Sketcher BSplineIncreaseDegree/it: Difference between revisions

From FreeCAD Documentation
(Updating to match new version of source page)
(Updating to match new version of source page)
 
Line 16: Line 16:
</div>
</div>


<span id="Description"></span>
==Descrizione==
==Descrizione==


Line 22: Line 23:
</div>
</div>


<span id="Usage"></span>
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).
==Utilizzo==

<div class="mw-translate-fuzzy">
# Selezionare un bordo da una B-spline esistente e premere {{Button|[[File:Sketcher_BSplineIncreaseDegree.svg|16px]] [[Sketcher_BSplineIncreaseDegree/it|Aumenta di grado]]}}.
</div>

==Example==

B-splines are basically a combination of [[B-Splines#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).

In this cubic B-spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots.


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]]}}):
The degree is indicated by the number in the center. See [[File:Sketcher_BSplineDegree.svg|16px]] [[Sketcher_BSplineDegree|Show/hide B-spline degree]].


[[File:Sketcher_BSplineDegree3.png|400px]]
[[File:Sketcher_BSplineDegree3.png|400px]]
{{Caption|B-spline with degree 3 and 2 knots that each have the multiplicity 1.}}
{{Caption|B-spline with degree 3 and 2 knots that each have 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 [[Sketcher_BSplineDecreaseKnotMultiplicity#Description|this page]] for an explanation of the multiplicity)
The outer segments each have 2 control points, the inner segment has none to ensure the knots have multiplicity 1. See [[Sketcher_BSplineDecreaseKnotMultiplicity#Description|this page]] for an explanation about multiplicity.


Increasing the degree will add control points and the shape of the spline is not changed:
Increasing the degree to 4 will add control points without changing the shape of the B-spline:


[[File:Sketcher_BSplineDegree4.png|400px]]
[[File:Sketcher_BSplineDegree4.png|400px]]
{{Caption|Same B-spline where the degree was changed from 3 to 4. Note that also the knot multiplicity was increased.}}
{{Caption|Same B-spline where the degree was changed from 3 to 4. Note that the knot multiplicity has also 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:
From this result you cannot get back to the initial state of the B-spline by decreasing the degree. Some information is lost when the degree of a B-spline is changed. Decreasing the degree back to 3 leads to this:


[[File:Sketcher_BSplineDegree3from4.png|400px]]
[[File:Sketcher_BSplineDegree3from4.png|400px]]
{{Caption|Same B-spline where the degree was changed back from 4 to 3. Note that the knot multiplicity was increased. Depending on the spline, the algorithm to decrease the degree may add a lot of knots to preserve the spline shape as happened in this example.}}
{{Caption|Same B-spline where the degree was changed back from 4 to 3. Note that the knot multiplicity has increased again. Depending on the B-spline, the algorithm to decrease the degree may add a lot of knots to preserve the shape as has happened here.}}


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)
Each segment now has 2 control points and each knot is coincident with an additional control point. The knots have ''C<sup>0</sup>'' continuity so that the B-spline will get "corners" if you move a control point. The information of a higher continuity is therefore lost. See [[Sketcher_BSplineDecreaseKnotMultiplicity#Description|this page]] for an explanation about continuity.

==Utilizzo==

<div class="mw-translate-fuzzy">
# Selezionare un bordo da una B-spline esistente e premere {{Button|[[File:Sketcher_BSplineIncreaseDegree.svg|16px]] [[Sketcher_BSplineIncreaseDegree/it|Aumenta di grado]]}}.
</div>





Latest revision as of 07:28, 22 April 2024

Aumenta di grado

Posizione nel menu
Sketch → Strumenti B-spline → Aumenta di grado
Ambiente
Sketcher
Avvio veloce
Nessuno
Introdotto nella versione
0.17
Vedere anche
Crea B-spline

Descrizione

Aumenta il grado della B-spline (vedere: B-spline).

Utilizzo

  1. Selezionare un bordo da una B-spline esistente e premere Aumenta di grado.

Example

B-splines are basically a combination of Bézier curves (nicely explained in this and this video).

In this cubic B-spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots.

The degree is indicated by the number in the center. See Show/hide B-spline degree.

B-spline with degree 3 and 2 knots that each have multiplicity 1.

The outer segments each have 2 control points, the inner segment has none to ensure the knots have multiplicity 1. See this page for an explanation about multiplicity.

Increasing the degree to 4 will add control points without changing the shape of the B-spline:

Same B-spline where the degree was changed from 3 to 4. Note that the knot multiplicity has also increased.

From this result you cannot get back to the initial state of the B-spline by decreasing the degree. Some information is lost when the degree of a B-spline is changed. Decreasing the degree back to 3 leads to this:

Same B-spline where the degree was changed back from 4 to 3. Note that the knot multiplicity has increased again. Depending on the B-spline, the algorithm to decrease the degree may add a lot of knots to preserve the shape as has happened here.

Each segment now has 2 control points and each knot is coincident with an additional control point. The knots have C0 continuity so that the B-spline will get "corners" if you move a control point. The information of a higher continuity is therefore lost. See this page for an explanation about continuity.