside an affine triangle without Grassmann algebra. The algorithmic method based on Grassmann algebra for this is extremely fast.
Also, this generalization can be used to compute the gradient of an embedded hat function efficiently.