Difference between revisions of "Sketcher BSplineIncreaseDegree"

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Increases the degree of the B-spline(see [https://en.wikipedia.org/wiki/B-spline B-spline]).
 
Increases the degree of the B-spline(see [https://en.wikipedia.org/wiki/B-spline B-spline]).
  
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]]}}):
+
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 + the 2 curve endpoints that also act as 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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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)
 
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)
  
Increasing the degree will add control points so that the shape of the spline is not changes. 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:
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Increasing the degree will add control points and the shape of the spline is not changed:
  
 
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{{Caption|Same B-spline where the degree was changed from 3 to 4. Note that also the knot multiplicity was increased.}}
 
{{Caption|Same B-spline where the degree was changed from 3 to 4. Note that also the knot multiplicity was increased.}}
  
If you take this result and decrease the degree, you cannot get the initial state of the spline because information was lost by the increase of the degree. For our example decreasing the degree again leads to this:
+
If you take this result and decrease the degree, you cannot get the initial state of the spline information will be lost by this operation. For our example decreasing the degree again leads to this:
  
 
</translate>
 
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[[File:Sketcher_BSplineDegree3from4.png|400px]]
 
[[File:Sketcher_BSplineDegree3from4.png|400px]]
 
<translate>
 
<translate>
{{Caption|Same B-spline where the degree was again changed from 4 to 3. Note that the knot multiplicity was not also decreased but increased again.}}
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{{Caption|Same B-spline where the degree was changed back from 4 to 3. Note that the knot multiplicity was increased.}}
 +
 
 +
You can see that now each segment has 2 control points and the knots are coincident with each a further control point. The knots have now ''C''<sup>0</sup> continuity so that the spline will get "edges" when you move a control point. So the information of a higher continuity is lost. (see [[Sketcher_BSplineDecreaseKnotMultiplicity#Description|this page]] to for an explanation of the continuity)
  
 
==Usage== <!--T:5-->
 
==Usage== <!--T:5-->

Revision as of 02:14, 2 November 2020

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Sketcher BSplineIncreaseDegree.svg Sketcher BSplineIncreaseDegree

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


Description

Increases the degree of the B-spline(see 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 + the 2 curve endpoints that also act as 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)

Increasing the degree will add control points and the shape of the spline is not changed:

Sketcher BSplineDegree4.png

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


If you take this result and decrease the degree, you cannot get the initial state of the spline information will be lost by this operation. For our example decreasing the degree again leads to this:

Sketcher BSplineDegree3from4.png

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


You can see that now each segment has 2 control points and the knots are coincident with each a further control point. The knots have now C0 continuity so that the spline will get "edges" when you move a control point. So the information of a higher continuity is lost. (see this page to for an explanation of the continuity)

Usage

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