Theory Builder Title

NURBS Circles: Accuracy and Free Sculpting

In Alias we think of circular shapes in two ways:

Examples of accurate circles and freeform loops

Summary of Settings affecting Circular Geometry

The different settings for circles are summarised below, and discussed in detail in the following sections.

Periodic and Rational Settings on Circles

Rational Geometry - Accurate Circles

Rational Geometry Accuracy

The 'R' in NURBS stands for 'Rational', and we can choose to work with either Rational or Non-Rational geometry, by changing the settings in the Construction Options.

Select Rational geometry in the Construction Options before creating circles or revolves, to ensure dimensional accuracy.

Rational circles are always accurately circular

Be careful with this setting, and turn it off after you have created the accurate circle or revolve. The CV layout that results cannot be successfully sculpted, and sometimes causes strange results when used in, for example, offsetting.

Evaluating Accuracy

Non-Rational Geometry: Periodic & Non Periodic Loops

Within the category of Non-Rational geometry, there is another setting, 'Periodic' which also affects circles.

When creating circles with different tools, you may notice different CV layouts. This difference can be explained by understanding the difference between 'Periodic' and 'Non-Periodic' geometry.

Example of Different Circle CV Layouts

How Periodic Circles Work - Open Curves and Closed Loops

There is a difference between 'open' and 'closed' curves.

An open curve (non-periodic) has free ends.

A periodic curve is joined or 'closed' to form a loop. It is similar to the idea of overlapping ends, but is not an exact analogy. Periodic geometry keeps the CVs evenly and symmetrically distributed, which keeps the curve as a smooth circle or loop shape, regardless of which CVs you move.

The difference between 'open' and 'closed' loops

Choosing Periodic & Non-Periodic

If you select 360 degrees for primitive geometry, it will typically default to a Periodic setting. In some tools however, there is an option to choose Non-Periodic.

How to apply the Periodic and Rational settings

Why Periodic Circles are Preferred for Sculpting

Each CV has the same effect on the circle, and there is no visible 'join'. This means you can sculpt the circles symmetrically and/or smoothly.

These examples have been created by moving CVs on a periodic circle.

Examples of sculpted 'closed' loops

Periodic Accuracy - (360 degrees)

Non-rational, periodic circles aren't perfectly circular.

The higher the degree and the more spans you use, the more accurate it will become. The circles below are all created at a nominal 100mm radius - notice how the min and max radius vary:

How accuracy is affected by Degree and Spans in Non-Rational circles

Non-Periodic Accuracy - (partial arcs)

It is possible to get a very accurate result with a 90 degree quarter-circle, if you choose degree 6 or higher.

How accuracy is affected by Degree for arcs

The mystery of the 'double' CVs...

You may notice an anomaly with periodic circles. Only one CV can be selected in each CV position, but in some locations two CVs appear in the Information Window. This has no effect on your modelling and is just a characteristic of the 'overlapping' that is used to create the loop.

Each CV will behave the same, and you can ignore the 'double CV' display in the Information Window.

CV structure of Periodic circles

Opening or Breaking a Periodic Circle

A closed, periodic circle can be made 'open' in three ways:

In Practice...

Preferred choice for accurate circles and revolves

Most users now prefer to create four accurate, 90 degree segments (using degree 6, single-span), instead of using rational geometry.

In the Revolve tool, there is a separate option which allows you to create all four, 90 degree segments in one operation (or any combination of segment size):

Creating an accurate circle from 4 segments

Avoiding using the wrong type of geometry

Experienced users learn to recognise the different CV layouts that you get with the Periodic and Rational settings, and so avoid using the wrong geometry. The key to this is to always display the CVs for a new circular curve or surface that you build, to check the CV structure.

Displaying CVs shows the structure of the geometry

Avoiding Rational on Construction Presets

If you are using one of the construction pre-sets that has a Rational flag on, then you may want to copy the pre-set and set the flags to off, so that you don't get rational geometry by mistake.

How to remove the Rational flag from a Contruction Preset

Limitations of Periodic and Rational Geometry

Circle examples