Difference between revisions of "Sketcher BSplineDecreaseDegree"

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|MenuLocation=Sketch → Sketcher B-spline tools → Decrease Degree of B-spline
 
|MenuLocation=Sketch → Sketcher B-spline tools → Decrease Degree of B-spline
 
|Version=0.19
 
|Version=0.19
|SeeAlso=[[Sketcher_CompCreateBSpline|Sketcher Create B-spline]], [[Sketcher_BSplineIncreaseDegree|Increase B-spline degree]]
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|SeeAlso=[[Sketcher_BSplineDegree|Show/hide B-spline degree]], [[Sketcher_BSplineIncreaseDegree|Increase B-spline degree]]
 
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Revision as of 02:49, 1 November 2020

Other languages:
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Sketcher BSplineDecreaseDegree.svg Sketcher BSplineDecreaseDegree

Menu location
Sketch → Sketcher B-spline tools → Decrease Degree of B-spline
Workbenches
Sketcher
Default shortcut
None
Introduced in version
0.19
See also
Show/hide B-spline degree, Increase B-spline degree


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 Sketcher BSplineDegree.svg Show/hide B-spline degree):

Sketcher BSplineDegree3.png

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


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:

Sketcher BSplineDegree2.png

Same B-spline where the degree was changed from 3 to 2. Note that also the knot multiplicity was increased to conserve the spline shape.


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

Sketcher BSplineDegree3again.png

Same B-spline where the degree was again changed from 2 to 3. Note that the knot multiplicity was not decreased but increased.


Usage

  1. Select an edge from an existing B-spline, and press Sketcher BSplineDecreaseDegree.svg Decrease B-spline degree.