Job: Controlling the curve continuity

Controlling the curve continuity

When editing control points with the Curve through Control Points command, you can:

Set the continuity conditions of the selected curve with other curves

Set the continuity conditions of the selected curve with surfaces or with a free point

Close the curve

Set the continuity conditions of the selected curve with other curves

After selecting the curve, select the Continuity constraints check box under Constraints. The Start Reference and End Reference selectors will be displayed in the selection list.

Select the Start Reference.

Select the control point(s) controlling the portion of the curve you want to apply the continuity conditions to.

In the Start continuity drop-down list, select the type of continuity you want to apply (continuity conditions will be enforced by moving individual control points the minimum distance required):

Position	specifies that only geometric continuity is required at the endpoints.
Tangent	specifies that the resulting curve must share the same tangent line as the start curve at the given end.
Curvature	specifies that the resulting curve must have the same value of curvature as the start curve at the given end.
Torsion	specifies that the resulting curve must have the same value of torsion as the start curve at the given end.
Smooth curvature	specifies that the start curve's curvature plot and the resulting curve's curvature plot must be tangent continuous at the specified end.
Curvature plot curvature	specifies that the start curve's curvature plot and the resulting curve's curvature plot must be curvature continuous at the specified end.
Perpendicular	specifies that the tangent vectors of the two curves in the common point must be perpendicular.

In the example above, the choice was Tangent, and the following was the result:

If necessary, you can invert the direction of the start curve by selecting the Invert box.

By selecting the Curve Curvature command, you can also display a curvature plot which will help you check the shape and the smoothness of the resulting curve.

You can proceed similarly for the end curve (End Reference).

Double-click to confirm the changes you made.

Set the continuity conditions of the selected curve with surfaces or with a free point

In addition to the possibility of having end points coincide with the end points of other curves used as references, additional options are available to enable constraining end points to:

A point on a surface
You can constrain an end point of the curve to coincide with a selected point on a surface.
After selecting the curve, in order to constrain the first end point, under Constraints- Continuity constraints, select Start Reference and then click on the surface you want to set continuity conditions with. You can redefine the length of the tangent vector (forced to move in the tangent plane of the surface) in the point of connection between the curve to be modified and the surface to be connected (through the appropriate 1st Tangent Length handle/mini-dialog box pair).

Higher order derivative information from the surface in this direction can be set using the Start Continuity drop-down list options to further smooth that transition from the curve to the surface. Further refinement of the point or direction or orientation of the cutting plane will be possible until the desired shape is achieved.
You can do the same at the second end point by selecting End Reference.
A free point
You can constrain an end point of the curve to the position of a free point.
After selecting the curve, in order to constrain the first end point, under Constraints- Continuity constraints, select Start Reference and then click on the point you want to set continuity conditions with.

You can do the same at the second end point by clicking End Reference.

Restricting selection to curves and surface boundaries only
Please note that you can enable the command to select points, curves and surfaces or restrict selection to curves and surface boundaries only. A context menu is available when right-clicking on Start Reference or End Reference:

Curves Only
restricts selection to curves and surface boundaries.
Points - Curves - Surfaces
allows selection of points, curves and surfaces, but does not allow selection of surface boundaries.

Close the curve

The options of the Close Curve node under Constraints- Continuity constraints enable you to close a curve by moving its first end point onto the second one or vice-versa and setting continuity conditions on the new common end point.

If you select Start point matches end point, the first end point will be moved onto the second one.
If you select End point matches start point, the second end point will be moved onto the first one.

The curve will be closed. To obtain an open curve, though keeping the endpoints overlapping, click Open Curve.

Use the Continuity drop-down list to set the appropriate continuity constraint ( Position, Tangent, Curvature).

In the Start point matches end point case, the start of the curve will be constrained to match the continuity conditions at the end of the curve to the level specified.
In the End point matches start point case, the end of the curve will be constrained to match the continuity conditions at the start of the curve to the level specified.