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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 ...

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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 
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                                                                                      ^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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...Volume number the need for descriptive geometry in a world of d modeling frank m croft jr ohio state university abstract traditionally has consisted projection three dimensional figures on two plane paper using successive auxiliary views through this method quantita tive measures length angles shapes and other geometric information were obtained tech nology required systematic approach to problem solving with accuracy projections trans fer distances from previous layout position essential solution modern cad methods that may be used solve problems no longer require positioned standard often sys tem will allow direct without an intermediate view as would by traditional tradi tional is cumbersome antiquated advent concepts have not changed however process which we obtain results introduction such many years technology shows true shape oblique surface should powerful system simply been dimension electronic pencil screen al being thus generate done these solutions are achieved graphics ser...

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