Tile-able Bezier Surfaces

Is it possible to make a bezier surface “tile-able”
Taking the same Bezier surface and putting it on all 4 sides of a similar center “tile” bezier surface.

Would save the world. Thanks!

To maintain C0 continuity (no gaps), the control points along one edge need to be offset from those on the opposite edge by the same amount.

To maintain C1 continuity (no sharp edges), the tangent vectors also need to be the same on opposing edges.

P[sub]i,3[/sub]-P[sub]i,0[/sub] = kv
P[sub]3,j[/sub]-P[sub]0,j[/sub] = ku
P[sub]i,1[/sub]-P[sub]i,0[/sub] = P[sub]i,3[/sub]-P[sub]i,2[/sub]
P[sub]1,j[/sub]-P[sub]0,j[/sub] = P[sub]3,j[/sub]-P[sub]2,j[/sub]

This gives you 16 equations, of which 4 are redundant. So, you get to pick 4 control points (one corner), and the other 12 are dictated by these constraints.

Okay. I feel stupid.

I will try to figure out how to read that.

I may not need bezier surfaces.
Not if I can find something to create an n-dimensional function (infinitely granular line/surface/(n-1)Dimensional-thing that continues in 1 direction. With all Y values unique) that has random (predictably random like md5() ) hills and valleys.