You can use one of two types of thinning parameters: Thinning Tolerance or Thinning Proportion. The Use tolerance check box on the Construct Surface and Construct Curve dialog boxes (Insert | Feature | Constructed | Surface and Insert | Feature | Constructed | Curve, respectively) lets you switch between either tolerance or proportion:
Thinning tolerance controls the tightness (or exactness) of the curve or surface fit. Valid thinning tolerances range from 0.0 to 5.0, with the default being 0.01. The smaller the thinning tolerance, the closer the curve comes to passing through the centroids of the features included in the input set. If the thinning tolerance is 0.0, the curve or surface will pass through all of the centroids. A larger thinning tolerance will result in a curve or surface that has fewer fluctuations (at the expense of not lying near the input set's features). To see this, construct a curve or surface and then change the input tolerance and examine how its shape changes.
Thinning proportion, alternately, may be used to control the quality of the fit. Valid thinning proportions range from between 0.0 and 1.0, with a default value of 0.33. The thinning proportion determines the number of degrees of freedom available in fitting the curve or surface to the centroids. At the lower extreme of 0, the algorithm will attempt to fit a straight line or plane to the centroids. At 1, it will compute a fit that passes through all of the centroids.
To make a DEPENDENT curve an INDEPENDENT curve (so that it is no longer associated with the input set):
Open the Edit window (View | Edit Window).
Select the curve feature that you constructed.
Navigate to the DEPENDENT field of that feature.
Press F7. It will change from DEPENDENT to INDEPENDENT.
You can change the shape of the curve by editing its control points.