# Making surface with common parametrization from bunch of other surfaces

I have bunch of surfaces, like in these two images:

Currently to make single surface with common parametrization I sample points uniformly from all source surfaces, and fit single NURBS surface from these points. And in most cases it works, but in some rare cases (When surfaces are more curved) this single surface fails to maintain acceptable accuracy at source regions. I tried to increase number of samples, and number of control points for NURBS, but it doesn't help. And btw, solution for images above will be simple planes, because source surfaces are trimmed planes too, but in general case source surfaces will be curvy.

1. Source surfaces are trimmed NURBS surfaces, but I can convert them to any other discrete format and work with it.

2. I don't care about free space between surfaces, values of a resulting surface in this space can be linear interpolation between nearby source surfaces, or even some constant value.

3. Source surfaces cannot overlap or coincide.

4. Resulting surface must contain all source regions inside (With some arbitrary tolerance), with common parametrization, also it must not have self-intersections.

Is there any other possible solution to this problem? Maybe some algorithm to order such surfaces in parameter space, or at least name of this problem to google it easily?

Thanks for any help.

• You might try asking on the math stack exchange site if you don't get an answer here. – Alan Wolfe Mar 8 '16 at 4:43
• I must say that i dont understand what the inaccuracy is. So I cant help. Basically your saying Im doing A but A does not work. Without explaining what thing that does not work is. – joojaa Mar 8 '16 at 7:17
• @joojaa, When i fit single surface from a set of sampled points (Each sampled point was sampled from one of the source surface), the resulting surface fails to achieve good accuracy (In sense of maximum deviation between resulting surface and the set of sampled points). So I'm asking if there is some another method to do same thing (Get single surface from different trimmed surfaces) with smaller loss in accuracy, because least squares method gives too rough results. – Olologin Mar 8 '16 at 11:37
• Make a picture showing the error. – joojaa Mar 8 '16 at 11:42
• Even if the error is not clearly visible, it may help to include in the question an image of a curved surface for which the accuracy is unacceptable, and the (possibly textual) evidence that the accuracy is not sufficient. This will give answerers a better idea of what you are dealing with. – trichoplax Mar 8 '16 at 20:00