Four-Sided

The Surface->Four-Sided command in the Model module allows you to create a patch or NURBS surface from four border curves.

If you use NURBS curves, the result is a NURBS surface. If you use Linear, Cardinal, Bezier, or B-Splines, the result is a patch surface of the same type as the curve.

You can use relation modelling concepts on the resulting object. Always make sure that the Preferences->Create Modelling Relation command is activated first.

For an overview of relational modelling, see the Relational Modelling section of the Modelling User's Guide.

Procedure

1. Draw two pairs of curves. Do not mix NURBS and non-NURBS curves.
2. Pairs of non-NURBS curves:

• Should be drawn counterclockwise (or bottom to top).
• Should be of the same type and have the same number of points.

3. Pairs of NURBS curves:

• Each pair must be of the same degree but can have different number of points.

4. Position each pair (top-bottom, left-right) opposite the other. The result is more predictable if the ends of the curves are close to each other.
5. Choose the Surface->Four-Sided command.
6. If you are using NURBS curves, the Four Sided Setup dialogue box is displayed, in which you can indicate the parameterization of the resulting NURBS surface.
7. Pick curves one at a time:

• Pick non-NURBS curves in any order.
• Pick NURBS curves clockwise.

8. Each one is highlighted as it is picked.

The result is a patch or NURBS surface. The curves remain displayed on the screen after the new four-sided object has been created, and can be used again to create more objects.

If you are using relational modelling, as you edit, transform, or scale the generator curves, you will see the object move and respond to your changes. The only operations that can be performed independently on the generated object are transformations and inversion of the object's surface normals.

Parameters

The Four Sided Setup dialogue box offers four options for knot parameterization of NURBS.

• Non-Uniform: The delta between successive knots is related to the distance between successive control points. The parameterization is not recomputed when you change the geometry of the curve (by moving, adding, or deleting points). Non-uniform is the default value used for creating a four-sided NURBS surface.
• Chord Length: The delta between successive knots is related to the actual length of the curve segment, which in turn is approximated to the distance between control points.
• Centripetal: The delta between successive knots is related to the square root of the length of the curve segment. This tends to make smoother curves (in some cases), but usually distorts texture mapping on surfaces.
• Uniform: The delta between successive knots is expressed in equal increments of 1, without regard for the actual length of the curve segment.

Note:

The effect of changes are more localized if you use Uniform or Non-uniform parameterization than if you use Chord Length and Centripetal.

Last updated 02-apr-1998