Difference between revisions of "Sketcher BSplineDecreaseDegree"

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m (change see also)
(remove statement about number of control points as discussed: https://forum.freecadweb.org/viewtopic.php?f=3&t=51600&p=444884#p444884)
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Decreases the degree (order) of the B-spline.
 
Decreases the degree (order) of the 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).
 +
 
 +
In this cubic spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots<br>(the 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]]}}):
  
 
</translate>
 
</translate>
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[[File:Sketcher_BSplineDegree2.png|400px]]
 
[[File:Sketcher_BSplineDegree2.png|400px]]
 
<translate>
 
<translate>
{{Caption|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.}}
+
{{Caption|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. In effect the knots have now ''C''<sup>0</sup> continuity so that the spline will get "edges" when you move a control point. (see [[Sketcher_BSplineDecreaseKnotMultiplicity#Description|this page]] to for an explanation of the continuity)}}
  
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:
+
If you take this result and increase the degree, you cannot get the initial state of the spline because information was lost by the prior decrease of the degree. For our example increasing the degree again leads to this:
  
 
</translate>
 
</translate>
 
[[File:Sketcher_BSplineDegree3again.png|400px]]
 
[[File:Sketcher_BSplineDegree3again.png|400px]]
 
<translate>
 
<translate>
{{Caption|Same B-spline where the degree was again changed from 2 to 3. Note that the knot multiplicity was not decreased but increased.}}
+
{{Caption|Same B-spline where the degree was changed back from 2 to 3. Note that the knot multiplicity increased too because the information for a possible higher continuity was lost.}}
  
 
==Usage== <!--T:5-->
 
==Usage== <!--T:5-->

Revision as of 03:12, 3 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).

In this cubic spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots
(the 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. In effect the knots have now C0 continuity so that the spline will get "edges" when you move a control point. (see this page to for an explanation of the continuity)


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

Sketcher BSplineDegree3again.png

Same B-spline where the degree was changed back from 2 to 3. Note that the knot multiplicity increased too because the information for a possible higher continuity was lost.


Usage

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