Rational Geometry
Rational Flags is a setting in the Preferences > Construction Options that is applied to circular and revolved geometry.
In practice non-rational geometry is preferred for modeling in Alias, and so the Rational Flags are typically set to Off.
Non-rational geometry
Non-rational geometry constrains all CVs to having the same weight value of 1 (CV weighting is displayed in the Information Window).
This has the advantage that each CV has the same influence over a curve or surface, making it easier to predict its effect on the shape. The only disadvantage of non-rational geometry is that it cannot create circular accuracy for periodic circles and revolves (conics).
Use non-rational geometry for:
Accurate circle in 4 segments (non-periodic) - This is the recommended method for building accurate circles and cylindrical shapes. Use degree 6 or higher to ensure accuracy.
Loop (periodic) - A periodic circle or primitive is not exactly circular, but it can be used as a starting shape and then CV sculpted. Using non-rational geometry is essential in this case so that all CVs have an equal effect on the shape.
Rational geometry
Rational geometry allows for different weights to be applied to CVs. This allows for accurate circles and revolves but also constrains them to being periodic only.
The geometry is more complex mathematically so modeling with rational geometry may not transfer successfully to downstream CAD packages. It also creates multi-knots, which give poor results or discontinuities when moving CVs.
The CV layout for rational and non-rational circles is different.
Tools
To select rational or non-rational geometry:
The following tools are affected by a Rational setting:
To check for Rational geometry:
- Query Edit
- Information Window (to check CV weighting).
To convert rational to non-rational geometry:
Deep dive: rational versus non-rational geometry
Non-rational geometry is a sum of polynomials. Rational geometry is a ratio of sums of polynomials. Rational geometry is considerably more complex mathematically. Therefore:
- It may not be transferable to downstream CAD packages that can't deal with complex descriptions
- It can be slower to manipulate when modeling and slower to render.
The following tables lists the differences between the two types of geometry.
| Nature | Pros | Cons |
|---|---|---|
| Non-rational | More flexibility for transformations. Faster. | Sacrifices some precision for modeling flexibility. |
| Rational | Precise geometry (exact circular accuracy). | Weighted CVs not supported by many CAD packages. Weighted CVs harder to manipulate. Creates multi-knots. Slower to display and render. |
Identifying rational and non-rational geometry
The nature of the geometry can be determined in three ways:
- The CV layout on rational and non-rational circles is different and is the most common way of identifying rational geometry.
- Use Query Edit and the right mouse to select the geometry. The nature of the geometry is displayed as the last entry in the information pop-up window.
- Select CVs and use the Information Window to identify if any weights are not set to 1.
