There is an exercise titled "Curve fairing to control surface quality" in the manual,
it teaches me that many curves in Rhino coming from many sources need to be optimized for quality. It mentions curve fairing as a technique used in Rhino to optimize a curve for 3D modeling. It defines fairing as "a technique used to simplify curves while improving their curvature graphs and keeping their shape
within tolerance." It also states: "it is especially important to fair curves that are generated from digitized data, intersections, extracted isocurves, or curves from two views."
It explains that single-span curves work better for this fairing process. What is a single span curve? A single span curve is a curve that has one more control point than the degree. For examples a degree 3 curve with 4 control points, and so on.
To fair a curve, it starts with rebuilding a curve. This is when Rebuild command is used. In the dialog window of Rebuild, the number of control points and the degree of curve can be updated. As a single-span curve works best in curve fairing, so it is seen in the following image that in the Rebuild Curve dialog, change the Degree to 5 and the Point Count to 6 points. Uncheck Delete input, check Create new object on current layer.
This makes the curves into single-span curves. Single-span curves are Bézier curves. A single-span curve is a curve that has degree +1 control points. While this is not necessary to get high quality surfaces, it produces predictable results. I can also combine Divide command with PointDeviation to detect the deviation of the points on a curve and to adjust the points' positions until the points are located within the range of good deviation and are identified in blue as "good points".
The end result of a new surface from these curves after fairing will be that the shape and quality of the surface has very few isocurves but it is very close to the shape of the first surface.
I can then analyze the surface with CurvatureAnalysis. It will shows the smooth transitions in the false color display, indicating smooth curvature transitions in the surface.
