Sketcher BSplineIncreaseKnotMultiplicity
Sketcher BSplineIncreaseKnotMultiplicity |
Menu location |
---|
Sketch → Sketcher B-spline tools → Increase knot multiplicity |
Workbenches |
Sketcher |
Default shortcut |
None |
Introduced in version |
0.17 |
See also |
Show/hide B-spline knot multiplicity, Decrease knot multiplicity |
Description
Increases the knot multiplicity of a B-spline curve knot (see B-spline).
B-splines are basically a combination of Bézier curves (nicely explained in this and this video). The points where two Bézier curves are connected to form the spline is called the knot. A knot with the multiplicity 1 means that the curve left and right to the knot has at least the same first order derivative (called C1 continuity).
Here is a spline whose knots have the multiplicity 1 (indicated by the number in parentheses,
indication can be changed using the toolbar button Show/hide B-spline knot multiplicity):
B-spline where both knots have the multiplicity 1. You can see that the second order derivatives left and right to the knots are not equal.
A multiplicity of 2 will change the spline so that the second order derivatives becomes equal (C2 continuity). Here is the same spline where the multiplicity was increased to 2:
File:Sketcher KnotMultiplicity multiplicity2.png
B-spline where both knots have now the multiplicity 2. Note that control points were added and changed to achieve this.
Another consequence of a multiplicity of 2 is that you gain local control. This means the change of one control point only affects the splice locally to this changed point. This can be seen in this example, where the splines from the images above were taken and their the second control point from the right side was moved up:
Effect of locality due to different multiplicity.
One can see that the spline with knot multiplicity 1is completely changed while the one with multiplicity 2 kept its form at its left side.
Usage
- Select a B-spline knot.
- Either:
- Press the button B-spline increase knot multiplicity.
- Use the menu Sketch → Sketcher B-spline tools → Increase knot multiplicity.
- General: Create sketch, Edit sketch, Attach sketch, Reorient sketch, Validate sketch, Merge sketches, Mirror sketch, Leave sketch, View sketch, View section, Toggle grid, Toggle snap, Configure rendering order, Stop operation
- Sketcher geometries: Point, Polyline, Line, Arc, Arc by 3 points, Arc of ellipse, Arc of hyperbola, Arc of parabola, Circle, Circle by 3 points, Ellipse, Ellipse by 3 points, Rectangle, Centered rectangle, Rounded rectangle, Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon, Regular polygon, Slot, Arc slot, B-spline by control points, Periodic B-spline by control points, B-spline by knots, Periodic B-spline by knots, Toggle construction geometry
- Sketcher constraints:
- Dimensional constraints: Dimension, Horizontal distance, Vertical distance, Distance, Auto radius/diameter, Radius, Diameter, Angle, Lock
- Geometric constraints: Coincident (unified), Coincident, Point on object, Horizontal/vertical, Horizontal, Vertical, Parallel, Perpendicular, Tangent or collinear, Equal, Symmetric, Block
- Other constraints: Refraction (Snell's law)
- Constraint tools: Toggle driving/reference constraint, Activate/deactivate constraint
- Sketcher tools: Fillet, Chamfer, Trim, Split, Extend, External geometry, Carbon copy, Select origin, Select horizontal axis, Select vertical axis, Array transform, Polar transform, Scale transform, Offset geometry, Symmetry, Remove axes alignment, Delete all geometry, Delete all constraints
- Sketcher B-spline tools: Convert geometry to B-spline, Increase B-spline degree, Decrease B-spline degree, Increase knot multiplicity, Decrease knot multiplicity, Insert knot, Join curves
- Sketcher visual: Select unconstrained DoF, Select associated constraints, Select associated geometry, Select redundant constraints, Select conflicting constraints, Show/hide circular helper for arcs, Show/hide B-spline degree, Show/hide B-spline control polygon, Show/hide B-spline curvature comb, Show/hide B-spline knot multiplicity, Show/hide B-spline control point weight, Show/hide internal geometry, Switch virtual space
- Additional: Sketcher Dialog, Preferences, Sketcher scripting
- 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, Assembly, BIM, CAM, Draft, FEM, Inspection, Mesh, OpenSCAD, Part, PartDesign, Points, Reverse Engineering, Robot, Sketcher, Spreadsheet, Surface, TechDraw, Test Framework
- Hubs: User hub, Power users hub, Developer hub