Sketcher BSplineIncreaseKnotMultiplicity: Difference between revisions
No edit summary |
|||
Line 57: | Line 57: | ||
<translate> |
<translate> |
||
<!--T:18--> |
<!--T:18--> |
||
{{Caption|B-spline |
{{Caption|Same B-spline with knot multiplicity 3. A control point was moved to show that the knot has ''C''<sup>0</sup> continuity.}} |
||
<!--T:19--> |
<!--T:19--> |
||
A consequence of a higher multiplicity is that for the price of loosing continuity you gain local control. This means changing one control point only |
A consequence of a higher multiplicity is that for the price of loosing continuity you gain local control. This means changing one control point will only affect the B-spline locally. This can be seen in this example, where the B-spline from the first image was taken and the second control point from the right was moved up: |
||
</translate> |
</translate> |
Revision as of 09:23, 2 April 2024
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
The Sketcher BSplineIncreaseKnotMultiplicity tool increases the multiplicity of a B-spline knot. See this page for more information about B-splines.
Usage
- Select a B-spline knot.
- There are several ways to invoke the tool:
- Press the Increase knot multiplicity button.
- Select the Sketch → Sketcher B-spline tools → Increase knot multiplicity option from the menu.
Example
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 with multiplicity m on a B-spline with degree d means the curve to the left and right of the knot has at least an equal n order derivative (called Cn continuity) where n = d - m.
In this cubic B-spline (degree 3) there are 3 segments, meaning 3 curves are connected at 2 knots. The knots have multiplicity 1.
The multiplicity is indicated by the number in round brackets. See Show/hide B-spline knot multiplicity.
B-spline where both knots have multiplicity 1.
A multiplicity of 3 will change this B-spline so that even the first order derivatives are not equal (C0 continuity). Here is the same B-spline where the left's knot multiplicity was increased to 3:
Same B-spline with knot multiplicity 3. A control point was moved to show that the knot has C0 continuity.
A consequence of a higher multiplicity is that for the price of loosing continuity you gain local control. This means changing one control point will only affect the B-spline locally. This can be seen in this example, where the B-spline from the first image was taken and the second control point from the right was moved up:
Effect of locality due to different multiplicity.
The B-spline with knot multiplicity 1 has changed completely while the one with multiplicity 2 has kept its form on the left side.
- General: Create sketch, Edit sketch, Map sketch to face, 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, 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 by control points, Periodic B-spline by control points, B-spline by knots, Periodic B-spline by knots, Polyline, Rectangle, Centered rectangle, Rounded rectangle, Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon, Regular polygon, Slot, Fillet, Corner-preserving 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 or weight, Diameter, Auto radius/diameter, Angle, Refraction (Snell's law)
- Constraint tools: Toggle driving/reference constraint, Activate/deactivate constraint
- Sketcher tools: Select unconstrained DoF, Select associated constraints, Select associated geometry, Select redundant constraints, Select conflicting constraints, Show/hide internal geometry, Select origin, Select horizontal axis, Select vertical 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, Join curves
- 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, Assembly, 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