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 |
Sketcher Show/hide B-spline knot multiplicity, Sketcher Decrease knot multiplicity |
Description
Increases the multiplicity of a B-spline knot. (See this page for more info about B-splines).
B-splines are basically a combination of Bézier curves (nicely explained in this and this video). The points where two Bézier pieces are connected are called knots. A knot on a spline with degree d and with the multiplicity m means that the curve left and right to the knot has at least an equal n order derivative (called C^{n} continuity) whereas .
Here is a cubic spline () whose knots have the multiplicity 1. The multiplicity is indicated by the number in parentheses. The indication can be changed using the toolbar button Show/hide B-spline knot multiplicity:
B-spline where both knots have the multiplicity 1.
A multiplicity of 3 will change this spline so that even the first order derivatives are not equal (C^{0} continuity). Here is the same spline where the left's knot multiplicity was increased to 3:
B-spline from above with knot multiplicity 3. A control point was moved to show that the knot has C^{0} continuity.
A consequence of a higher multiplicity is that for the price of loosing continuity you gain local control. This means the change of one control point only affects the spline locally to this changed point. This can be seen in this example, where the spline from the first image above was taken and its 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 1 is 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 Increase knot multiplicity.
- Use the menu Sketch → Sketcher B-spline tools → Increase knot multiplicity.
- General: Create sketch, Edit sketch, Leave sketch, View sketch, View section, Map sketch to face, Reorient sketch, Validate sketch, Merge sketches, Mirror sketch, Stop operation
- Sketcher geometries: Point, Line, Arc, Arc by 3 points, Circle, Circle by 3 points, Ellipse, Ellipse by 3 points, Arc of ellipse, Arc of hyperbola, Arc of parabola, B-spline, Periodic B-pline, Polyline, Rectangle, Centered rectangle, Rounded rectangle, Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon, Regular polygon, Slot, Fillet, Trim, Extend, Split, External geometry, Carbon copy, Toggle construction geometry
- Sketcher constraints:
- Geometric constraints: Coincident, Point on object, Vertical, Horizontal, Parallel, Perpendicular, Tangent, Equal, Symmetric, Block
- Dimensional constraints: Lock, Horizontal distance, Vertical distance, Distance, Radius, Diameter, Radiam, Angle, Snell's law, Internal alignment
- Constraint tools: Toggle driving/reference constraint, Activate/deactivate constraint
- Sketcher tools: Select unconstrained DoF, Close shape, Connect edges, Select associated constraints, Select associated geometry, Select redundant constraints, Select conflicting constraints, Show/hide internal geometry, Select origin, Select vertical axis, Select horizontal axis, Symmetry, Clone, Copy, Move, Rectangular array, Remove axes alignment, Delete all geometry, Delete all constraints
- Sketcher B-spline tools: 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, Convert geometry to B-spline, Increase B-spline degree, Decrease B-spline degree, Increase knot multiplicity, Decrease knot multiplicity, Insert knot
- Sketcher virtual space: 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, Arch, Draft, FEM, Image, Inspection, Mesh, OpenSCAD, Part, PartDesign, Path, Points, Raytracing, Reverse Engineering, Sketcher, Spreadsheet, Start, Surface, TechDraw, Test Framework, Web
- Deprecated or unmaintained workbenches: Complete, Drawing, Robot
- Hubs: User hub, Power users hub, Developer hub