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GuiCommand: Name: Sketcher BSplineIncreaseDegree MenuLocation: Sketch , Sketcher B-spline tools , Increase B-spline degree Workbenches: Sketcher_Workbench Version: 0.17 SeeAlso: Sketcher_BSplineDecreaseDegree

Sketcher BSplineIncreaseDegree

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 → Sketcher B-spline tools → Increase B-spline degree option from the menu.

    • (v1.0)

      : 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 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 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 C^0^ 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.

⏵ documentation index > Sketcher > Sketcher BSplineIncreaseDegree

This page is retrieved from https://github.com/FreeCAD/FreeCAD-documentation/blob/main/wiki/Sketcher_BSplineIncreaseDegree.md

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