Sketcher BSplineIncreaseDegree/fr: Difference between revisions

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<languages/>
<languages/>
<div class="mw-translate-fuzzy">
{{Docnav/fr
{{Docnav/fr
|[[Sketcher_BSplineConvertToNURB/fr|Convertir en NURB]]
|[[Sketcher_BSplineConvertToNURB/fr|Convertir en NURB]]
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|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg
|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg
}}
}}
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<div class="mw-translate-fuzzy">
{{GuiCommand/fr
{{GuiCommand/fr
|Name=Sketcher BSplineIncreaseDegree
|Name=Sketcher BSplineIncreaseDegree
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|SeeAlso=[[Sketcher CompCreateBSpline|Sketcher Créer une B-spline]]
|SeeAlso=[[Sketcher CompCreateBSpline|Sketcher Créer une B-spline]]
}}
}}
</div>


==Description==
==Description==
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Augmente le degré de la B-spline(voir [https://en.wikipedia.org/wiki/B-spline B-spline]).
Augmente le degré de la B-spline(voir [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).
[[File:Sketcher_SampleBSplineIncreaseDegree.png|350px]]


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]]}}):
{{Caption|Même B-spline avec degré augmenté.}}

[[File:Sketcher_BSplineDegree3.png|400px]]
{{Caption|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 [[Sketcher_BSplineDecreaseKnotMultiplicity#Description|this page]] for an explanation of the multiplicity)

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

[[File:Sketcher_BSplineDegree4.png|400px]]
{{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 information will be lost by this operation. For our example decreasing the degree again leads to this:

[[File:Sketcher_BSplineDegree3from4.png|400px]]
{{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)


==Utilisation==
==Utilisation==


<div class="mw-translate-fuzzy">
# Sélectionnez une arête à partir d'une B-spline existante et appuyez sur {{Button|[[File:Sketcher_BSplineIncreaseDegree.svg|16px]] [[Sketcher_BSplineIncreaseDegree/fr|Augmenter le degré]]}}.
# Sélectionnez une arête à partir d'une B-spline existante et appuyez sur {{Button|[[File:Sketcher_BSplineIncreaseDegree.svg|16px]] [[Sketcher_BSplineIncreaseDegree/fr|Augmenter le degré]]}}.
</div>


{{Emphasis|Remarque:}} pour le moment il n'y a pas de commande {{Button|[[File:Sketcher_BSplineDecreaseDegree.svg|16px]] Diminuer le degré}}.


<div class="mw-translate-fuzzy">
{{Docnav/fr
{{Docnav/fr
|[[Sketcher_BSplineConvertToNURB/fr|Convertir en NURB]]
|[[Sketcher_BSplineConvertToNURB/fr|Convertir en NURB]]
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|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg
|IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg
}}
}}
</div>


{{Sketcher Tools navi{{#translation:}}}}
{{Sketcher Tools navi{{#translation:}}}}

Revision as of 13:52, 2 December 2020

Sketcher Augmenter le degré d'une BSpline

Emplacement du menu
Sketch → Sketcher B-spline tools → Augmenter le degré
Ateliers
Sketcher
Raccourci par défaut
Aucun
Introduit dans la version
0.17
Voir aussi
Sketcher Créer une B-spline

Description

Augmente le degré de la B-spline(voir 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
(degree is indicated by the number, indication can be changed using the toolbar button Show/hide B-spline degree):

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:

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:

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)

Utilisation

  1. Sélectionnez une arête à partir d'une B-spline existante et appuyez sur Augmenter le degré.