Difference between revisions of "Sketcher BSplineIncreaseDegree"
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|[[Sketcher_Workbench|Sketcher]] | |[[Sketcher_Workbench|Sketcher]] | ||
|IconL=Sketcher_BSplineConvertToNURB.svg | |IconL=Sketcher_BSplineConvertToNURB.svg | ||
+ | |IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg | ||
|IconC=Workbench_Sketcher.svg | |IconC=Workbench_Sketcher.svg | ||
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}} | }} | ||
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{{GuiCommand | {{GuiCommand | ||
|Name=Sketcher BSplineIncreaseDegree | |Name=Sketcher BSplineIncreaseDegree | ||
+ | |MenuLocation=Sketch → Sketcher B-spline tools → Increase Degree of B-spline | ||
|Workbenches=[[Sketcher_Workbench|Sketcher]] | |Workbenches=[[Sketcher_Workbench|Sketcher]] | ||
− | |||
|Version=0.17 | |Version=0.17 | ||
− | |SeeAlso=[[ | + | |SeeAlso=[[Sketcher_BSplineDegree|Sketcher Show/hide B-spline degree]], [[Sketcher_BSplineDecreaseDegree|Sketcher Decrease B-spline degree]] |
}} | }} | ||
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<!--T:10--> | <!--T:10--> | ||
Increases the degree of the B-spline(see [https://en.wikipedia.org/wiki/B-spline B-spline]). | Increases the degree of the B-spline(see [https://en.wikipedia.org/wiki/B-spline B-spline]). | ||
+ | |||
+ | <!--T:19--> | ||
+ | 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). | ||
+ | |||
+ | <!--T:20--> | ||
+ | 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]]}}): | ||
+ | |||
+ | </translate> | ||
+ | [[File:Sketcher_BSplineDegree3.png|400px]] | ||
+ | <translate> | ||
+ | <!--T:21--> | ||
+ | {{Caption|B-spline with degree 3 and 2 knots that each have the multiplicity 1.}} | ||
+ | |||
+ | <!--T:22--> | ||
+ | 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) | ||
+ | |||
+ | <!--T:23--> | ||
+ | Increasing the degree will add control points and the shape of the spline is not changed: | ||
</translate> | </translate> | ||
− | [[File: | + | [[File:Sketcher_BSplineDegree4.png|400px]] |
<translate> | <translate> | ||
+ | <!--T:24--> | ||
+ | {{Caption|Same B-spline where the degree was changed from 3 to 4. Note that also the knot multiplicity was increased.}} | ||
− | <!--T: | + | <!--T:25--> |
− | {{Caption|Same B-spline | + | 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: |
+ | |||
+ | </translate> | ||
+ | [[File:Sketcher_BSplineDegree3from4.png|400px]] | ||
+ | <translate> | ||
+ | <!--T:26--> | ||
+ | {{Caption|Same B-spline where the degree was changed back from 4 to 3. Note that the knot multiplicity was increased.}} | ||
+ | |||
+ | <!--T:27--> | ||
+ | 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) | ||
==Usage== <!--T:5--> | ==Usage== <!--T:5--> | ||
<!--T:17--> | <!--T:17--> | ||
− | # Select an edge from an existing B-spline, and press {{Button|[[File:Sketcher_BSplineIncreaseDegree.svg|24px]] | + | # Select an edge from an existing B-spline, and press {{Button|[[File:Sketcher_BSplineIncreaseDegree.svg|24px]] '''Increase B-spline degree'''}}. |
+ | |||
<!--T:8--> | <!--T:8--> | ||
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|[[Sketcher_Workbench|Sketcher]] | |[[Sketcher_Workbench|Sketcher]] | ||
|IconL=Sketcher_BSplineConvertToNURB.svg | |IconL=Sketcher_BSplineConvertToNURB.svg | ||
+ | |IconR=Sketcher_BSplineIncreaseKnotMultiplicity.svg | ||
|IconC=Workbench_Sketcher.svg | |IconC=Workbench_Sketcher.svg | ||
− | |||
}} | }} | ||
Latest revision as of 20:48, 2 December 2020
Menu location |
---|
Sketch → Sketcher B-spline tools → Increase Degree of B-spline |
Workbenches |
Sketcher |
Default shortcut |
None |
Introduced in version |
0.17 |
See also |
Sketcher Show/hide B-spline degree, Sketcher Decrease B-spline degree |
Contents |
Description
Increases the degree of the B-spline(see 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 C^{0} 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)
Usage
- The tools: New sketch, Edit sketch, Leave sketch, View sketch, View section, Map sketch to face, Reorient sketch, Validate sketch, Merge sketches, Mirror sketch
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- Dimensional constraints Lock, Horizontal Distance, Vertical Distance, Distance, Radius, Internal Angle, Snell's Law, Internal Alignment, Toggle reference/driving constraint,
- Sketcher tools Select solver DOFs, Close Shape, Connect Edges, Select Constraints, Select Origin, Select Vertical Axis, Select Horizontal Axis, Select Redundant Constraints, Select Conflicting Constraints, Select Elements Associated with constraints, Show/Hide internal geometry, Symmetry, Clone, Copy, Move, Rectangular Array, 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, Convert Geometry to B-spline, Increase degree, Increase knot multiplicity, Decrease knot multiplicity
- Sketcher virtual space Switch Virtual Space
- Getting started
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