Sketcher BSplineDecreaseDegree: Difference between revisions

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|[[Sketcher_Workbench|Sketcher]]
|[[Sketcher_Workbench|Sketcher]]
|IconL=Sketcher_BSplineIncreaseDegree.svg
|IconL=Sketcher_BSplineIncreaseDegree.svg
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|IconC=Workbench_Sketcher.svg
|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg
|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg
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{{GuiCommand
{{GuiCommand
|Name=Sketcher BSplineDecreaseDegree
|Name=Sketcher BSplineDecreaseDegree
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|MenuLocation=Sketch → Sketcher B-spline tools → Decrease B-spline degree
|Workbenches=[[Sketcher_Workbench|Sketcher]]
|Workbenches=[[Sketcher_Workbench|Sketcher]]
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|MenuLocation=Sketch → Sketcher B-spline tools → Decrease Degree of B-spline
|Version=0.19
|Version=0.19
|SeeAlso=[[Sketcher_BSplineDegree|Show/hide B-spline degree]], [[Sketcher_BSplineIncreaseDegree|Increase B-spline degree]]
|SeeAlso=[[Sketcher_BSplineIncreaseDegree|Sketcher BSplineIncreaseDegree]]
}}
}}


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The [[Image:Sketcher_BSplineDecreaseDegree.svg|24px]] [[Sketcher_BSplineDecreaseDegree|Sketcher BSplineDecreaseDegree]] tool decreases the degree (order) of [[B-Splines|B-splines]].
Decreases the degree (order) of the B-spline.


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==Usage== <!--T:5-->
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>(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]]}}):


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# Select one or more B-splines.
[[File:Sketcher_BSplineDegree3.png|400px]]
# There are several ways to invoke the tool:
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#* Press the {{Button|[[Image:Sketcher_BSplineDecreaseDegree.svg|16px]] [[Sketcher_BSplineDecreaseDegree|Decrease B-spline degree]]}} button.
{{Caption|B-spline with degree 3 and 2 knots that each have the multiplicity 1.}}
#* Select the {{MenuCommand|Sketch → Sketcher B-spline tools → [[Image:Sketcher_BSplineDecreaseDegree.svg|16px]] Decrease B-spline degree}} option from the menu.
#* {{Version|0.22}}: Right-click in the [[3D_view|3D view]] and select the {{MenuCommand|[[Image:Sketcher_BSplineDecreaseDegree.svg|16px]] Decrease B-spline degree}} option from the context menu.


==Example==
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)


See [[Sketcher_BSplineIncreaseDegree#Example|Sketcher BSplineIncreaseDegree]].
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:

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[[File:Sketcher_BSplineDegree2.png|400px]]
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{{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 prior decrease of the degree. For our example increasing the degree again leads to this:

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[[File:Sketcher_BSplineDegree3again.png|400px]]
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{{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.}}

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==Usage== <!--T:5-->

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# Select an edge from an existing B-spline, and press {{Button|[[File:Sketcher_BSplineDecreaseDegree.svg|24px]] '''Decrease B-spline degree'''}}.




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|[[Sketcher_Workbench|Sketcher]]
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|IconL=Sketcher_BSplineIncreaseDegree.svg
|IconL=Sketcher_BSplineIncreaseDegree.svg
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|IconC=Workbench_Sketcher.svg
|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg
|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg
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|IconC=Workbench_Sketcher.svg
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Latest revision as of 11:15, 2 April 2024

Other languages:
This documentation is a work in progress. Please don't mark it as translatable since it will change in the next hours and days.

Sketcher BSplineDecreaseDegree

Menu location
Sketch → Sketcher B-spline tools → Decrease B-spline degree
Workbenches
Sketcher
Default shortcut
None
Introduced in version
0.19
See also
Sketcher BSplineIncreaseDegree

Description

The Sketcher BSplineDecreaseDegree tool decreases the degree (order) of B-splines.

Usage

  1. Select one or more B-splines.
  2. There are several ways to invoke the tool:

Example

See Sketcher BSplineIncreaseDegree.


Sketcher
User documentation
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