Sketcher BSplineIncreaseDegree: Difference between revisions

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


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Revision as of 20:15, 1 April 2024

This documentation is a work in progress. Please don't mark it as translatable since it will change in the next hours and days.

Sketcher BSplineIncreaseDegree

Menu location
Sketch → Sketcher B-spline tools → Increase B-spline degree
Workbenches
Sketcher
Default shortcut
None
Introduced in version
0.17
See also
Sketcher Show/hide B-spline degree, Sketcher Decrease B-spline degree

Description

The Sketcher BSplineIncreaseDegree tool increases the degree (order) of a B-spline. See this page for more information about B-splines.

Usage

  1. Select a B-spline.
  2. There are several ways to invoke the tool:

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 Show/hide 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 fulfill the constraint that 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 as some information was lost in this operation. 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 was increased. Depending on the B-spline, the algorithm to decrease the degree may add a lot of knots to preserve the shape as happened in this example.

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