Creating Parallel Curves

This task shows you how to create a curve that is parallel to a reference curve.

Open the ParallelCurves1.CATPart document.

  1. Click Parallel Curve .

    The Parallel Curve Definition dialog box appears.
  2. Select the reference Curve to be offset.

  3. Select the Support plane or surface on which the reference curve lies.

  4. Specify the offset of the parallel curve either by:

    • entering a value or using the graphic manipulator in the Constant field.
    • selecting a point in the Point field (in both Geodesic and Euclidean mode)
      In that case, Constant is grayed.
  5. Choose the parallelism mode to create the parallel curve.

    • Euclidean: the distance between both curves will be 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 Laws.
      The law can be negative, providing the curves are curvature continuous.
      • 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.

    1. Click Law... to display the Law Definition dialog box. In this case, you need to select a law as defined in Creating Laws.
      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 to the mouse),
      • trace the law coordinates by using the manipulator,
      • change the viewer size by changing the panel size
      • reframe on by using the viewer contextual menu
      • change the law evaluation step by using the viewer contextual menu (from 0.1 (10 evaluations) to 0.001 (1000 evaluations)).
    2. Enter Start and End values.

    3. Choose the law type.
      Four law types are available:
      • 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
      • Advanced: allowing to select a Law element as defined in Creating Laws.
      For the S type, you need to define a second value. The distance will vary between these two values.
    4. Check Inverse law to reverse the law as defined using the above options.

    5. Click OK to return to the Parallel Curve Definition dialog box.

    • Geodesic: the distance between both curves will be the shortest possible one, taking the support curvature into account. 
      In this case, the offset always is constant in every points of the curves and you do not need to select a corner type.
  6. Select corner type (useful for curves presenting sharp angles):

    • Sharp: the parallel curve takes into account the angle in the initial curve
    • Round: the parallel curve is rounded off as in a corner
      This type is only effective with acute angles, not with obtuse or re-entrant angles. It corresponds to the trace left by a ball rolling on a profile.
  7. Click Preview.

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

    The curve (identified as is added to the specification tree.
    Parallel curve defined by an constant offset value Parallel curve defined by a passing point
    Parameters can be edited in the 3D geometry. To have further information, please refer to the Editing Parameters chapter.

Optional Parameters

  • You can click Reverse Direction to display the parallel curve on the other side of the reference curve or click the arrow directly on the geometry.
  • When the selected curve is a planar curve, its plane is selected by default. However, you can explicitly select any support.
  • when you modify an input value through the dialog box, such as the offset value or the direction, the result is computed only when you click Preview or OK.
  • Would the value be inconsistent with the selected geometry, a warning message is displayed, along with a warning sign onto the geometry. If you move the pointer over this sign, a longer message is displayed to help you continue with the operation.
  • Check Both Sides to create two parallel curves, symmetrically in relation to the selected curve, and provided it is compatible with the initial curve's curvature radius.
    The second parallel curve has the same offset value as the first parallel curve. In that case it appears as aggregated under the first element.
    Therefore both parallel curves can only be edited together and the aggregated element alone cannot be deleted.
    If you use the Datum mode, the second parallel is not aggregated under the first one, but two datum elements are created.
  • Click Repeat object after OK to create several parallel curves, each separated from the initial curve by a multiple of the offset value.
    Simply indicate in the Object Repetition dialog box the number of instances that should be created and click OK.


  You can smooth the curve by checking either:

  • 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

You can specify the maximum deviation for G1 or G2 smoothing by entering a value or using the spinners. 

In the case of an Euclidian parallel curve, only small discontinuities are smoothed, especially discontinuities that are introduced during the parallel operation.

Moreover, 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. Refer to the Customizing General Settings chapter.
    This option is available if you previously select the Tangency or Curvature smoothing type.
    Open the ParallelCurves2.CATPart document.
    With 3D smoothing option checked With 3D smoothing option unchecked