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Volume 62 Number 3
The Need (?) for Descriptive Geometry
in a World of 3D Modeling
Frank M. Croft, Jr.
The Ohio State University
ABSTRACT
Traditionally, descriptive geometry has consisted of the projection of three-dimensional figures on
a two-dimensional plane of paper using successive auxiliary views. Through this method quantita-
tive measures of length, angles, shapes and other geometric information were obtained. The tech-
nology required a systematic approach to problem solving with accuracy in projections and trans-
fer of distances from previous views. The layout and position of the successive auxiliary views were
essential in the solution of the problem.
Modern CAD methods that may be used to solve descriptive geometry problems no longer require
that the auxiliary views be positioned in the standard layout of auxiliary views. Often the CAD sys-
tem will allow for a direct solution of the problem without an intermediate auxiliary view as would
be required by the traditional two-dimensional successive auxiliary view approach. Using tradi-
tional two-dimensional successive auxiliary views with CAD is cumbersome and antiquated. With
the advent of CAD, the concepts of descriptive geometry have not changed; however, the process
through which we obtain the results has changed.
Introduction such that an auxiliary view is required that
For many years, the technology used to shows the true shape of an oblique surface?
solve descriptive geometry problems has Should this powerful CAD system be simply
been through projection of three-dimension- used as an electronic pencil with the screen
al figures on a two-dimensional plane of being the paper and thus generate the two-
paper using successive auxiliary views. dimensional views as has been done for
These solutions are achieved through a years using pencil and paper graphics?
series of geometric manipulations of two- Ritter (1990) used this concept in the com-
dimensional views to determine lengths, puter layout of the true size of oblique sur-
angles, shapes, and other geometric informa- face. CADKEY 1.4E, a three-dimensional
tion (Earle, 1994). Today, a three-dimen- CAD package, is used to layout a series of
sional CAD system with solid modeling is two-dimensional views with reference lines
the state-of-the-art technology used to create as you would expect to see using pencil and
many engineering designs which often paper. Knoblock and Jensen (1997) report
include some form of descriptive geometry that "modem texts", both comprehensive
for complete presentation. The CAD system and specialized, continue to treat descriptive
facilitates the creation of the three-dimen- geometry as solely a two-dimensional sub-
sional model and then from this model the ject. They further report that even texts that
orthographic views can be extracted for the embellish titles with CAD/CAE only use
final engineering design drawings. What CAD to emulate manual methods. The con-
happens when the geometry of the design is cepts and geometric rules have not changed
Engineering Design Graphics Journal
regarding descriptive geometry solutions; tained in the oblique plane ABC, then ABC
however, the tool has changed. The purpose must be an edge view where AB is a point
of this paper is to introduce a more modern view. View 1-2 is a successive auxiliary
approach to CAD solutions to descriptive view that shows a normal view of ABC
geometry problems. which is the true size view.
Descriptive Geometry with CAD - Not a New The same problem solved using a three-
Concept dimensional CAD system is really no differ-
Many professionals in the field of graphics ent. The technology allows us to create a
have a hard time with new technologies and true size view of the oblique surface directly
find it very difficult to forget the "old" way without the intermediate step of getting an
in favor of the new way. For example, in edge view. Therefore, instead of having two
determining the true size of an oblique sur- auxiliary views to create the true size view,
face, the basic concept is to view the surface there is only one auxiliary view. How can
normally. The only way this can be accom- this view be documented on the drawing?
plished using two-dimensional auxiliary One simple method is to place it on the
view technology is to first get an auxiliary drawing with a note of explanation. See
view that shows the surface as an edge, then Figure 2. In this case, the three-dimension-
get another auxiliary view off the edge view al data base is manipulated to create a new
that shows the surface in true size. Figure 1 view with line CB being the new X axis and
shows this solution. Since the horizontal point A depicting the direction of the new Y
view shows AB as a true length line, a point axis relative to the X axis. Note that the true
view of AB can be obtained through an aux- size view is not in projection with any other
iliary view H-l. Since AB is a line con- view. This type of layout may bother some
Figure 1 - True size of an oblique plane - successive auxiliary view technique.
Croft 5
EsmaacEEH
B
A [
Y
A B \
7
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p
u
^v. ' y
Ch
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AUXILIARY VIEW
TRUE SIZE ABE
Figure 2 - True size of an oblique plane - CAD technique.
since it "breaks tradition"; however, in this surface, another auxiliary view showing the
format, there is no view appropriate from edge view can be created. Then in the two-
which to project the true size view. It simply dimensional layout mode that most CAD
is obtained through CAD manipulation of systems offer, the auxiliary views can be
the three-dimensional model. shown in their "traditional locations". This
type of layout is shown in Figure 3. The lay-
Kelso (1995) recognized the fact that com- out shown in Figure 3 is similar to what
puter geometric modeling need not use Kelso (1995) suggest except that there are no
orthodirectional projection. He offers three phantom lines connecting geometric ele-
alternatives in the presentation of traditional ments and there are no fold lines. It should
multiviews which consist of a series of phan- be emphasized that the true size view is
tom lines connecting the geometric elements determined first and then from the true size
of the model in each view and a double line view an edge view is created. Unlike tradi-
depicting the "fold line". Why is it neces- tional descriptive geometry techniques, the
sary to show phantom projectors and fold edge view is not necessary to determine the
lines when the CAD system manipulates the true size in the CAD technique.
geometry to obtain the desired results and
these results can be verified through a query In the Winter 1997 issue of the EDGD
of the system? The procedure described Journal, Kelso (1997) shows a another
above and shown in Figure 2 simplifies the method by which one can facilitate the draw-
presentation and fully utilizes the power of ing of auxiliary views using CAD. The
the CAD system. premise of his presentation is simply to
ensure that "glass box" theory is not violat-
For the purist, there is an alternative. After ed and that the distance from the fold-line to
obtaining the true size view of the oblique the auxiliary view matches the distance from
6 Engineering Design Graphics Journal
Autumn 1.998
two fold lines back (two 90 degree turns in process through which we obtain the results
space). This approach is fine when two- has changed making the successive auxiliary
dimensional graphics is being used; howev- view format cumbersome and antiquated.
er, with three-dimensional CAD, it is cum- CAD often times allows us to get the desired
bersome and really serves no useful purpose. result directly from the three-dimensional
In the problem illustrated all that was need- data base without having to create a prelim-
ed was the true angle between the protrud- inary auxiliary view first as was described in
ing angle jig and the base. Figure 4 shows the true size of an oblique surface problem.
a similar problem. The angle between the It only makes good sense to use the power of
protruding angle jig and the base is deter- the CAD system for what it was intended; to
mined from an auxiliary view taken in the help us solve our design problems efficient-
direction of A-B. The geometric informa- ly and to increase productivity.
tion is determined once the view is shown.
It does not matter how this auxiliary view is Is there a need for descriptive geometry in
placed on the drawing; however it is shown the world of three-dimensional modeling?
in its projected position in Figure 4. The answer to this question should be a
resounding YES!! The technology has
Conclusion changed and the challenge is to determine
Before CAD (BC?), descriptive geometry how to make the best use of this technology
problems were solved using successive aux- as was done decades ago when traditional
iliary views. Precise projections and precise projective geometry was the state-of-the-art.
transfer of measurements had to be made in Descriptive geometry using CAD techniques
order to get the desired results. With the requires an even greater command of spatial
advent of CAD, the concepts of descriptive relationships than what is required for tradi-
geometry have not changed; however, the tional projective geometry. CAD enables us
Figure 3 - True size of an oblique surface - CAD technique with traditional
views.
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