After numerous operations on my object, I have more isocurves than needed on some of the flat surfaces. Is there a way to reduce the number of isocurves to the minimum needed? I know how to turn them off, but not how to clean them up.
Are you sure they are isocurves? I would guess they are surface edges. If that is the case, you can run MergeAllFaces to turn multiple joined flat surfaces into single flat surfaces where possible.
If that’s not the issue, could you post a model?
Even better, just post a screen capture. I’m not a big fan of downloading, saving, opening, and reviewing ,… especially if a quick-pic-post will do the same job faster and easier.
Mergeallfaces doesn’t do it. Here’s the file. I’m referring to all the lines on the flat surfaces going in the x-direction. They appeared when I scaled the whole part in the y direction.Bolster1.3dm (625.7 KB)
Here’s the screenshot. 
Did you scale the part or use some sort of transformation like Stretch or CageEdit? Scaling won’t affect surface structure, but the other types of transformation may. What you are seeing appear to be increased surface isocurves caused by increased number of knots caused by a stretching operation…
From your model, the surfaces are degree 3 in both directions, if they were originally flat planar surfaces, the object did undergo some sort of transformation other than scaling.
–Mitch
Rebuild the flat surfaces as simple, trimmed planar surfaces. Use Rebuild with degree 1 in both directions, 2 points in both directions and Retrim checked.
Nice, that did it… thanks much.
Mitch, scaling is the only operation I performed before all the lines appeared. However, now I understand what’s going on (for now). 
I do have another question though. I’ve never understood what u and v represent. x and y? The tutorials I’ve used seem to mention them without explaining them. rex
X, Y, and Z are the coordinates in normal 3D space, like the room you’re in.
On a deformed surface, those do not apply, so we use U,V, and W.
A great example is a Rhino sphere or a globe.
You can think of the U and V isocurves as latitude and longitude.
They follow the surface wherever it goes (and cross each other at 90°)
The W would then be altitude above the surface.
XYZ → normal world space coordinates
UVW → curved surface coordinates
More details in this lynda video.
If you don’t have a subscription, click for 10-days free. Sweet.
Great, thanks.
Rhino does not use W, only U and V for surfaces and only U for curves. (Rhino represents volumes by the boundary surfaces, and each boundary surface has an independent UV parameter system. This is different than solid modelers which may have U, V and W parameters associated with a volume.)
Each point on a surface in Rhino has a unique UV coordinate associated with it, and also XYZ values. All the points with the same U value form a curve which is a U isocurve, and all the points with the same V value form a curve which is a V isocurve.
Similarly, every point on a curve in Rhino has a unique U value associated with it, and also XYZ values.