Sketcher BSplineIncreaseKnotMultiplicity/fr: Difference between revisions
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{{Docnav/fr |
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|[[Sketcher_BSplineIncreaseDegree/fr|Incrémenter les degrés]] |
|[[Sketcher_BSplineIncreaseDegree/fr|Incrémenter les degrés]] |
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|IconR=Sketcher_BSplineDecreaseKnotMultiplicity.svg |
|IconR=Sketcher_BSplineDecreaseKnotMultiplicity.svg |
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{{GuiCommand/fr |
{{GuiCommand/fr |
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|Name=Sketcher BSplineIncreaseKnotMultiplicity |
|Name=Sketcher BSplineIncreaseKnotMultiplicity |
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|SeeAlso=[[Sketcher_CompCreateBSpline|Sketcher Créer une B-spline]] |
|SeeAlso=[[Sketcher_CompCreateBSpline|Sketcher Créer une B-spline]] |
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==Description== |
==Description== |
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Augmente la multiplicité de nœud d'un nœud de courbe B-spline (voir [https://en.wikipedia.org/wiki/B-spline B-spline]). |
Augmente la multiplicité de nœud d'un nœud de courbe B-spline (voir [https://en.wikipedia.org/wiki/B-spline B-spline]). |
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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). The points where two Bézier curves are connected to form the spline are called knots. A knot on a degree ''d'' spline with the multiplicity ''m'' means that the curve left and right to the knot has at least an equal ''n'' order derivative (called ''C''<sup>''n''</sup> continuity) whereas n=d-m.<br/> |
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[[File:Sketcher_SampleBSplineIncreaseKnotMultiplicity_example.png]] |
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Here is a cubic (degree 3) spline whose knots have the multiplicity 1 (indicated by the number in parentheses, <br/>indication can be changed using the toolbar button {{Button|[[File:Sketcher_BSplineKnotMultiplicity.svg|24px]] [[Sketcher_BSplineKnotMultiplicity|Show/hide B-spline knot multiplicity]]}}): |
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{{Caption|Courbe B-spline montrant une multiplicité de nœuds croissante.}} |
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[[File:Sketcher_KnotMultiplicity_multiplicity1.png|386px]] |
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{{Caption|B-spline where both knots have the multiplicity 1.}} |
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A multiplicity of 3 will change this spline so that even the first order derivatives are not equal (''C''<sup>0</sup> continuity). Here is the same spline where the left's knot multiplicity was increased to 3: |
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[[File:Sketcher_KnotMultiplicity_multiplicity3.png|386px]] |
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{{Caption|B-spline from above with knot multiplicity 3. A control point was moved to show that the knot has ''C''<sup>0</sup> continuity.}} |
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A consequence of a higher multiplicity is that for the price of loosing continuity you gain local control. This means the change of one control point only affects the spline locally to this changed point. This can be seen in this example, where the spline from the first image above was taken and its second control point from the right side was moved up: |
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[[File:Sketcher_KnotMultiplicity_locality.png]] |
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{{Caption|Effect of locality due to different multiplicity.}} |
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One can see that the spline with knot multiplicity 1 is completely changed while the one with multiplicity 2 kept its form at its left side. |
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==Utilisation== |
==Utilisation== |
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# Sélectionnez un nœud B-spline |
# Sélectionnez un nœud B-spline |
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# Lancez l'outil à l'aide de plusieurs méthodes: |
# Lancez l'outil à l'aide de plusieurs méthodes: |
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#* Appuyez sur le bouton {{Button|[[File:Sketcher_BSplineIncreaseKnotMultiplicity.svg|16px]] [[Sketcher_BSplineIncreaseKnotMultiplicity/fr|B-spline Augmenter la multiplicité des nœuds]]}}. |
#* Appuyez sur le bouton {{Button|[[File:Sketcher_BSplineIncreaseKnotMultiplicity.svg|16px]] [[Sketcher_BSplineIncreaseKnotMultiplicity/fr|B-spline Augmenter la multiplicité des nœuds]]}}. |
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#* Utilisez l'entrée {{MenuCommand|Sketch → Sketcher B-spline tools → [[File: Sketcher_BSplineIncreaseKnotMultiplicity.svg|16px]] Augmenter la multiplicité des nœuds}} dans le menu supérieur. |
#* Utilisez l'entrée {{MenuCommand|Sketch → Sketcher B-spline tools → [[File: Sketcher_BSplineIncreaseKnotMultiplicity.svg|16px]] Augmenter la multiplicité des nœuds}} dans le menu supérieur. |
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<div class="mw-translate-fuzzy"> |
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{{Docnav/fr |
{{Docnav/fr |
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|[[Sketcher_BSplineIncreaseDegree/fr|Incrémenter les degrés]] |
|[[Sketcher_BSplineIncreaseDegree/fr|Incrémenter les degrés]] |
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|IconR=Sketcher_BSplineDecreaseKnotMultiplicity.svg |
|IconR=Sketcher_BSplineDecreaseKnotMultiplicity.svg |
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{{Sketcher Tools navi{{#translation:}}}} |
{{Sketcher Tools navi{{#translation:}}}} |
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Revision as of 13:53, 2 December 2020
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| Emplacement du menu |
|---|
| Sketch → Sketcher B-spline tools → Augmenter la multiplicité de noeuds |
| Ateliers |
| Sketcher |
| Raccourci par défaut |
| Aucun |
| Introduit dans la version |
| 0.17 |
| Voir aussi |
| Sketcher Créer une B-spline |
Description
Augmente la multiplicité de nœud d'un nœud de courbe B-spline (voir B-spline).
B-splines are basically a combination of Bézier curves (nicely explained in this and this video). The points where two Bézier curves are connected to form the spline are called knots. A knot on a degree d spline with the multiplicity m means that the curve left and right to the knot has at least an equal n order derivative (called Cn continuity) whereas n=d-m.
Here is a cubic (degree 3) spline whose knots have the multiplicity 1 (indicated by the number in parentheses,
indication can be changed using the toolbar button 
Show/hide B-spline knot multiplicity):
B-spline where both knots have the multiplicity 1.
A multiplicity of 3 will change this spline so that even the first order derivatives are not equal (C0 continuity). Here is the same spline where the left's knot multiplicity was increased to 3:
B-spline from above with knot multiplicity 3. A control point was moved to show that the knot has C0 continuity.
A consequence of a higher multiplicity is that for the price of loosing continuity you gain local control. This means the change of one control point only affects the spline locally to this changed point. This can be seen in this example, where the spline from the first image above was taken and its second control point from the right side was moved up:
Effect of locality due to different multiplicity.
One can see that the spline with knot multiplicity 1 is completely changed while the one with multiplicity 2 kept its form at its left side.
Utilisation
- Sélectionnez un nœud B-spline
- Lancez l'outil à l'aide de plusieurs méthodes:
- Appuyez sur le bouton
B-spline Augmenter la multiplicité des nœuds. - Utilisez l'entrée Sketch → Sketcher B-spline tools → Augmenter la multiplicité des nœuds dans le menu supérieur.
- Appuyez sur le bouton
Sketcher
- Général : Créer une esquisse, Modifier l'esquisse, Esquisse sur une face, Réorienter l'esquisse, Valider l'esquisse, Fusionner les esquisses, Esquisse miroir, Quitter l'esquisse, Vue de l'esquisse, Vue de section, Grille, Aimantation, Ordre de rendu, Arrêt de l'opération
- Géométries : Point, Ligne, Arc, Arc par 3 points, Cercle, Cercle par 3 points, Ellipse par son centre, Ellipse par 3 points, Arc d'ellipse, Arc d'hyperbole, Arc de parabole, B-spline simple, B-spline périodique, B-spline par des nœuds, B-spline périodique par des nœuds, Polyligne, Rectangle, Rectangle centré, Rectangle arrondi, Triangle, Carré, Pentagone, Hexagone, Heptagone, Octogone, Polygone régulier, Contour oblong, Congé, Congé avec contrainte, Ajuster, Prolonger, Diviser, Géométrie externe, Copie carbone, Géométrie de construction
- Contraintes :
- Contraintes geometriques : Coïncidence, Point sur objet, Vertical, Horizontal, Parallèle, Perpendiculaire, Tangente, Égalité, Symétrie, Blocage
- Contraintes de dimension : Fixe, Distance horizontale, Distance verticale, Dimensionnelle, Rayon ou poids, Diamètre, Rayon automatique, Angle, Contrainte de réfraction
- Outils de contraintes : Contraintes pilotantes, Activation des contraintes
- Outils : Degrés de liberté non contraints, Contraintes associées, Éléments associés aux contraintes, Contraintes redondantes, Contraintes conflictuelles, Géométrie interne, Origine, Axe horizontal, Axe vertical, Symétrie, Clone, Copie, Déplacer, Réseau rectangulaire, Supprimer l'alignement des axes, Supprimer tous les éléments de géométrie, Supprimer toutes les contraintes
- Outils B-spline : Degré de la B-spline, Polygone de contrôle de la B-spline, Peigne de courbure, Multiplicité des nœuds, Poids des points de contrôle, Convertir une géométrie en B-spline, Augmenter le degré, Diminuer le degré, Augmenter la multiplicité des nœuds, Diminuer la multiplicité des nœuds, Insérer un nœud, Joindre des courbes
- Espace virtuel : Espace virtuel
Hub utilisateurs
- Démarrer avec FreeCAD
- Installation : Téléchargements, Windows, Linux, Mac, Logiciels supplémentaires, Docker, AppImage, Ubuntu Snap
- Bases : À propos de FreeCAD, Interface, Navigation par la souris, Méthodes de sélection, Objet name, Préférences, Ateliers, Structure du document, Propriétés, Contribuer à FreeCAD, Faire un don
- Aide : Tutoriels, Tutoriels vidéo
- Ateliers : Std Base, Arch, Assembly, CAM, Draft, FEM, Inspection, Mesh, OpenSCAD, Part, PartDesign, Points, Reverse Engineering, Robot, Sketcher, Spreadsheet, Start, Surface, TechDraw, Test, Web