[Algorithms] Re: Heightfield to NURBS conversion

[Dave F. <df...@ra...>]

>Could anyone of you point me to an algorithm on heightfield
>to NURBS conversion i.e an algorithm which takes as input
>an heightfield and returns the control points of the NURBS-
>surface which APPROXIMATES the heightfield to a user given
>error?

 There are many techniques for this, ranging from the top-down
 approach that Dave suggests to the bottom-up approach that
 removes knots from a dense NURBS mesh.

 When you say it must be NURBS, do you mean it must have non-uniform
 knot spacing and non-zero wieghts for the control points, or
 would you be just as happy with a rational form of a standard
 B-spline? (ie. uniform knots + all wieghts at one).

 Do you want quadratic, cubic or quartic surfaces?

 Another way of putting this is to ask if you are happy with a
 smooth approximation or do you want a surface that has sharp
 edges in it? 

 Also do you want just a single surface to do the approximation
 or are multiple surfaces ok? (If the latter then NURBs with triple
 end knots are equivalent to Bezier patches).

 Is the hieghtfield a grid or scattered data?

 What modelling system are you using? Most have some sort of "shrink-wrap"
 facility built-in (or with a plug-in) that you can wrangle
 into doing this for you (though probably quite slowly).

 Finally, how many times do you have to do this? If it is just once,
 then contract a company like Paraform to do the fitting for you.
 (or you can buy their software).

   Dave