Sketcher BSplineDecreaseDegree

Description
Decreases the degree (order) of the B-spline.

B-splines are basically a combination of Bézier curves (nicely explained in this and this video). These curves have degree - 1 control points. In this cubic spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots (degree is indicated by the number, indication can be changed using the toolbar button ):



The outer segments have each 2 control points, the inner one none to fulfill the constraint that the knots have multiplicity 1. (see this page for an explanation of the multiplicity)

Decreasing the degree will not delete control points but conserves instead the shape of the spline. Therefore segments will be added. In our example you see a lot of new spline segments with each one control point and the shape of the spline has not been changed:



If you take this result and increase the degree, you cannot get the initial state of the spline because, as you have seen, the same spline shape can be achieved using different number of segments. For our example increasing the degree leads to this:



Usage

 * 1) Select an edge from an existing B-spline, and press.