Sketcher BSplineDecreaseDegree/pl

Description
Decreases the degree (order) of a B-spline (see this page for more info about B-splines).

B-splines are basically a combination of Bézier curves (nicely explained in this and this video).

In this cubic spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots (the 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 try instead to conserve the shape of the spline. Therefore segments will be added. For our example you see a lot of new spline segments with each one control point and the shape of the spline has only slightly been changed:



If you take this result and increase the degree, you cannot get the initial state of the spline because information was lost by the prior decrease of the degree. For our example increasing the degree again leads to this:



Usage

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