Sketcher BSplineIncreaseKnotMultiplicity/it

Aumenta di grado

Diminuisci la molteplicità

Sketcher

Aumenta la molteplicità di nodo
Posizione nel menu
Sketch → Strumeti B-spline → Aumenta la molteplicità di nodo
Ambiente
Sketcher
Avvio veloce
Nessuno
Introdotto nella versione
0.17
Vedere anche
Crea B-spline

Descrizione

Aumenta la molteplicità del nodo di curva B-spline (vedere: 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.

Utilizzo

1. Selezionare un nodo di una B-spline
2. Richiamare lo strumento usando uno di questi metodi:
   • Premere il pulsante Aumenta la molteplicità del nodo nella barra degli strumenti.
   • Usare la voce Sketch → Strumenti B-spline → Aumenta la molteplicità del nodo dal menu principale.

Aumenta di grado

Diminuisci la molteplicità

Sketcher

Sketcher

• General: Create sketch, Edit sketch, Map sketch to face, Reorient sketch, Validate sketch, Merge sketches, Mirror sketch, Leave sketch, View sketch, View section, Toggle grid, Toggle snap, Configure rendering order, Stop operation

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• Sketcher geometries: Point, Line, Arc, Arc by 3 points, Circle, Circle by 3 points, Ellipse, Ellipse by 3 points, Arc of ellipse, Arc of hyperbola, Arc of parabola, B-spline by control points, Periodic B-spline by control points, B-spline by knots, Periodic B-spline by knots, Polyline, Rectangle, Centered rectangle, Rounded rectangle, Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon, Regular polygon, Slot, Fillet, Corner-preserving fillet, Trim, Extend, Split, External geometry, Carbon copy, Toggle construction geometry

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• Sketcher constraints:
  • Geometric constraints: Coincident, Point on object, Vertical, Horizontal, Parallel, Perpendicular, Tangent, Equal, Symmetric, Block
  • Dimensional constraints: Lock, Horizontal distance, Vertical distance, Distance, Radius or weight, Diameter, Auto radius/diameter, Angle, Refraction (Snell's law)
  • Constraint tools: Toggle driving/reference constraint, Activate/deactivate constraint

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• Sketcher tools: Select unconstrained DoF, Select associated constraints, Select associated geometry, Select redundant constraints, Select conflicting constraints, Show/hide internal geometry, Select origin, Select horizontal axis, Select vertical axis, Symmetry, Clone, Copy, Move, Rectangular array, Remove axes alignment, Delete all geometry, Delete all constraints

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• Sketcher B-spline tools: Show/hide B-spline degree, Show/hide B-spline control polygon, Show/hide B-spline curvature comb, Show/hide B-spline knot multiplicity, Show/hide B-spline control point weight, Convert geometry to B-spline, Increase B-spline degree, Decrease B-spline degree, Increase knot multiplicity, Decrease knot multiplicity, Insert knot, Join curves

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• Sketcher virtual space: Switch virtual space

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• Additional: Sketcher Dialog, Preferences, Sketcher scripting

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