Sketcher BSplineIncreaseDegree: Difference between revisions

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<languages/>
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{{Docnav
{{Docnav|[[Sketcher_ConvertToNURB|Convert Geometry to B-spline]]|[[Sketcher_BSplineIncreaseKnotMultiplicity|Increase knot multiplicity]]|[[Sketcher_Workbench|Sketcher]]|IconL=Sketcher_BSplineApproximate.svg|IconC=Workbench_Sketcher.svg|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg}}
|[[Sketcher_BSplineConvertToNURBS|Convert geometry to B-spline]]
|[[Sketcher_BSplineDecreaseDegree|Decrease B-spline degree]]
|[[Sketcher_Workbench|Sketcher]]
|IconL=Sketcher_BSplineConvertToNURBS.svg
|IconR=Sketcher_BSplineDecreaseDegree.svg
|IconC=Workbench_Sketcher.svg
}}


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{{GuiCommand
{{GuiCommand
|Name=Sketcher BSplineIncreaseDegree
|Name=Sketcher BSplineIncreaseDegree
⚫
|MenuLocation=Sketch → Sketcher B-spline tools → Increase B-spline degree
|Workbenches=[[Sketcher Workbench|Sketcher]]
|Workbenches=[[Sketcher_Workbench|Sketcher]]
⚫
|MenuLocation=Sketch → Sketcher B-spline tools → Increase Degree of B-spline
|Version=0.17
|Version=0.17
|SeeAlso=[[Sketcher CompCreateBSpline|Create B-spline]]
|SeeAlso=[[Sketcher_BSplineDecreaseDegree|Sketcher BSplineDecreaseDegree]]
}}
}}


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The [[Image:Sketcher_BSplineIncreaseDegree.svg|24px]] [[Sketcher_BSplineIncreaseDegree|Sketcher BSplineIncreaseDegree]] tool increases the degree (order) of [[B-Splines|B-splines]].
Increases the degree of the B-spline(see [https://en.wikipedia.org/wiki/B-spline B-spline]).

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

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# Select one or more B-splines.
# There are several ways to invoke the tool:
⚫
#* Press the {{Button|[[Image:Sketcher_BSplineIncreaseDegree.svg|16px]] [[Sketcher_BSplineIncreaseDegree|Increase B-spline degree]]}} button.
#* Select the {{MenuCommand|Sketch → Sketcher B-spline tools → [[Image:Sketcher_BSplineIncreaseDegree.svg|16px]] Increase B-spline degree}} option from the menu.
#* {{Version|0.22}}: Right-click in the [[3D_view|3D view]] and select the {{MenuCommand|[[Image:Sketcher_BSplineIncreaseDegree.svg|16px]] Increase B-spline degree}} option from the context menu.

==Example==

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B-splines are basically a combination of [[B-Splines#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).

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In this cubic B-spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots.

The degree is indicated by the number in the center. See [[File:Sketcher_BSplineDegree.svg|16px]] [[Sketcher_BSplineDegree|Show/hide B-spline degree]].


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[[File:Sketcher_SampleBSplineIncreaseDegree.png|350px]]
[[File:Sketcher_BSplineDegree3.png|400px]]
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{{Caption|B-spline with degree 3 and 2 knots that each have multiplicity 1.}}


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The outer segments each have 2 control points, the inner segment has none to ensure the knots have multiplicity 1. See [[Sketcher_BSplineDecreaseKnotMultiplicity#Description|this page]] for an explanation about multiplicity.
{{Caption|Same B-spline with increasing Degree.}}


==Usage== <!--T:5-->
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Increasing the degree to 4 will add control points without changing the shape of the B-spline:


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[[File:Sketcher_BSplineDegree4.png|400px]]
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# Select an edge from an existing B-spline, and press {{Button|[[File:Sketcher_BSplineIncreaseDegree.svg|16px]] [[Sketcher_BSplineIncreaseDegree|B-spline increase degree]]}}.
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{{Caption|Same B-spline where the degree was changed from 3 to 4. Note that the knot multiplicity has also increased.}}

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From this result you cannot get back to the initial state of the B-spline by decreasing the degree. Some information is lost when the degree of a B-spline is changed. Decreasing the degree back to 3 leads to this:

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[[File:Sketcher_BSplineDegree3from4.png|400px]]
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{{Caption|Same B-spline where the degree was changed back from 4 to 3. Note that the knot multiplicity has increased again. Depending on the B-spline, the algorithm to decrease the degree may add a lot of knots to preserve the shape as has happened here.}}

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Each segment now has 2 control points and each knot is coincident with an additional control point. The knots have ''C<sup>0</sup>'' continuity so that the B-spline will get "corners" if you move a control point. The information of a higher continuity is therefore lost. See [[Sketcher_BSplineDecreaseKnotMultiplicity#Description|this page]] for an explanation about continuity.


⚫
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{{Emphasis|Note:}} at the moment there is no {{Button|[[File:Sketcher_BSplineDecreaseDegree.svg|16px]] B-spline decrease degree}} command.


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{{Docnav
{{Docnav|[[Sketcher_ConvertToNURB|Convert Geometry to B-spline]]|[[Sketcher_BSplineIncreaseKnotMultiplicity|Increase knot multiplicity]]|[[Sketcher_Workbench|Sketcher]]|IconL=Sketcher_BSplineApproximate.svg|IconC=Workbench_Sketcher.svg|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg}}
|[[Sketcher_BSplineConvertToNURBS|Convert geometry to B-spline]]
|[[Sketcher_BSplineDecreaseDegree|Decrease B-spline degree]]
|[[Sketcher_Workbench|Sketcher]]
|IconL=Sketcher_BSplineConvertToNURBS.svg
|IconR=Sketcher_BSplineDecreaseDegree.svg
|IconC=Workbench_Sketcher.svg
}}


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{{Sketcher_Tools_navi{{#translation:}}}}
{{Userdocnavi{{#translation:}}}}
{{Userdocnavi{{#translation:}}}}
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Latest revision as of 11:14, 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 BSplineIncreaseDegree

Menu location
Sketch → Sketcher B-spline tools → Increase B-spline degree
Workbenches
Sketcher
Default shortcut
None
Introduced in version
0.17
See also
Sketcher BSplineDecreaseDegree

Description

The Sketcher BSplineIncreaseDegree tool increases the degree (order) of B-splines.

Usage

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

Example

B-splines are basically a combination of Bézier curves (nicely explained in this and this video).

In this cubic B-spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots.

The degree is indicated by the number in the center. See Show/hide B-spline degree.

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

The outer segments each have 2 control points, the inner segment has none to ensure the knots have multiplicity 1. See this page for an explanation about multiplicity.

Increasing the degree to 4 will add control points without changing the shape of the B-spline:

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

From this result you cannot get back to the initial state of the B-spline by decreasing the degree. Some information is lost when the degree of a B-spline is changed. Decreasing the degree back to 3 leads to this:

Same B-spline where the degree was changed back from 4 to 3. Note that the knot multiplicity has increased again. Depending on the B-spline, the algorithm to decrease the degree may add a lot of knots to preserve the shape as has happened here.

Each segment now has 2 control points and each knot is coincident with an additional control point. The knots have C0 continuity so that the B-spline will get "corners" if you move a control point. The information of a higher continuity is therefore lost. See this page for an explanation about continuity.


Sketcher
User documentation
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