Difference between revisions of "Sketcher BSplineDecreaseDegree"

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Decreases the degree of the B-spline(see [https://en.wikipedia.org/wiki/B-spline B-spline]).
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Decreases the degree (order) of the B-spline.
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B-splines are basically a combination of [https://en.wikipedia.org/wiki/Bezier_curve#Constructing_B%C3%A9zier_curves Bézier curves] (nicely explained in [https://www.youtube.com/watch?v=bE1MrrqBAl8 this] and [https://www.youtube.com/watch?v=xXJylM2S72s this] video).  These curves have degree - 1 control points.<br/>In this cubic spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots<br>(degree is indicated by the number, indication can be changed using the toolbar button {{Button|[[File:Sketcher_BSplineDegree.svg|24px]] [[Sketcher_BSplineDegree|Show/hide B-spline degree]]}}):
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[[File:Sketcher_BSplineDegree3.png|350px]]
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<translate>
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{{Caption|B-spline with degree 3 and 2 knots that each have the multiplicity 1.}}
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The outer segments have each 2 control points, the inner one none to fulfill the constraint that the knots have multiplicity 1. (see [[Sketcher_BSplineDecreaseKnotMultiplicity#Description|this page]] for an explanation of the multiplicity)
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Decreasing the degree will not delete control points but conserves instead the shape of the spline. Therefore segments will be added. In our example you see a lot of new spline segments with each one control point and the shape of the spline has not been changed:
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</translate>
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[[File:Sketcher_BSplineDegree2.png|350px]]
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<translate>
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{{Caption|Same B-spline where the degree was changed from 3 to 2.}}
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If you take this result and increase the degree, you cannot get the initial state of the spline because, as you have seen, the same spline shape can be achieved using different number of segments. For our example increasing the degree leads to this:
  
 
</translate>
 
</translate>
[[File:Sketcher_SampleBSplineIncreaseDegree.png|350px]]
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[[File:Sketcher_BSplineDegree3again.png|350px]]
 
<translate>
 
<translate>
  
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{{Caption|Same B-spline where the degree was again changed from 2 to 3.}}
{{Caption|Same B-spline with different Degrees.}}
 
  
 
==Usage== <!--T:5-->
 
==Usage== <!--T:5-->

Revision as of 02:29, 1 November 2020

Other languages:
English • ‎français

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
Sketcher Create B-spline, 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 conserves instead the shape of the spline. Therefore segments will be added. In our example you see a lot of new spline segments with each one control point and the shape of the spline has not been changed:

Sketcher BSplineDegree2.png

Same B-spline where the degree was changed from 3 to 2.


If you take this result and increase the degree, you cannot get the initial state of the spline because, as you have seen, the same spline shape can be achieved using different number of segments. For our example increasing the degree leads to this:

Sketcher BSplineDegree3again.png

Same B-spline where the degree was again changed from 2 to 3.


Usage

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