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Periodic Geometry

Periodic refers to the difference between open and closed geometry. For example, there are two ways to create a circular shaped curve:

  • Periodic - A closed curve that forms a loop. Moving any CV has the same effect on the curve shape as any other, and the curve remains a loop.

    Periodic geometry keeps the CVs evenly and symmetrically distributed, which keeps the curve as a smooth loop shape regardless of which CVs you move.

  • Open - An open curve has free ends. Moving an end CV has a different effect to moving an interior CV.

Creating periodic geometry

Circle curves and revolved surfaces have an option to create periodic geometry, which are always 360 degrees.

Sphere, Cylinder, and Cone surface primitives (set to 360 degrees) are always created as periodic geometry in one direction. A Torus is periodic in both U and V.

Periodic geometry is only accurately circular if the Rational Flags are selected in the Construction Options. Periodic geometry is therefore typically used for concept modeling rather than for accurate circular geometry:

Tools

The following tools have options to create periodic or open geometry:

The following tools create periodic geometry by default:

To modify periodic geometry:

To check for periodic geometry:

Deep dive: Switching between periodic and open geometry

Periodic geometry is listed in the meta data under Form and can displayed using Query Edit (select geometry with the right mouse button) or the Information Window in the Curve or Surface geometry sections.

Open/Close

The Open/Close tool opens closed geometry and closes open geometry. The number of CVs is maintained but the spans are reduced creating a change in the shape.

A surface can be periodic in U or V directions, or in both (a torus for example). To select which direction to make a surface open or closed in, select the U or V isoparm.

Detach

The Detach tool can be used to change from periodic to open geometry.

Detach maintains or increases number of spans and so adds CVs to maintain the smoothness at the new end points or edges. This maintains the shape after the detach, unlike the Open/Close tool. Use Ctrl to detach at an edit point or isoparm.

Deep dive: CVs on periodic geometry

Periodic geometry has some CVs that appear to be double CVs in the Information Window, but this is only a technical representation.

In all selection and modeling situations, these are treated as single CVs.

Deep dive: Limitations of periodic geometry

Some tools have limitations when working with periodic geometry:

  • The Align tool doesn't work on periodic geometry. Use the Align 2008 instead.

  • Extend

    • You cannot extend periodic curves.
    • You can only extend periodic surfaces proportionally (one manipulator).
  • When data is exported to other CAD systems, periodic geometry may be detached into non-periodic segments.

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