Cad Guidebook: A Basic Manual for Understanding and Improving Computer-Aided Design (47 page)

Swept parts are created by modeling an arbitrary path for sweeping. This
path is used to guide some geometry along the path. The geometry forms a sort of
cross section for the part. A tube or wire that makes various turns and bends in
arbitrary directions would be an application of a swept part. For simple parts such
as a pipe that has a few elbows, surface modeling may not be needed since stand-
ard extrudes and revolves could be used instead.

Another class of parts that might be considered an application of surface
modeling is called sheet metal. These parts are meant to be thin sheet metal parts
(such as used to form a metal box or enclosure). The physical parts are made by
cutting out a shape on a flat sheet of metal (this geometry is usually called a flat
pattern). Then, at specific locations, the metal is bent to form the final part. Sheet
metal part models in the 3-D CAD system need to have this ability to fold and
unfold in order to develop the flat pattern (taking into account the proper bend
allowances where material is deformed). At the moment, however, there does not
seem to be any standardized approach to developing these kinds of part models
among CAD systems. The reader must consult the documentation available for
their specific CAD system for more information. Of course, these part models are
still subject to the issues of creating solid models based on properly shaped
and/or stitched surfaces.

Finally, surface modeling can be quite complicated, and this chapter is not
intended to be a complete work on the subject. If the reader is not interested in
these kinds of parts at all, then this chapter could be skipped altogether. It is not
necessary to understand everything in this chapter before proceeding with the re-
maining chapters.

226 Chapter 9

9.2 SURFACES

Since surface modeling is concerned with creating 3-D part models by working
with individual surfaces, it is clear that users should have some idea of what is
meant by a surface. Although different 3-D CAD systems may define them some-
what differently, they have some basically common characteristics.

9.2.1 Common Characteristics

First of all, surfaces are very general shapes. A flat plane (such as a face of a
cube) is a surface; it can be referred to as a planar surface. The curved shape of a
cylinder is a surface; it can be referred to as a cylindrical surface. The curved
shape of a cone is a surface; it can be referred to as a conical surface. And, very
arbitrary or free-form shapes such as the body panel of a car are surfaces; these
can be referred to as free-form surfaces. The planar, cylindrical, and conical sur-
faces are typical of the extruding and revolving procedures presented in the previ-
ous chapter (these types of parts are often referred to as prismatic parts). Surface
modeling, on the other hand, often implies the use of the free form surfaces.
These surfaces are very 3-D in nature (since they can warp and twist). Figure 9.1
shows an example of a free-form surface.

Individual surfaces also have no thickness. They are “paper thin” and have
no volume. However, the 3-D CAD system will often keep track of the side of the
surface that is supposed to be on the inside of a solid model (versus facing the
outside). If surfaces are used to construct a solid model, then eventually there is

FIGURE
9.1

A free form surface.

Surface Modeling 227

an inside and an outside. But, when working with the surfaces alone, one may
notice that one side of a surface is very dark, but the other side is bright. This is
because the CAD system or the graphics adapter is assuming that the dark side is
the inside of the part, even though there is no real inside or outside yet. Usually,
the system can be forced to make both sides bright by enabling an option called
backlighting. In this case, the surface will be easier to see, but there has probably
been no change in the way the CAD system recognizes the surface in an analyti-
cal sense. Another issue to consider is material side. This affects how the surface
operates on a model by indicating which side or sides of the surface can be con-
sidered to have material for cutting.

Next, surfaces have clearly defined boundaries or edges. This allows them
to be used in the creation of the solid models. The CAD system knows where
every edge is in 3-D space (these edges being defined by some sort of mathemat-
ical relationship or formula with appropriate constants or coefficients). Then, as
surfaces are brought together through various modeling methods, the CAD sys-
tem can then attempt to figure out how the edges of those surfaces can go to-
gether to form a solid (a stitching process). Another important use for edges is
that they form the geometrical data needed for creating drawings from 3-D mod-
els. It turns out that what is shown in drawings for parts is really driven by the
edges of surfaces.

Surfaces should also generally be considered as analytical objects. The sur-
faces are stored by the 3-D CAD system as numerical data and mathematical re-
lationships that are totally refined or accurate. Therefore, in a mathematical sense
a curved surface can be “perfectly curved” and accurate within the CAD system
itself. However surfaces are often displayed to some given minimum accuracy on
the monitor (indeed one might see small flat faces on curved surfaces). But, as
the user “zooms in” closer to the model, the surface’s appearance can be regener-
ated by the CAD system to a greater and greater accuracy (with less and less ap-
proximation shown on the monitor) because the surfaces are analytical.

9.2.2 NURBS

It turns out that most 3-D CAD systems use a mathematical definition for the
surfaces based on something called NURBS. A full explanation of NURBS is be-
yond the scope of this book, but since it is a common term with respect to 3-D
CAD systems, a little information is presented here. NURBS stands for Non-Uni-
form Rational B-Splines (and B-Splines refers to Basis-Splines). Recall from an
earlier 2-D chapter that splines are special geometric entities that can be found in
drawings and 2-D CAD. Splines are special because they can define very arbi-
trary shapes. They can loop back on themselves, for instance. They are also spe-
cial because the user can pick a sequence of points and then the CAD system
would create a smooth curve automatically to follow those points. Splines also

228 Chapter 9

have control points that can guide the shape from a distance. These control points
can have different weights to indicate how much the curve should be influenced
by them. These special characteristics of splines are applicable to the NURBS,
as well.

In the case of the 3-D surfaces, the NURBS representation is used to con-
tain the mathematics of a whole surface (instead of just a 2-D spline). NURBS
are very flexible; they can form all sorts of shapes (from planar surfaces to very
warped free form surfaces). The NURBS mathematics can model the different
shapes by using the mathematical concept of orders or degrees. Lower orders can
represent simple surfaces (such as a conical surface), and then higher order rela-
tionships can be used for free-form surfaces (such as a car body panel). NURBS
can even be used to create a surface from a large number of points in 3-D space
(called a point cloud). All this makes NURBS very advantageous for CAD sys-
tem programming.

9.2.3 Trimming

Another important issue for the surfaces in a 3-D CAD system is that they are
usually trimmed. The mathematical definition of a surface (such as the NURBS)
really defines a rectangular-type of surface. It is like a rubber sheet that starts out
flat and rectangular, and then no matter how it is deformed or stretched, the 4
rectangular edges remain. Since many surfaces for part models are not rectangu-
lar in shape, the CAD system allows curves to be overlaid onto the rectangular
surface. Then these curves trim the full surface down to the shape needed. Figure
9.2 shows an example. This trimming issue is usually taken care of by the CAD
system automatically, but occasionally trimming can become a problem for sur-
faces, too. It often arises from importing 3-D data from one CAD system to an-
other and the two systems do not have the same algorithms or tolerance for the

FIGURE
9.2

Example of a trimmed and untrimmed form of a surface.

Surface Modeling 229

curves and/or surfaces. In this case, undesirable untrimmed surfaces may appear
in models.

9.2.4 Surface Qualities

Imagine the untrimmed rectangular surface with an X- and Y-value to each point
on the surface. However, instead of the X-value being a horizontal distance and
the Y-value being a vertical distance on a flat drawing, these values are usually a
percentage of the travel along each of the edges of the rectangular surface. These
values are often shown as the variables s and t, and the location of any point on
the surface would be identified by an (s,t) pair. These values of s and t can vary
from 0 to 1 on the untrimmed surface, where 0 is at the beginning of the edge
direction, and 1 is at the end of the edge direction. However, the trimmed sur-
face’s edges will often not reach the 0 or 1 values since they will be inside the
bounds of the untrimmed surface.

At each (s,t) location, 3-D CAD systems allow the properties or the quality
of the surface to be evaluated. An important property of a point on a surface is
curvature. This is a parameter that indicates how sharply the shape of the surface
is changing at that point. Of course, a free-form surface’s topography is changing
in many directions, so one may select a plane or planes at this point in which to
evaluate the curvature. A good surface is one that would show a smooth change
in curvature in many directions. This becomes a particularly important issue at
points where surfaces are stitched and a degree of continuity is desired between
separate but mating surfaces; there may need to be a smooth transition from one
surface to the next by having the curvature property the same for both surfaces at
the location of the stitching.

9.3 SURFACE MODELING OPERATIONS

There are a number of operations that are used in surface modeling. Recall that in
part modeling, a typical technique is extruding. This creates what is generally
called a prismatic part. The operations for surface modeling, though, generally
create the free-form surfaces and parts. Extruding can still be used in the context
of surface modeling, but surface modeling uses more advanced techniques such
as open part modeling, lofting, sweeping, and surfaces by edges or points.

9.3.1 Open Part Modeling

Open part modeling can be done in a number of ways. In this technique, the part
model is simply not solid at some point in the part history; there is no bounded
volume in some way. Once an open part is created, then an operation such as
shelling can apply a material thickness to all the exposed surfaces (in a direction
that is normal to the surfaces). If multiple open parts are created, then they can

230 Chapter 9

also be brought together to form a solid. Of course, if only the outer face of an
object is of interest (like the surface of a bottle in a mold), then the open part
model may be all that is really needed.

Figure 7.12 shows an example of open part modeling followed by shelling.
The first part of the figure shows a normal solid part with a hole. The second part
of the figure shows a face deleted from the part which then creates the open part.
Note that the cylindrical surface for the hole is exposed from within the part. The
third part of the figure shows the shell operation. Now the part is solid again; it
has volume. Note that the hole is now a hollow shaft in the middle of the part.

The deletion of a surface is just one technique of creating an open part.
Table 9.1 lists some other techniques for creating open parts.