# Smoothing

Smoothing smoothes curves using Shoenberg and Reinsch smoothing function. Smooth is done by minimizing distance square plus curvature square. User can specify how smooth points be by specifying approximation factors at discrete input points. Fugen provides two smoothing methods. One is smoothing with free end condition, and the other is smoothing with tangent fixed at the ends. End points can be relatively fixed by setting adequate relative weights at the ends.

## Step 1

Specify a curve prompting is displayed, select a curve. Upon selection, smoothed curve and curvature lines are depicted, and Smoothing parameter input dialogue shows.

Curvature lines have two types of display: curvature length and curvature radius.

## Step 2

Specigy smoothing points prompting is displayed, locate a point on the curve to press mouse cursor left button. This "locate" action adds a weight specified in the dialogue at that point. The larger the weight is, the smoother the curve around weight points becomes. The weight can be canceled by inputting backspace as an ordinal point's backspace.

## Step 3

When desired smoothed curve is obtained, press enter key to finish input and to fix the curve. This Enter key terminates the smoothing command.

## Deviation

Deviation controls how far the new curve can move from the original.

Mean Deviation is the mean of each deviation at the curve knots.

Maximum Deviation is the maximum deviation at the curve knots.

For both deviation kind, the value is not real deviation, rather, weight multiplied deviation.