Isoparametric curves

Isoparametric curves are lines running along the surface in the U and V directions, showing the shape of the surface as defined by the CVs.

Alias draws a NURBS surface as a mesh of curves, called isoparametric curves, running in the U and V directions.

Isoparametric curves are sometimes called isoparms.

Unfortunately, the term “isoparametric curve” is used to describe two related but subtly different features of a surface:

Edit point isoparametric curves

A line of constant parameter at an edit point. The isoparametric curves at edit points are special, since they represent the boundaries between “patches”. Like CVs, these isoparametric curves are important in representing the surface within the system.

Alias draws these types of isoparametric curves using solid lines.

• This is the type of isoparametric curve created by the Insert tool. Adding this type of isoparametric curve actually changes the geometry of the surface.
• You can only delete isoparametric curves of this type.
• Using this definition, a surface has the same number of isoparametric curves in the U and V directions as it has edit points.

Descriptive isoparametric curves

Any line of constant parameter in either U or V. For example, if you join together every point on the surface where U=1.5, the resulting line is a U isoparametric curve:

Alias draws these types of isoparametric curves using dotted lines.

• You can increase the number of this type of isoparametric curve that is drawn for a surface with the Patch precision tool.
• Using this definition, a surface has an infinite number of isoparametric curves.
• You can use these isoparametric curves to help you understand the surface shape, but the system doesn’t use them to represent the surface internally.