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, in 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.
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 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.
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. From the
Color list, choose a color for highlighting the resulting objects selection. See
Selection Colors.
