A parametric curve is a curve in 2D and 3D where you use a parameter to define the coordinates of the curve. For example, the coordinates (s·cos(s), s·sin(s)) for a parameter s that runs from 0 to 10 π defines a spiral in 2D. To create a parametric curve, on the Geometry toolbar, from the More Primitives (3D or 2D ) menu, select Parametric Curve (). You can also right-click the Geometry node to add this node from the context menu. Then enter the properties of the parametric curve using the following sections:

Define the parameter name in the Name field (default name: s). Also define the interval for the parameter values in the Minimum (default: 0) and Maximum (default: 1) fields.

Enter the expressions that define the functions of the parameter for each spatial coordinate in the x, y (r and z in 2D axial symmetry, xw and yw in work planes), and (3D only) z fields. To create the spiral described earlier with the parameter s, type s*cos(s) in the x field and s*sin(s) in the y field.

By default, the x, y (r and z in 2D axial symmetry, xw and yw in work planes), and (in 3D) z expressions define the coordinates of points on the curve in the standard coordinate system. It is, however, possible to change this using the settings in the Position, Axis (3D only), and Rotation Angle sections. This is useful if you have created a parametric curve with the right shape but want to move it to another position or orientation. These settings can be thought of as defining a local coordinate system in which the parametric curve is defined.

Enter the position of the local coordinate system origin using the x, y (r and z in 2D axial symmetry, xw and yw in work planes), and (3D only) z fields.

In 3D, enter the axis that you want to rotate the local coordinate system about. The axis can be chosen parallel to one of the coordinate axes or entered in Cartesian or spherical coordinates. The z-axis of the local coordinate system is parallel to this axis.

Enter the angle you want the local coordinate system to be rotated (default: 0 degrees). In 2D the local coordinate system is rotated about its origin. In 3D, the local coordinate system is rotated about its z-axis, which is parallel to the axis defined in the previous section.

The coordinate system in which the position, axis, and rotation angles above are interpreted. From the Work plane list, select xy-plane (the default, for a standard global Cartesian coordinate system) or select any work plane defined above this node in the geometry sequence. If you choose a work plane, the work plane and its coordinate system appear in the Graphics window, using an extra coordinate triad with the directions xw, yw, and zw (which are the used to specify the curve’s position).

Internally, the software represents the parametric curve by a B-spline, which is computed to approximate the mathematical curve defined by the x, y in 2D, r and z in 2D axial symmetry, xw and yw in work planes, and x, y, and z in 3D expressions. The number of knot points in the spline increases automatically until the curve approximation satisfies the tolerance specified in the Relative tolerance field or until it reaches the number of knots specified in the Maximum number of knots field. The tolerance is measured relative to the space diagonal of the bounding box of the parametric curve.

If the parameterization of the curve is uneven or includes singularities, select the Reparameterize using arc length check box to reparameterize the curve, possibly providing a better parameterization without singularities.

If the coordinate expressions contain user-defined functions, changes in those functions do not always cause the parametric curve feature to be rebuilt. To rebuild the feature after a change in a user-defined function, click the Rebuild with Updated Functions button.

If you want to make the resulting entities contribute to a cumulative selection, select a cumulative selection from the Contribute to list (the default, None, gives no contribution), or click the New button to create a new cumulative selection (see Cumulative Selections).

Select the Resulting objects selection check box to create predefined selections (for all levels — objects, domains, boundaries, edges, and points — that are applicable) in subsequent nodes in the geometry sequence. To also make all or one of the types of resulting entities (domains, boundaries, edges, and points) that the parametric curve consists of available as selections in all applicable selection lists (in physics and materials settings, for example), choose an option from the Show in physics (Show in instances if in a geometry part; Show in 3D in a plane geometry under a work plane in a 3D component) list: All levels, Boundary selection (2D only), Edge selection (3D only), or Point selection. The default is Edge selection in 3D and Boundary selection in 2D. These selections do not appear as separate selection nodes in the model tree. Select Off to not make any selection available outside of the geometry sequence.