Surfaces

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

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.

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 an 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:

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.

Patches

The four-sided regions between adjacent edit point isoparametric curves or edges are called patches.

You rarely need to think about patches, since the focus in AliasStudio is on the isoparametric curves.

One tool that works with patches is the Patch precision tool, which sets how many U and V isoparametric curves are drawn for each patch.

What NURBS surfaces can't do

Because of the underlying representation of NURBS surfaces, there are some things they cannot model:

Topologies that are not equivalent to a rectangular sheet.

Spheres, cones, tori, and triangles can all be built from sheets by attaching or collapsing sides. But more complex shapes, for example a star shape, cannot be represented with a simple NURBS surface. To get a complex surface outline, you must use a trimmed surface or a network or collection of four-sided surfaces.

Holes.

To create a hole in a surface, use a trimmed surface.

Surfaces that cannot be mapped with regular U and V coordinates.

For example, you can model the shape of a Mobius strip, but the surface will have a seam.

Curves-on-surface

Curves-on-surface are special curves that are drawn in the UV space of a surface, rather than in the XYZ space of the scene. Curves-on-surface do not have CVs. They are controlled by moving on-curve edit points.

You can create curves-on-surface by drawing directly on the surface, by projecting existing curves onto a surface, and by intersecting existing geometry with a surface.

Curves-on-surface are usually used to trim surfaces, or to form the edge of new surfaces.

Trimming

Since NURBS surfaces are intrinsically four-sided and do not allow holes, you need a way to visually simulate irregular shapes and holes when using NURBS. The answer is trimming.

Trimming lets you visually cut or divide a surface along a curve-on-surface so it appears to have holes or missing pieces. The trimmed surface, however, is not actually cut. It exists in a hidden form that does not render or affect modeling. You can recover the trimmed part of a surface using the Untrim tool.

Creating curves-on-surface and then trimming is the most common way to combine NURBS surfaces in industrial design.

Shells

Shells are collections of adjacent NURBS surfaces. Every surface stitched into a shell must meet the edge of another surface in the shell at some point.

Shells can be open or closed. For closed shells, the normals should always point outward. This is necessary for the Boolean operations.

To improve data transfer to some CAD packages.

Some CAD packages deal with shells much better than normal trimmed NURBS surfaces.

To prepare for Boolean operations.

The Boolean tools (Shell subtract, Shell intersect, and Shell union) only work on shells. Often you will simply stitch surfaces into shells, apply a boolean operation, then unstitch back into surfaces.

To check adjacencies between surfaces.

Surfaces can only be stitched into shells if they are within an adjacency tolerance.

If the tolerance is set correctly, you can easily check whether a group of surfaces will export or build properly by checking whether they will stitch together into a shell.

To identify open edges in stitched shells:

Use Object edit > Query edit to check for open edges in shells. Red arrows clearly mark gaps in the shell.

Depending on the options in the Shell stitch option window, a stitched shell may not match the original surfaces exactly.

In this case, unstitching will not produce surfaces that match the originals exactly either.

You can not edit CVs of a shell. If you need to reshape the surface of a shell, you must unstitch the shell.

You cannot use the isoparametric curves of shell surfaces as input for other tools.

You cannot maintain continuity with a shell in tools such as Square and Rail Surface.

You cannot create fillet surfaces on shells or between shells and other surfaces.

If you stitch an object, then scale it, then unstitch it, you not be able to re-stitch the object. This is because the scaling operation can increase the gaps between surfaces, thereby causing any subsequent stitch operations to fail (within the current tolerance settings). In this case, scale the object before you first stitch it.