Theory Builder Title

G2 Curvature Deviation - Interpretation and Limitations

The G0 Position and G1 Tangent tolerances are simple distance and angle measures that are easy to interpret.

In contrast, the G2 Curvature measure is a calculation of the ratio between the two radii of the adjoining curves or surfaces, and this makes it more difficult to interpret intuitively.

In practice, this calculation is mostly used internally by the software to make pass/fail decisions. As users, we get more useful information from iso-angle shaders and curvature plots, and the calculated value is less important.

Illustration of the G0, G1 and G2 measurements

G2 Deviation Calculation

The curvature of a surface has to be defined in a particular direction (see 4.1 - Intro: Curvature in Different Directions for a detailed explanation). For a boundary, the radius values are measured along lines on the surface that are perpendicular to the boundary, at intervals determined by the checkpoints.

Illustration of the G0, G1 and G2 measurements

The calculation is a 'relative' way of calculating the curvature :

First the difference in the two radius values is calculated (Radius 1 - Radius 2)...

...and then the calculation takes account of the physical size of the surfaces (Radius 1 + Radius 2). This means that a simlar visual result on a small or large object will give a similar value for curvature deviation.

Note: In the software the actual calculation ignores negative curvature by using absolute values, and is more accurately stated as:

Inconsistencies and Errors

You may occasionally find yourself in a situation where your surface tool tells you that curvature continuity has been established across a boundary while an evaluation tool asserts the opposite.

Inconsistencies between the curvature continuity status assigned to a boundary by different tools have a variety of causes. Possibilities are:

In conclusion, if any tool warns you of a discontinuity or problem where you didn’t expect one, examine your geometry closely. Some continuity calculations, especially those done at the time a new surface is built, tend to be more “forgiving” than those that check the boundary after the surface has been built.

Notes

Absolute 'v' Relative Calculation

Older versions of Alias (version 12 and earlier) used an absolute method of caculating the curvature, but this was replaced by this relative method for two reasons:

Other CAD Systems

There are other software packages that use a similar relative curvature continuity check but have a factor of 2 built into their deviation calculation. In other words, their method of calculating can be expressed as:

Users need to be aware of this so that they can specify their tolerances to match those of other software packages if so required.

Circle examples