Sketcher BSplinePoleWeight/pl: Difference between revisions

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(Created page with "# Wybierz krzywą złożoną i użyj przycisku na pasku narzędzi {{Button|16px '''Pokaż / ukryj wagę punktu kontrolnego krzywej złożonej'''}}.")
(Created page with "Krzywe złozone są w zasadzie kombinacją Krzywych Béziera ''(ładnie wyjaśnione w filmie [https://www.youtube.com/watch?v=bE1MrrqBAl8 From Bézier curves to B-spline curves] oraz [https://www.youtube.com/watch?v=xXJylM2S72s Properties of B-spline curves])''.")
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==Objaśnienie wagi==
==Objaśnienie wagi==


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).
Krzywe złozone w zasadzie kombinacją [[B-Splines/pl#Krzywe_Béziera|Krzywych Béziera]] ''(ładnie wyjaśnione w filmie [https://www.youtube.com/watch?v=bE1MrrqBAl8 From Bézier curves to B-spline curves] oraz [https://www.youtube.com/watch?v=xXJylM2S72s Properties of B-spline curves])''.


The Bézier curve is calculated using this formula:
The Bézier curve is calculated using this formula:

Revision as of 16:37, 7 May 2023

Szkicownik: Pokaż / ukryj wagę punktu kontrolnego krzywej złożonej

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Szkic → Narzędzia szkicownika krzywej złożonej → Pokaż / ukryj wagę punktu kontrolnego krzywej złożonej
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Zobacz także
Komponent utwórz krzywą złożoną

Opis

Pokazuje lub ukrywa wyświetlanie wag dla punktów kontrolnych krzywej złożonej (zobacz poniższy akapit dla wyjaśnienia wag).

Krzywa złożona z wagami punktów kontrolnych podanymi w nawiasach.

Użycie

  1. Wybierz krzywą złożoną i użyj przycisku na pasku narzędzi Pokaż / ukryj wagę punktu kontrolnego krzywej złożonej.

Objaśnienie wagi

Krzywe złozone są w zasadzie kombinacją Krzywych Béziera (ładnie wyjaśnione w filmie From Bézier curves to B-spline curves oraz Properties of B-spline curves).

The Bézier curve is calculated using this formula:

n is hereby the degree of the curve. So a Bézier curve of degree n is a polygon with order n. The factors are hereby in fact the coordinates of the Bézier curves' control points. For a visualization see this page.

The term weight in FreeCAD is a bit misleading because in literature the factors are often called weights as well. FreeCAD's weights are something different. The idea of these weights is to modify the spline so that the different control points are "weighted". The idea is that a point with weight 2 should have twice as much influence than a point with weight 1. This is achieved by using this different formula to calculate the spline:

whereby is the weight for the point .

This is a new class of Bézier curves because despite the points are indeed weighted as desired, the curve is no longer a polynomial but a fractional polynomial. Therefore these curves are called rational Bézier curves and the B-splines is then called rational B-splines.

The consequence is that you gain more flexibility in defining the spline shape. If all weights are equal, the shape of the spline does not change. So the weights relative to each other is important, not the value alone. For example this spline has exactly the same shape as the one in the first image:

Same B-spline as in first image but with different absolute weight values

A weight of zero would be a singularity in the equation to calculate the rational Bézier curves, therefore FreeCAD assures that it cannot become zero. Nevertheless, small values have the same effect as if the control point would almost not exist:

Same B-spline with an almost zero weight control point

Changing Weights

How to change weights is described in this Wiki page.