Im trying to build a surface with a nice curve. but when I turn on the curvature graph it is really messy. I try to use fitcrv to smooth it out and minimize the change of shape. But it change too much. I don’t understand the term “fitting tolerance” and “angle tolerance”.

What is the difference between control point, knot point and kink?
I feels kink should be just a point breaking the curve into 2. But I have no idea of difference of the other. but somehow they perform difference in curvature graph

And also the I found after I use the the add control point or knot command the curvature graph is no longer smooth. Some very sharp angle appear in the curvature graph. Unless I delete the point I originally added. How should I decide to add control point or knot?

also some topic already cover most of your questions:

fitting-tolerance
the maximum distance between the input and the new output curve / geometry

angle tolerance
if you fit a curve with kinks (G0-continuity), for example a polyline, polygon …
The Fitting algorithm will consider kinks below this threshold as smooth.

for example if you start with a hexagon (6-side polygon) and set angle Tolerance to 61 Degree and Tolerance really wide / big / high(?) you should get something like similar to a circle…

hope this helps.
maybe you can check above resources and narrow your questions ?

Hello- keep in mind that a kink in the curvature graph is not a link in the curve - a degree 3 curve with more than one span will generally show a graph like this but that is a break in the rate of change of curvature, not in curvature.
Try drawing your curves as degree 5 (at least six points must be placed.) and look at the graph of those.