Sketcher BSplineDecreaseKnotMultiplicity: Difference between revisions

Latest revision as of 11:18, 2 April 2024

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Increase knot multiplicity

Insert knot

Sketcher

Menu location
Sketcher BSplineDecreaseKnotMultiplicity
Sketch → Sketcher B-spline tools → Decrease knot multiplicity
Workbenches
Sketcher
Default shortcut
None
Introduced in version
0.17
See also
Sketcher BSplineIncreaseKnotMultiplicity

Description

The Sketcher BSplineDecreaseKnotMultiplicity tool decreases the multiplicity of a B-spline knot.

Usage

Select a B-spline knot.
There are several ways to invoke the tool:
- Press the Decrease knot multiplicity button.
- Select the Sketch → Sketcher B-spline tools → Decrease knot multiplicity option from the menu.

Example

See Sketcher_BSplineIncreaseKnotMultiplicity

Notes

If you decrease the multiplicity of a knot to zero, the knot vanishes. Mathematically it then appears zero times in the knot vector, meaning there is no longer a basis function. Understanding this requires some math, but it will also be clear if you look at the multiplicity. For example a knot with multiplicity 0 on a B-spline with degree 3 means that at the position of the knot two Bézier pieces are connected with C³ continuity. So the third derivative should be equal on both sides of the knot. However for a cubic Bézier curve this means that both sides must be part of the same curve. There is then effectively no longer a knot connecting 2 Bézier curves.

Increase knot multiplicity

Insert knot

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

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

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

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

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

Sketcher virtual space: Switch virtual space

Additional: Sketcher Dialog, Preferences, Sketcher scripting

User documentation

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@@ Line 1: / Line 1: @@
 <languages/>
+{{Page_in_progress}}
 <translate>
 <!--T:11-->
 {{Docnav
 |[[Sketcher_BSplineIncreaseKnotMultiplicity|Increase knot multiplicity]]
+|[[Sketcher_BSplineInsertKnot|Insert knot]]
-|[[Sketcher_SwitchVirtualSpace|Switch Virtual Space]]
 |[[Sketcher_Workbench|Sketcher]]
 |IconL=Sketcher_BSplineIncreaseKnotMultiplicity.svg
+|IconR=Sketcher_BSplineInsertKnot.svg‎
 |IconC=Workbench_Sketcher.svg
+}}
-|IconR=Sketcher_SwitchVirtualSpace.svg
-‎}}
 <!--T:1-->
 {{GuiCommand
 |Name=Sketcher BSplineDecreaseKnotMultiplicity
-|Workbenches=[[Sketcher Workbench|Sketcher]]
 |MenuLocation=Sketch → Sketcher B-spline tools → Decrease knot multiplicity
+|Workbenches=[[Sketcher_Workbench|Sketcher]]
 |Version=0.17
-|SeeAlso=[[Sketcher CompCreateBSpline|Create B-spline]]
+|SeeAlso=[[Sketcher_BSplineIncreaseKnotMultiplicity|Sketcher BSplineIncreaseKnotMultiplicity]]
 }}
@@ Line 23: / Line 25: @@
 <!--T:9-->
+The [[Image:Sketcher_BSplineDecreaseKnotMultiplicity.svg|24px]] [[Sketcher_BSplineDecreaseKnotMultiplicity|Sketcher BSplineDecreaseKnotMultiplicity]] tool decreases the multiplicity of a [[B-Splines|B-spline]] knot.
-Decreases the knot multiplicity of a B-spline curve knot (see [https://en.wikipedia.org/wiki/B-spline B-spline]).
-</translate>
-[[File:sketcher_SampleBSplineDecreaseKnotMultiplicity.png]]
-<translate>
-<!--T:10-->
-{{Caption|B-spline curve showing decreasing knot multiplicity.}}
 ==Usage== <!--T:5-->
-# Select a B-spline knot
+<!--T:14-->
-# Invoke the tool using several methods:
+# Select a B-spline knot.
-#* Press the {{KEY|[[Image:Sketcher_BSplineDecreaseKnotMultiplicity.svg|24px]]}} button in the toolbar.
+# There are several ways to invoke the tool:
-#* Use the {{MenuCommand|Sketch → Sketcher B-spline tools → Decrease knot multiplicity}} entry in the top menu.
+#* Press the {{Button|[[File:Sketcher_BSplineDecreaseKnotMultiplicity.svg|16px]] [[Sketcher_BSplineDecreaseKnotMultiplicity|Decrease knot multiplicity]]}} button.
+#* Select the {{MenuCommand|Sketch → Sketcher B-spline tools → [[Image:Sketcher_BSplineDecreaseKnotMultiplicity.svg|16px]] Decrease knot multiplicity}} option from the menu.
+==Example==
+See [[Sketcher_BSplineIncreaseKnotMultiplicity#Example|Sketcher_BSplineIncreaseKnotMultiplicity]]
+==Notes==
+<!--T:21-->
+If you decrease the multiplicity of a knot to zero, the knot vanishes. Mathematically it then appears zero times in the knot vector, meaning there is no longer a basis function. Understanding this requires some math, but it will also be clear if you look at the multiplicity. For example a knot with multiplicity 0 on a B-spline with degree 3
+means that at the position of the knot two Bézier pieces are connected with ''C<sup>3</sup>'' continuity. So the third derivative should be equal on both sides of the knot. However for a cubic Bézier curve this means that both sides must be part of the same curve. There is then effectively no longer a knot connecting 2 Bézier curves.
 <!--T:8-->
 {{Docnav
 |[[Sketcher_BSplineIncreaseKnotMultiplicity|Increase knot multiplicity]]
+|[[Sketcher_BSplineInsertKnot|Insert knot]]
-|[[Sketcher_SwitchVirtualSpace|Switch Virtual Space]]
 |[[Sketcher_Workbench|Sketcher]]
 |IconL=Sketcher_BSplineIncreaseKnotMultiplicity.svg
+|IconR=Sketcher_BSplineInsertKnot.svg‎
 |IconC=Workbench_Sketcher.svg
+}}
-|IconR=Sketcher_SwitchVirtualSpace.svg
-‎}}
-<!--T:12-->
-{{Sketcher Tools navi}}
-<!--T:13-->
-{{Userdocnavi}}
 </translate>
+{{Sketcher_Tools_navi{{#translation:}}}}
-{{clear}}
+{{Userdocnavi{{#translation:}}}}