Creating a Curve from a Law

You can create a curve by defining its equation as a law.

Before you begin: You must have access to the Engineering Rules Capture app. Ensure that the Relations and Parameters options are selected in Me > Preferences > Common Preferences > Object Properties > 3D Shape> Display, 3D Shape Infrastructure area, Display in Tree section.
  1. In the Generative Shape Design app, define a working support using Work on Support .
    The Work On Support dialog box appears.
  2. In the Support box, select the yz plane, for instance.
  3. Click OK without modifying any other parameter.
    The Working Support.1 is created, and the system automatically moves into this plane. You now want to create a horizontal line as the abscissa axis.
  4. Click Line .
    The Line dialog box appears.
  5. Right-click in the Point 1 box, and choose the Insert Wireframe > Create Point.

    The Point Definition dialog box appears, the Point type and Plane boxes being automatically filled.

  6. Create a point at H:0mm and V:0mm and click OK.
  7. Repeat the operation, right-click the Point 2 box from the Line Definition dialog box to create another point at H:100mm and V:0mm, then click OK in the Point Definition dialog box.
  8. Click OK in the Line Definition dialog box to create the line.


    Important: You can hide the grid by selecting the Hide grid check box from the Work On Support dialog box.
  9. From the Tools section of the action bar, click Law .
    The Law Editor dialog box appears in which you name the law to be created, give it a description and a storage location.
  10. Click OK.
    The Law Editor dialog box is updated. The right-hand part allows you to create the parameters to be used in the law. The left-hand part is the law edition box.
  11. Create two real type parameters FormalReal.1 and FormalReal.2, then enter the law below into the edition window: FormalReal.1 = 5*sin(5*PI*1rad*FormalReal.2)+ 10

    Note: It is not advised to create laws that involve n-th roots of parameters (because their derivatives get infinite when they tend to zero and so the geometry at the extremities is of poor quality); it is advised to create extra parameters to get an equivalent relationship, but without n-th roots.

    Example: instead of writing "y=(1-x**0.5)**2", write rather "x=t**2" and "y=(1-t)**2".

  12. Click OK to create the law.
  13. In the Generative Shape Design app, click Parallel Curve .
    The Parallel Curve Definition dialog box appears.
  14. Select the line created in Step 7 as the reference Curve.
  15. Click Law... and select Law.1 from the tree.
  16. Click OK.

    A curve parallel to the selected one is created, taking the law into account, that is, it is defined by the equation entered as a law using Engineering Rules Capture.