Rysunek Roboczy: Sześcienna krzywa Béziera

From FreeCAD Documentation
Revision as of 15:52, 22 November 2023 by Kaktus (talk | contribs) (Created page with "{{Caption|Krzywa Spline składająca się z trzech sześciennych segmentów Béziera. Pierwszy segment jest zdefiniowany przez cztery punkty. Kolejne segmenty wykorzystują ponownie dwa punkty z poprzedniego segmentu, a zatem wymagają tylko dwóch dodatkowych punktów.}}")

Rysunek Roboczy: Sześcienna krzywa Beziera

Lokalizacja w menu
Drafting → Bézier tools → Sześcienna krzywa Beziera
Środowisko pracy
Rysunek Roboczy, Architektura
Domyślny skrót
brak
Wprowadzono w wersji
0.19
Zobacz także
Krzywa Bezier'a, Krzywa złożona

Opis

Polecenie Sześcienna krzywa Beziera tworzy krzywą Béziera trzeciego stopnia (wymagane są cztery punkty).

Krzywa Béziera jest jedną z najczęściej używanych krzywych w grafice komputerowej. Polecenie to pozwala utworzyć ciągły splajn składający się z kilku segmentów Béziera trzeciego stopnia, w sposób podobny do narzędzia Bézier w Inkscape. Ogólną krzywą Béziera dowolnego stopnia można utworzyć za pomocą polecenia Krzywa Bezier'a.

Polecenia Krzywa Bezier'a i Sześcienna krzywa Bezier'a używają punktów kontrolnych do zdefiniowania położenia i krzywizny odcinka krzywej. Z kolei polecenie Krzywa złożona określa dokładne punkty, przez które będzie przechodzić krzywa.

Krzywa Spline składająca się z trzech sześciennych segmentów Béziera. Pierwszy segment jest zdefiniowany przez cztery punkty. Kolejne segmenty wykorzystują ponownie dwa punkty z poprzedniego segmentu, a zatem wymagają tylko dwóch dodatkowych punktów.

Usage

See also: Draft Tray, Draft Snap and Draft Constrain.

  1. There are several ways to invoke the command:
    • Press the Draft CubicBezCurve button.
    • Select the Drafting → Bézier tools → Cubic Bézier curve option from the menu.
  2. The Cubic Bézier curve task panel opens. See Options for more information.
  3. It is not possible the enter points via the task panel.
  4. For the following Mouse Navigation Models a keyboard key must to be held down:
    • If you are using OpenInventor Navigation the Ctrl key must be held down throughout the command.
    • If you are using Gesture Navigation the Alt key must be held down for each click-hold-release sequence, but is also possible to keep this key held down throughout the command.
  5. Pick the first point in the 3D view and hold the mouse button (1), this is the first endpoint.
  6. Drag the pointer to another point in the 3D view and release the mouse button (2), this is the first control point.
  7. Move the pointer to another point in the 3D view, pick this point and hold the mouse button (3), this is the second endpoint.
  8. Move the pointer to another point in the 3D view to adjust the final curvature of the segment and release the mouse button (4), this is the second control point.
  9. You now have one Bézier curve of the 3rd degree.
  10. Optionally repeat the process of clicking and holding (5), and dragging and releasing (6) to add more segments.
  11. Each subsequent segment will use the second endpoint and second control point of the previous segment as its first endpoint and first control point respectively.
  12. Press Esc or the Close button to finish the command.

Options

See Draft BezCurve.

Notes

  • A Draft CubicBezCurve can be edited with the Draft Edit command.

Preferences

See Draft BezCurve.

Properties

See Draft BezCurve.

Scripting

See also: Autogenerated API documentation and FreeCAD Scripting Basics.

See Draft BezCurve for general information. A cubic Bézier is created by passing the option degree=3 to makeBezCurve().

For each cubic Bézier segment four points must be used, of which the two extreme points indicate where the spline passes through, and the two intermediate points are control points.

  • If only 3 points are given, it creates a quadratic Bézier instead, with only one control point.
  • If only 2 points are given, it creates a linear Bézier, that is, a straight line.
  • If 5 points are given, the first 4 create a cubic Bézier segment; the 4th and the 5th points are used to create a straight line.
  • If 6 points are given, the first 4 create a cubic Bézier segment; the 4th and the other two points are used to create a quadratic Bézier segment.
  • If 7 points are given, the first 4 create a cubic Bézier segment; the 4th and the other three points are used to create a second cubic Bézier segment.
  • In general, the last point in a group of four is shared with the following three points maximum to create another Bézier segment.
  • To have smooth curves, with no straight segments, the number of points should be 3n + 1 or 3n, where n is the number of segments, for n >= 1.

Examples of Bézier curves produced by using 2, 3, 4, 5, 6, 7, and 8 points. The solid lines indicate cubic Bézier segments; the other lines are quadratic or linear.

Example:

import FreeCAD as App
import Draft

doc = App.newDocument()

p1 = App.Vector(-3500, 0, 0)
p2 = App.Vector(-3000, 2000, 0)
p3 = App.Vector(-1100, 2000, 0)
p4 = App.Vector(0, 0, 0)

p5 = App.Vector(1500, -2000, 0)
p6 = App.Vector(3000, -1500, 0)
p7 = App.Vector(5000, 0, 0)
p8 = App.Vector(6000, 1500, 0)
rot = App.Rotation()

c1 = Draft.make_circle(100, placement=App.Placement(p1, rot), face=False)
c1.Label = "B1_E1"
c2 = Draft.make_circle(50, placement=App.Placement(p2, rot), face=True)
c2.Label = "B1_c1"
c3 = Draft.make_circle(50, placement=App.Placement(p3, rot), face=True)
c3.Label = "B1_c2"
c4 = Draft.make_circle(100, placement=App.Placement(p4, rot), face=False)
c4.Label = "B1_E2"
c5 = Draft.make_circle(50, placement=App.Placement(p5, rot), face=True)
c5.Label = "B2_c3"
c6 = Draft.make_circle(50, placement=App.Placement(p6, rot), face=True)
c6.Label = "B2_c4"
c7 = Draft.make_circle(100, placement=App.Placement(p7, rot), face=False)
c7.Label = "B2_E3"
c8 = Draft.make_circle(50, placement=App.Placement(p8, rot), face=True)
c8.Label = "B3_c5"

doc.recompute()

B1 = Draft.make_bezcurve([p1, p2], degree=3)
B1.Label = "B_lin"
B1.ViewObject.DrawStyle = "Dashed"

B2 = Draft.make_bezcurve([p1, p2, p3], degree=3)
B2.Label = "B_quad"
B2.ViewObject.DrawStyle = "Dotted"

B3 = Draft.make_bezcurve([p1, p2, p3, p4], degree=3)
B3.Label = "B_cub"
B3.ViewObject.LineWidth = 4

B4 = Draft.make_bezcurve([p1, p2, p3, p4, p5], degree=3)
B4.Label = "B_cub+lin"
B4.ViewObject.DrawStyle = "Dashed"

B5 = Draft.make_bezcurve([p1, p2, p3, p4, p5, p6], degree=3)
B5.Label = "B_cub+quad"
B5.ViewObject.DrawStyle = "Dotted"

B6 = Draft.make_bezcurve([p1, p2, p3, p4, p5, p6, p7], degree=3)
B6.Label = "B_cub+cub"
B6.ViewObject.LineWidth = 2

B7 = Draft.make_bezcurve([p1, p2, p3, p4, p5, p6, p7, p8], degree=3)
B7.Label = "B_cub+cub+lin"
B7.ViewObject.DrawStyle = "Dashed"

doc.recompute()