A parametric surface is a surface in 3D where you use two parameters to define the coordinates of the surface. For example, the coordinates (s1·cos(s2), s1·sin(s2), s2) for a parameter s1 that runs from 0 to  π, and a parameter s2 that runs from −1 to 1  define a “twisted rectangle”. To create a parametric surface, in the Geometry toolbar, from the More Primitives () menu, select Parametric Surface (). You can also right-click the Geometry node to add this node from the context menu. Then enter the properties of the parametric surface using the following sections:

Define the parameter names in the Name fields (default names: s1 and s2). Also define the intervals 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, and z fields. To create the twisted rectangle described earlier with the parameters s1 and s2, type s1*cos(s2) in the x field, s1*sin(s2) in the y field, and s2 in the z field.

By default, the x, y, and z expressions define the coordinates of points on the surface in the standard coordinate system. It is, however, possible to change this using the settings in the Position, Axis, and Rotation Angle sections. This is useful if you have created a parametric surface 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 surface is defined.

Surfaces with self intersections might look correct when displayed but are not handled correctly by other geometry and meshing operations. This also applies to surfaces where one edge touches the surface of another edge, and to surfaces with singular points. If necessary, several parametric surfaces can be combined to overcome this limitation. For example, constructing a cylindrical shell by typing cos(s1) in the x field, sin(s1) in the y field, and s2 in the z field, where s1 runs from 0 to 2π, and s2 runs from 0 to 1, is incorrect because two edges of the parametric surface touch each other. Instead, use two parametric surfaces, with the same coordinate expressions, and where s1 runs from 0 to  π in the first surface and from π to 2π in the second one.

Enter the position of the local coordinate system origin using the x, y, and z fields.

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. 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 then used to specify the position).

Internally, the software represents the parametric surface by a B-spline, which is computed to approximate the mathematical surface defined by the x, y, and z expressions. The number of knot points in the spline increases automatically until the surface 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 surface.

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 surface 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) list: All levels, Boundary selection, Edge selection, or Point selection. The default is Boundary selection. 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. From the Color list, choose a color for highlighting the resulting objects selection. See Selection Colors.

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).