Curva de Bezier Cúbica
|Drafting → Bézier tools → Cubic Bézier curve|
|Introduced in version|
|Draft BezCurve, Draft BSpline|
The Draft CubicBezCurve command creates a Bézier curve of the third degree (four points required).
The Bézier Curve is one of the most commonly used curves in computer graphics. This command allows you to create a continuous spline made up of several 3rd-degree Bézier segments, in a way that is similar to the Bézier tool in Inkscape. A general Bézier curve of any degree can be created with the Draft BezCurve command.
The Draft BezCurve and the Draft CubicBezCurve commands use control points to define the position and curvature of the spline. The Draft BSpline command, on the other hand, specifies the exact points through which the curve will pass.
Spline consisting of three cubic Bézier segments. The first segment is defined by four points. Subsequent segments reuse two points from the previous segment and therefore require only two additional points.
See also: Draft Tray, Draft Snap and Draft Constrain.
- 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.
- The Cubic Bézier curve task panel opens. See Options for more information.
- It is not possible the enter points via the task panel.
- 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.
- Pick the first point in the 3D view and hold the mouse button (1), this is the first endpoint.
- Drag the pointer to another point in the 3D view and release the mouse button (2), this is the first control point.
- Move the pointer to another point in the 3D view, pick this point and hold the mouse button (3), this is the second endpoint.
- 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.
- You now have one Bézier curve of the 3rd degree.
- Optionally repeat the process of clicking and holding (5), and dragging and releasing (6) to add more segments.
- 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.
- Press Esc or the Close button to finish the command.
See Draft BezCurve.
- A Draft CubicBezCurve can be edited with the Draft Edit command.
See Draft BezCurve.
See Draft BezCurve.
See also: Autogenerated API documentation and FreeCAD Scripting Basics.
See Draft BezCurve for general information. A cubic Bézier is created by passing the option
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 + 1or
nis 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.
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()
- Drafting: Line, Polyline, Fillet, Arc, Arc by 3 points, Circle, Ellipse, Rectangle, Polygon, B-spline, Cubic Bézier curve, Bézier curve, Point, Facebinder, ShapeString, Hatch
- Annotation: Text, Dimension, Label, Annotation styles, Annotation scale
- Modification: Move, Rotate, Scale, Mirror, Offset, Trimex, Stretch, Clone, Array, Polar array, Circular array, Path array, Path Link array, Point Array, Point Link array, Edit, Subelement highlight, Join, Split, Upgrade, Downgrade, Wire to B-spline, Draft to Sketch, Set slope, Flip dimension, Shape 2D view
- Draft Tray: Select Plane, Set style, Toggle construction mode, AutoGroup
- Snapping: Snap Lock, Snap Endpoint, Snap Midpoint, Snap Center, Snap Angle, Snap Intersection, Snap Perpendicular, Snap Extension, Snap Parallel, Snap Special, Snap Near, Snap Ortho, Snap Grid, Snap WorkingPlane, Snap Dimensions, Toggle Grid
- Miscellaneous: Apply current style, Layer, Manage layers, Add a new named group, Move to group, Select group, Add to Construction group, Toggle normal/wireframe display, Create working plane proxy, Heal, Toggle continue mode, Show snap toolbar
- Additional: Constraining, Pattern, Preferences, Import Export Preferences, DXF/DWG, SVG, OCA, DAT
- Context menu:
- Layer container: Merge layer duplicates, Add new layer
- Layer: Activate this layer, Select layer contents
- Working plane proxy: Write camera position, Write objects state
- Getting started
- Installation: Download, Windows, Linux, Mac, Additional components, Docker, AppImage, Ubuntu Snap
- Basics: About FreeCAD, Interface, Mouse navigation, Selection methods, Object name, Preferences, Workbenches, Document structure, Properties, Help FreeCAD, Donate
- Help: Tutorials, Video tutorials
- Workbenches: Std Base, Arch, Draft, FEM, Inspection, Mesh, OpenSCAD, Part, PartDesign, Path, Points, Reverse Engineering, Robot, Sketcher, Spreadsheet, Start, Surface, TechDraw, Test Framework, Web
- Hubs: User hub, Power users hub, Developer hub