Cad Guidebook: A Basic Manual for Understanding and Improving Computer-Aided Design (48 page)

Open part modeling can also involve the use of the Boolean operations
mentioned in the chapter on part modeling. In this case, separate part models can
be created for different areas of a part. Then they can be brought together to be a
new single part. Figure 9.3 shows an example of taking two open parts, using an
Add
operation to bring the surfaces together, and then using a shell operation to
make the part solid. Note that the operation to put the surfaces together was Add.
If surfaces are just brought together like this, and the CAD system is not going to
figure out where edges are shared, then it can be referred to as just an add opera-
tion. In this case, the user must then do the stitch
operation manually to make the
connection between surfaces where they share edge geometry (if that is what is
desired). Instead of the add operation, the join
operation probably could have

TABLE
9.1

Open Part Modeling Techniques

Open part technique Description

Deleting a surface In this technique, a normal solid part is created and then a

face or faces are deleted from the part.

Extruding an open section In this technique, an open section is extruded. Recall

from Chapter 8 on part modeling that when 2-D geom-

etry is sketched in preparation for making a 3-D fea-

ture, the 2-D geometry usually needs to form a section.

If the section is totally closed (no disconnected seg-

ments), then a 3-D feature results. If this section is not

totally closed, then an open feature results. This open

feature can be used for open part modeling.
Revolving an open section This is the same operation as extruding an open section;

however, in this case the open section is revolved.
Building panels or surfaces In this technique, a closed boundary for surfaces are cre-

ated in 3-D space or on a sketch plan, and then this

boundary is used to create a trimmed surface.

Surface Modeling 231

FIGURE
9.3

A process of using Boolean-type operations with open part models.

been used. In this case, the join
would do the stitching automatically (at least if
the surface edges are within the default tolerance).

9.3.2 Lofting

Another common technique used in surface modeling is called lofting. Lofting
involves creating a set of cross-sectional geometry. Then the 3-D CAD system
creates surfaces that loft or stretch across to connect them. Figure 9.4 shows an
example of some cross sections. Note that the cross sections could be dimen-
sioned and/or constrained, and note that the cross sections are somewhat dissimi-
lar shapes. Figure 9.5 shows a lofted open part that results from these cross
sections. A different part can be created from these same cross sections depend-
ing on the tangency dictated at the cross sections. Figure 9.6 shows a part model
that forces the surfaces to be tangent along the Z direction at the two larger cross
sections.

9.3.3 Sweeping

The next technique discussed for surface modeling is called sweeping. Sweeping
could also be considered solid modeling depending on whether the beginning
and/or ending of the sweep has surfaces to close off the volume (i.e. the part has
endcap-like surfaces). Sweeping involves creating geometry for a path (either 2-
D or 3-D geometry), and it involves creating the cross sectional geometry that
follows the path (some CAD systems will support 2-D or 3-D cross-sectional ge-
ometry). Figure 8.3 shows a simple example of a solid swept part.

There are a number of special considerations to keep in mind with swept
surface models. First of all, the nature of the path is important since it affects how
the part may or may not be constrained. Recall that basic features-based model-

232 Chapter 9

FIGURE
9.4

An example of cross sections for a lofted part.

ing was dependent on the use of sketch planes, and these sketch planes were used
to create and manage constraints (dimensions, perpendicular or parallel relation-
ships, etc.). So, making the path for a swept-part using 2-D planes may allow the
swept part to be better constrained in some cases because it could be controlled
by the standard sketch plane constraints.

Secondly, the path can not have too high of a curvature (or the rate of
change of the direction vector along the path). The curvature should not be so
high such that the cross sections begin to interfere along the path. If the cross
sections are small, then very sharp bends (high curvature) can be tolerated. If the
cross sections are large, then the curvature must be reduced (at least to make a
physically realistic part that does not have surfaces interfering). Of course, the
worst case of this is to have a sharp corner in the path (or an infinite curvature).
This is generally called a discontinuity, and discontinuities can prevent the CAD
system from creating the swept surfaces at all. Figure 9.7 shows a case where the
curvature is too high, and surfaces are interfering.

If an arbitrary 3-D path is needed for the sweep, then often 3-D splines are
used to create the path. The 3-D splines, in turn, need to have 3-D points to fol-
low (and perhaps tangency vectors). In this case, 3-D dimensions from one point
in space (or relative 3-D dimensions between points) could be used for locating

Surface Modeling 233

FIGURE
9.5

One open part model that can result from the cross sections.

FIGURE
9.6
cross sections.

Another open part model resulting from a different tangency at 2 of the

234 Chapter 9

FIGURE
9.7

Example of curvature too high on a swept surface.

these 3-D points. Then these dimensions would control the spline to some degree.
However, the weight or tension of the spline will also need to be specified and/or
constrained to fully define the path. Figure 9.8 shows how multiple 3-D splines
can be made between the same constrained 3-D point locations.

9.3.4 Surface by Edges or Points

The last operation presented for surface modeling is creating a surface by edges
or points. This is a very manual approach to modeling. In this case, the user cre-
ates a set of geometric entities in 3-D space with perhaps no assistance from
sketch planes at all. The entities may be created by just specifying their appropri-
ate 3-D or X,Y,Z data. For instance, a circle could be specified by a center point
with three values (X, Y, and Z), a radius or diameter, and a plane orientation for
the circle (for instance using X, Y, and Z components of a unit vector for the
plane’s orientation in space).

The left half of Figure 9.9 shows some 3-D lines that have been created in
the modeling space. This sort of data can be referred to as a wireframe model.
Assuming the end points of these lines are connected, then a very general surface
could then be created to fit these edges (assuming the 3-D CAD system provides
this functionality). The right half of Figure 9.9 shows a surface that could be fit to
the edges shown. After more such surfaces are created, they could be stitched
into a solid part. Obviously, creating these wireframe-type entities and figuring
out how to connect them as surfaces could become quite cumbersome for even

Surface Modeling 235

FIGURE
9.8

Multiple 3-D splines through the same 3-D points.

FIGURE
9.9
Example of 3-D entities in a “wireframe” model and a surface that can be
created from them.

236 Chapter 9

FIGURE
9.10

Example of a surface from a “point cloud.”

the simplest sort of parts. Therefore, this approach would generally only be used
in cases where all the other methods have been exhausted. Constraining or con-
trolling these parts would present even more difficulties (since there were never
any sketch planes).

Another method of creating surfaces with basic 3-D geometry is with
points. In this case, there is a relatively large number of points that are positioned
in 3-D space. This grouping of points can be referred to as a point cloud. As with
the edge method, the 3-D CAD system creates a rather general purpose surface
by using these points. This approach can be used when parts are reverse engi-
neered. There are also 3-D laser scanning devices that can be placed in a physical
environment. The environment is scanned and recorded as a very large set of 3-D
points. These points can be used as the basis for creating 3-D surfaces. Figure
9.10 shows an example of a surface created from a set of points. Notice that the
surface is untrimmed. This surface does pass through the points, but it is obvi-
ously covering more area than the original points.

9.4 STITCHING AND BASIC PART TOLERANCE

Once surfaces are created by surface modeling techniques, they can be used to
stitch together a solid model. Stitching is an essential step in turning an open part

Surface Modeling 237

into a closed part (assuming this is what the designer desires). Stitching may also
be needed to merge surfaces together so that a new surface with new and different
surface characteristics can be created.

A fundamental issue for the stitching operation is that 3-D CAD systems
are designed to determine successful stitching using a basic part tolerance or part
modeling tolerance. This is some small value of distance that is used to assess the
distance between the edges (a typical value is 0.01 mm). If the edges are within
the basic part tolerance, then the stitching would be considered successful. If
there is some amount of gap where the edges of the surfaces spread apart more
than the basic part tolerance, then the stitching would be unsuccessful. If it is un-
successful, then either the edges need to be modified, or the basic part tolerance
needs to be increased (i.e., a looser tolerance). It can be quite dangerous to
change the basic part tolerance. There may be cases where the system determines
that surfaces stitch due to a loosened tolerance, but then the underlying mathe-
matical model does really produce a solid. If other designers work with the part,
they may not know its tolerance became nonstandard.

Of course, if very small parts are modeled, then the basic part tolerance
may need to be modified just so that the parts can be stitched at all. In this case,
the tolerance would probably be tightened to an even smaller value, so in some
sense, it is safer.

Basic tolerance is not standardized between 3-D CAD systems. This often
causes problems when transferring data between systems. The system with the
tighter tolerance may not stitch together surfaces since their edges are not found
close enough together.

9.5 ABSTRACTIONS

Surface modeling can also create unrealistic parts. These parts are not physically
realistic, but they may be useful for various analysis methods, visualizations, or
calculations. They can be referred to as abstractions.

One example of abstraction is a midsurface model. In this case, a normal
solid part may have been created by surfacing or other methods. For analysis or
visualization reasons, a surface may be needed that is just between the pairs of
faces (surfaces) of the part. Figure 9.11 shows a midsurface sandwiched between
two real faces of the part model.

Clearly this midsurface can not be physically manufactured into the part.
However, it would allow calculations to be made for the overall characteristics of
the design in this region without being concerned with the thickness of the part in
this region. This can be a very useful calculation. Also, notice that the midsurface
edges meet at the middle of the outer faces (not at edges); there is a sort of T

238 Chapter 9