"Now you have 2n of these values. Interpolate between them down to your point, using an S-shaped cross-fade curve (eg: 3t^2-2t^3) to weight the interpolant in e

"Now you have 2n of these values. Interpolate between them down to your point, using an S-shaped cross-fade curve (eg: 3t^2-2t^3) to weight the interpolant in each dimension. This step will require computing n S curves, followed by 2n-1 linear interpolations" I don't get this part. If it's 2D and I have 4 grid points, how does that figure into the S-shaped cross-fade curve? ie, I see a parametric function with time, but I'm not sure where the grid point dot products figure into it. Anyone care to illuminate, or point me to some article?