Sketcher "Увеличение кратности узлов"
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| Системное название |
|---|
| Sketcher_BSplineIncreaseKnotMultiplicity |
| Расположение в меню |
| Sketch → B-сплйан инструменты эскиза → Увеличение кратности узлов |
| Верстаки |
| Sketcher |
| Быстрые клавиши |
| Нет |
| Представлено в версии |
| 0.17 |
| См. также |
| Показать/скрыть кратность узлов B-сплайна, Уменьшение кратности узлов |
Описание
The 
Sketcher BSplineIncreaseKnotMultiplicity tool increases the multiplicity of a B-spline knot.
Применение
- 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.
- Press the
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 numbers 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 multiplicity of the knot on the left 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. Meaning changing one control point will only affect the B-spline locally.
This can be seen in this example, where the B-spline with knot multiplicity 1 from the first image above was taken, and the second control point from the right was moved up. As a result the complete shape of the B-spline has changed:
After increasing the multiplicity of the knots to 2, moving the second control point from the right results in significant changes on the right side of the shape only:
Notes
- Knot multiplicity can also be increased with Sketcher BSplineInsertKnot.
Sketcher
- 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
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