Creating Parallel Curves

You can create a curve parallel to a reference curve.

Each point of the parallel curve is located at a distance to the input curve equal to the offset value defined for this point.

This task shows you how to:

Before you begin: Create a 3D shape containing a curve.
See Also
About Parallel Curves
In the Knowledge Base
Why does a parallel curve created using a radius law introduce angular discontinuities?

Create the Parallel Curve

You can create a curve parallel to an existing curve at a specified offset distance.

  1. From the section of the action bar, click Parallel Curve .
  2. In the Curve box, select the reference curve to be offset.
  3. In the Support box, select the plane or surface on which the reference curve lies.
  4. To specify the offset of the parallel curve, do one of the following:
    • Enter a value in the Constant box or use the handle in the work area.

    • Select a point in the Point box.

  5. Select the Parallel mode.
    OptionDescription
    Euclidean The distance between both curves is the shortest possible one, regardless of the support. If you select this mode, you can choose to offset the curve at a constant distance from the initial element, or according to a law. In this case, you need to select a law as defined in Creating Law. The law can be negative, providing the curves are curvature continuous.
    Note:
    • It is advised to use curvature continuous laws.
    • It is possible to create a parallel curve with a law that reverses (which means becoming either positive or negative) only on a curve that is tangency continuous.
    Geodesic The distance between both curves is the shortest possible one, taking the support curvature into account. In this case, the offset always is constant to every point on the curve and you do not need to select a corner type.
  6. Select the Parallel corner type, applicable for curves presenting sharp angles.

    Note: This option is unavailable when the Geodesic mode is selected.

    OptionDescription
    Sharp The parallel curve takes into account the angle in the initial curve.

    By default, the Parallel corner type is Sharp.
    Round The parallel curve is rounded off as in a corner.

  7. Optional: Select Both Sides to create parallel curves at both sides of the original curve.


  8. Optional: Select Repeat object after OK to create multiple parallel curves.


  9. Optional: Select Extrapolate up to support to extrapolate the parallel curve to the support boundaries.


  10. Click Preview.
    The parallel curve is displayed on the support surface and normal to the reference curve.
  11. Click OK to create the parallel curve.

Smooth the Curve

You can smoothen the parallel curves by defining a continuity.

To smooth the curve, select on of the following options:
OptionDescription
None Deactivates the smoothing result.
With a support surface:  
Tangency Enhances the current continuity to tangent continuity.
Curvature Enhances the current continuity to curvature continuity.
 
Note:
  • You can specify the maximum deviation for G1 or G2 smoothing by entering a value or using the arrows.
  • In an Euclidian parallel curve, only small discontinuities are smoothed, especially discontinuities that are introduced during the parallel operation.
  • A topology simplification is automatically performed for G2 vertices: cells with a curvature continuity are merged.
Without support surface:  
3D Smoothing The smoothing is performed without specifying any support surface. As a consequence, the resulting smoothed curve has a better continuity quality and is not exactly laid down on the surface. As a consequence, you may need to activate the Tolerant laydown option in Me > Preferences > App Preferences > 3D Modeling > 3D Modeling Core > Generative Shape Design, General tab, Tolerant Modeling section. This option is available if you previously select the Tangency or Curvature smoothing type.

3D Smoothing selected 3D Smoothing cleared

Use a Law

You can define a law to create parallel curves.

  1. Click Law . In this case, you need to select a law as defined in Creating Law.

    The 2D viewer enables you to preview the law evolution before applying it.

    The Law Viewer allows you to:

    • visualize the law evolution and the maximum and minimum values.
    • navigate into the viewer by panning and zooming (using the mouse).
    • trace the law coordinates by using the handle.
    • change the viewer size by changing the panel size.
    • reframe on by using the viewer context menu.
    • change the law evaluation step by using the viewer context menu (from 0.1 (10 evaluations) to 0.001 (1000 evaluations)).
  2. Enter the Start value and the End value.
  3. Select the law types
    OptionDescription
    Constant A regular law, only one value is needed.
    Linear A linear progression law between the Start and End indicated values.
    S type An S-shaped law between the two indicated values. For this type, you need to define a second value. The distance varies between these two values.
    Advanced Lets you select a Law element as defined in Creating Law.

    Important: When an advanced law presents vertical tangencies inside its definition domain, disconnecting the law and the input wire at this position may enable to improve the precision of the result.

  4. Select the Inverse law check box to reverse the law as defined using the above options.
  5. Click Close.