Curvature Display

Examining curvature distribution is the principal means of assessing fairness of curves. The curvature values at points along a curve are represented by the lengths of 'tuft' lines, plotted normal to the tangents at these points. The curvature value at a point on a curve is a measure of how tightly the curve is bending at that point. Curvature plots draw attention to features in a curve that may be causing it to be unfair, but that are not apparent from the display of the curve alone (especially with the limitations imposed by a VDU).

A fair curve is generally characterised by having a curvature plot free from excessive undulations. In the following example, the greatest difference between points on the two curves is slight, but one is significantly more fair:

Figure 3:37. An example of poor curvature distribution.

Figure 3:38. An example of good curvature distribution.

Inflexion points are indicated by a change in sign of curvature (tufts switch from one side of a curve to the other). Undulations involving inflexions are usually undesirable and can occur, for instance, when fitting to points that lie almost in a straight line:

Figure 3:39. An example of terrible curvature distribution.

In these situations, the best remedy often involves the removal of data points.

The display of curvature tufts for individual curves is switched on and off from the Curves grid of the Data Bar, and from the active curves popup menu. In order to be useful, the scale of the tufts should be great enough to make them clearly visible, but small enough that the majority are fully visible within the view window. In order to achieve this the curvature tuft lengths in a particular view are scaled by a constant factor, the value of which can be changed. This is purely a display property, and has no effect on the geometry of the curve.

View Tools method

1. Hold the Left Mouse button down on the curvature-scaling tool, .

2. Moving the mouse forward increases the scaling, moving it back reduces it.

Default method

3. Hold <Ctrl + Shift>.

   The cursor changes to the icon.

4. Hold down the the Left Mouse button in the view of interest, and move the mouse forward and backward to increase and reduce the scaling.

Figure 3:40. Excessive scale used for curvature tufts.

Figure 3:41. Sensible scale used for curvature tufts.