Sketcher BSplineIncreaseDegree/cs

Sketcher BSplineIncreaseDegree
Menu location
Sketch → B-Spline Tools → Increase B-Spline Degree
Workbenches
Sketcher
Default shortcut
None
Introduced in version
0.17
See also
Sketcher BSplineDecreaseDegree

Description

The Sketcher BSplineIncreaseDegree tool increases the degree (order) of B-splines.

Usage

1. Select one or more B-splines.
2. There are several ways to invoke the tool:
   • Press the Increase B-Spline Degree button.
   • Select the Sketch → B-Spline Tools → Increase B-Spline Degree option from the menu.
   • introduced in 1.0: Right-click in the 3D View and select the Increase B-Spline Degree option from the context menu.

Example

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

In this cubic B-spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots.

The degree is indicated by the number in the center. See Toggle B-Spline Degree.

B-spline with degree 3 and 2 knots that each have multiplicity 1.

The outer segments each have 2 control points, the inner segment has none to ensure the knots have multiplicity 1. See this page for an explanation about multiplicity.

Increasing the degree to 4 will add control points without changing the shape of the B-spline:

Same B-spline where the degree was changed from 3 to 4. Note that the knot multiplicity has also increased.

From this result you cannot get back to the initial state of the B-spline by decreasing the degree. Some information is lost when the degree of a B-spline is changed. Decreasing the degree back to 3 leads to this:

Same B-spline where the degree was changed back from 4 to 3. Note that the knot multiplicity has increased again. Depending on the B-spline, the algorithm to decrease the degree may add a lot of knots to preserve the shape as has happened here.

Each segment now has 2 control points and each knot is coincident with an additional control point. The knots have C⁰ continuity so that the B-spline will get "corners" if you move a control point. The information of a higher continuity is therefore lost. See this page for an explanation about continuity.