I know about fitting cubic splines to a set of 2D points {xI,yI} for I = 1 to n: Sort the points into order of increasing x. Fit cubic to points A B C D. Let that be the curve from A to C. Work out that curve's slope (= differential coefficient) at C. Use that slope and yC yD yE to fit a curve to C D E. That is the 2nd spline. Work out the slope at D. Use that slope and yD yE yF ... etc etc. The last spline is applied between x[n-2] and x[n]. This method avoid slope discontinuities (= kinks) where splines join. I have programmed this method in my MAKEOBJ and it works.

But I need a method for THREE dimensions: given a set of points {xI, yI, zI} for I = 1 to n: fild z for some given value of {x,y}. I could divide the {x,y} area into polygons (if the coordinates are a 3D mesh, that has already been done). Then fit a spline within each polygon. But how to avoid creases in the 3D curve at the {x,y} polygon boundaries? As it is 3D, I can't merely run from one end to the other.

Message edited on: 10/22/2004 00:45