Sketcher BSplineIncreaseDegree/fr: Difference between revisions
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{{Docnav/fr |
{{Docnav/fr |
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|[[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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{{GuiCommand/fr |
{{GuiCommand/fr |
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|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]] |
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==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]). |
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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). |
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[[File:Sketcher_SampleBSplineIncreaseDegree.png|350px]] |
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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]]}}): |
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{{Caption|Même B-spline avec degré augmenté.}} |
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[[File:Sketcher_BSplineDegree3.png|400px]] |
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{{Caption|B-spline with degree 3 and 2 knots that each have the multiplicity 1.}} |
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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) |
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Increasing the degree will add control points and the shape of the spline is not changed: |
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[[File:Sketcher_BSplineDegree4.png|400px]] |
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{{Caption|Same B-spline where the degree was changed from 3 to 4. Note that also the knot multiplicity was increased.}} |
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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: |
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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 was increased.}} |
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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) |
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==Utilisation== |
==Utilisation== |
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# 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]]}}. |
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{{Emphasis|Remarque:}} pour le moment il n'y a pas de commande {{Button|[[File:Sketcher_BSplineDecreaseDegree.svg|16px]] Diminuer le degré}}. |
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<div class="mw-translate-fuzzy"> |
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{{Docnav/fr |
{{Docnav/fr |
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|[[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> |
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{{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 |
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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
- Sélectionnez une arête à partir d'une B-spline existante et appuyez sur Augmenter le degré.
- 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
- 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, Surface, TechDraw, Test