Development of an Educational Software Tool for Interpretations
of Multiview Engineering Drawings
Y. S. Suh and J. MacCasland
Department of Mechanical Engineering
California State University, Sacramento, Sacramento, CA 95819-6031
ABSTRACT – One of the ways for engineering
the
students to practice skills of interpreting multiviews of
explanations are often required, but limited instructors’
engineering drawings is to construct isometric views
time has been always an issue as typical engineering
from orthographic multiviews of various objects. Many
graphics courses have large number of enrolled
times, students need instructors’ explanations and
students.
illustrations, but not all students can get the required
personal attentions due to limited instructors’ time.
answer.
Instructors’
personal
attention
and
A software tool is under development by the
authors to help students understand and practice
A software tool has been under development to
interpretations of multiview and isometric view
help the students to perform many drawing exercises.
drawings. Students can learn independently, as the
The software can give immediate interactive feedback
software tool gives interactive feedback while they are
to students according to their chosen level of difficulty,
working on it, and they can check the result by
and they can check and verify the results during and
comparing the 3D models built from the isometric
after the exercise without direct instructors’ guidance.
drawing they make with the multiviews.
In this paper, the design and components of the
software will be described, followed by a brief
I. Introduction
An
engineering
drawing
with
multiple
description of relevant background.
orthographic views is a standard way of communicating
product design information and serves as a legal
II. Background
document. Engineers need to develop their spatial skills
Company et al. (2004) and Contero et al. (2005)
to describe products with complex shapes and fits,
present an educational software tool. They have been
which are typically described in terms of multiview and
working on constructing 3D models from a single
isometric drawings.
isometric view for many years. They applied the
Although
the
mapping
principles
are
algorithms they have developed to the educational
mathematically simple and clear, students tend to have
software with which students can construct 3D models
difficulty doing the tasks as the drawings become more
and multiview drawings by drawing isometric views.
complex. Even if a student is able to complete an
There are an infinite number of solutions (3D
exercise, it is not clear to the student whether or not the
models) from a single isometric sketch and is a
answer is correct unless the exercise is accompanied by
mathematically ill-defined problem. It is very difficult,
63rd Annual ASEE/EDGD Mid-Year Conference Proceedings, Berkeley, California – January 4-7, 2009
if possible, to make a robust and practical program.
•
If there is a junction point in one sketch of a
Hence, the software must impose a lot of limitations on
view, there are always matching points found
the geometry of the models. Company et al. can handle
in the other two views.
some
specific
polyhedral
models
called
quasi-
normalons in which most of the faces must be aligned
with the coordinate axes.
IV. User Interface
Microsoft Windows is chosen as the platform
Many three-view drawings, although not all, can
simply because of its ubiquitous availability. The
describe a unique 3D model, so the software can be
software is being implemented in C# language using
much more robust and practical with some user
Microsoft Visual Studio 2005. The components of user
interaction. There have been many research works on
interfaces are built on top of the Windows Forms, and
automatic construction of 3D models from multiview
the OpenGL graphics library is used for displaying the
drawings. Interested readers may read survey papers on
drawings and models.
this area (Company, 2005b; Varley, 2007; Veselov,
The layout of the program is shown in Figure 1.
2007; Wang, 1993).
Kim et al. (2001) describes operators for building
3D solid models from 2D orthographic views.
This paper is not about reporting a new algorithm
on the automatic construction; instead, it applies the
known algorithms to building educational software tool
for engineering graphics students.
III. Assumptions and Limitations
The current implementation of the software has the
following limitations and assumptions.
•
It can only handle line drawings; thus, only
polyhedral models can be created.
•
•
•
Figure 1. User Interface layouts.
It assumes that there are three-view drawings
(Front, Top, and Right view) arranged
The screen is divided into four windows, and each
according to the third angle projection
window shows Front, Top, Right, and Isometric views
standard. Two views or one view drawings
according to the ASME drawing layout. The sizes of
cannot be handled.
the view can be easily adjusted by dragging the two
It assumes the three views completely describe
sashes (vertical and horizontal) between the views. In
the model.
each individual view, users can pan and zoom in or out
All hidden lines are drawn in the views with
the hidden-line font (dotted line).
each individual view, but the Front and Right views
always maintain horizontal alignment, while the Front
and Top views always maintain the vertical alignment.
For example, if the Right view is panned vertically, the
Front view also pans the same amount to maintain the
63rd Annual ASEE/EDGD Mid-Year Conference Proceedings, Berkeley, California – January 4-7, 2009
alignment, but the Right view can be panned side-to-
VI. Learning Levels
side freely. The isometric view can be rotated in
The software provides three different levels of
addition to panning and zooming and the view can be
feedback depending on students’ choices and levels of
modified independently from the multiviews.
confidences. The lowest level gives the students the
most feedback and automations while the highest level
V. Authoring and Learning Modes
will give little or no feedback. As the students’ skills
Students draw an isometric view based on the
improve, they can set a higher level at any time.
multiviews provided by the instructors. Of course,
Currently, there are three levels, and each level gives a
students should not be allowed to modify the
different set of feedback as summarized in the
multiviews either intentionally or accidentally. Running
following table.
the software in two different modes provides the
protection mechanism. There are Authoring and
Table 1. Levels and Feedback.
Learning modes. Each mode also defines how the
Feedbacks
program should respond to the user’s interactions.
In the Authoring Mode, the multiviews (Front,
Levels
1
2
3
Bounding Box
Top, and Right views) are editable so that the
instructors can create assignments. Authors can easily
add sketch lines as the lines automatically snap to the
grids.
The
authoring
user
can
undo
previous
Position Matching
Unmatched Point Warning
Show all 3D Points
commands, and an Erase tool is also provided for
Highlight Faces1
removing unwanted sketch entities. Also, dragging the
sketch entities is supported, so users can easily modify
Show Viewing Ray
the lengths and orientations of the sketch entities.
Segment Matching
Students can also create their own problems or copy
any problems from a textbook. Once the multiviews are
Different line colors2
complete, the file can be saved from which a database
3D Model
of quizzes could be easily built by collecting the
Glass Projection3
problems from students and instructors.
Students can create an isometric view by opening a
Checking Missing Lines
file with multiviews, after switching to the Learning
Mode. In the learning mode, only the isometric views
are modifiable. The multiviews, however, will give
Each type of feedback is explained in the following
section.
helpful feedbacks such as highlighting matching points
and other features detailed in the next section. The
sketch commands in this mode also support undoing,
1
Feature planned or under development
2
Feature planned or under development
3
Feature planned or under development
erasing, and modifying the sketching entities.
63rd Annual ASEE/EDGD Mid-Year Conference Proceedings, Berkeley, California – January 4-7, 2009
VII. Visual Feedbacks
Displaying Bounding Box
The instructor provides the size of the bounding
box, and the bounding box is visible in the multiviews.
The bounding box helps in creating the multiview
sketches.
In the Learning mode, students first need to input
the correct bounding box size (Figure 2) from the threeview drawings. If the student input matches the actual
size, the bounding box is also displayed in the isometric
view. Figure 1 shows the bounding boxes drawn with
Figure 3. View ray displayed.
green dotted lines in the views.
Position Matching
As a user moves the mouse over the isometric
grids in the learning mode, the point under the cursor is
highlighted provided that the point exists on the object.
Figure 3 shows an example in which the mouse point is
highlighted as a cyan point in the isometric view, and
the corresponding points in the multiviews are
highlighted as red dots.
Figure 2. Bounding Box Dialog.
If there is more than one point under the cursor
intersecting with the line of view, all the intersecting
Showing View Rays
points are highlighted in different colors and the user
The view direction vector of an isometric view is (-
can choose one by double-clicking the matching color
1, -1, -1). When a user clicks a mouse button at a grid
from the color list panel. In Figure 4, two points are
point on the isometric screen, the user is selecting all
under the current cursor point in the isometric view.
the points in the line of the view including the mouse
Users can select either the blue or the orange points to
point. As the mouse hovers in the isometric view
draw the next line.
window, the software checks if any junction points of
the multiview sketches are intersecting with the line of
view. The line of view in each view can be displayed,
so that students can understand the relationship
between the isometric view and multiviews. Figure 3
illustrates the view rays displayed in the views. In
Figure 3, the magenta lines in the multiviews represent
the view rays corresponding to the cyan point (cursor
point) in the isometric view.
63rd Annual ASEE/EDGD Mid-Year Conference Proceedings, Berkeley, California – January 4-7, 2009
PYZ = (c, yj, zj), j=1, …, NYZ (Right View)
(1)
PZX = (xk, c, zk), k=1,…,NZX (Top View)
where c is any value.
For a set of three points ( PXY, PYZ, PZX ), one from
each view, to be the projection points of a point PXYZ,
then the following relations must be satisfied. (Idesawa
1975)
|xi-xk| < ε and |yi – yj| < ε and |zj – zk| < ε
(2)
where ε is a small real value to handle any drawing
errors.
Figure 4. Selection of multiple points.
By searching for all the matching tuples that
satisfies the above relations, all the 3D points (PXYZ)
Warning on Unmatched Point
can be found from the points in the multiviews. The
If a student selects a point on the isometric view
points can be drawn in the 3D view to allow the
that doesn’t match any point in the multiviews, a
students to investigate and better understand the overall
warning dialog pops up indicating the point doesn’t
shape of the object. It will also help students
have any match. An example is shown in Figure 5.
understand how each point matches the 3D point. An
example is shown in Figure 6.
Figure 5. Warning on unmatched point.
User can either cancel the selection by accepting
the warning or override the warning and move on.
Showing all 3D points
A point, PXYZ, in a 3D space is projected to the
Front, Right, and Top views. Let the points in each
view be represented in the XYZ coordinate system as
Figure 6. Automatic 3D point of a model below.
PXY = (xi, yi, c), i=1, …, NXY (Front View)
63rd Annual ASEE/EDGD Mid-Year Conference Proceedings, Berkeley, California – January 4-7, 2009
Notice, however, that not all points computed
using this method are valid points to be part of the 3D
model. The invalid points are not automatically
removed but students must remove them manually.
Segment Matching
As the user draws a line in the isometric view, the
matching lines in the three multiviews are highlighted.
Figure 7 illustrates an example where the line drawn in
the isometric view matches three lines in the
multiviews where the lines are highlighted in red.
Figure 8. Constructed 3D model.
Checking Missing Lines
As the multiviews are drawn manually, it is easy to
miss one or two lines. There is an option to check if
there are any junction points that don’t have matching
points in other views. Although this is not a complete
check of missing lines (which is not a trivial problem),
it can give some level of indication that the drawing is
not complete. (See Figure 9.)
Figure 7. Highlighting matching lines.
3D Model Generation
As the user draws the isometric view, the
corresponding 3D model is constructed. Students can
check the 3D model even before finishing the isometric
view as the models are constructed concurrently when
the sketch entities are added to the isometric view.
Figure 8 shows a constructed 3D model of the
multiview drawing shown in Figure 7. The view is
rotated so that the model is viewed at a different angle.
Figure 9. Missing line checker.
Currently, only the wireframe view is available.
63rd Annual ASEE/EDGD Mid-Year Conference Proceedings, Berkeley, California – January 4-7, 2009
VIII. Conclusions and Future Works
A software tool being developed for engineering
graphics
students
to
practice
interpretations
of
multiview drawings is described. Authors expect that
students will be encouraged to do more exercises by
using the software tool as it provides immediate
interactive feedback. This will facilitate greater spatial
skills and better ability to read and create engineering
Technology to Sketch-Based Modeling, Computers &
Graphics, 29(6): 892-904
Contero, M., Company, P., Saorin, J.L., Consea, J.,
(2005) Improving visualization skills in engineering
education, IEEE Computer Graphics and Applications,
25(5): 24-31
Hubbard, C., Kim, Y.S., (2001) Geometric Assistance
for Visual Reasoning and Construction of Solids with
Curved Surfaces from 2D Orthographic Views,
Advances in Engineering Software, 32:21-35
drawings and reduce the need to seek individual aid
from instructors.
Further development of the software is still
required in the following areas.
•
Elliptic curves will be added as sketching tool so
that cylindrical faces can be handled.
•
More feedbacks will be added such as glass view
projections and face highlights, etc. These are
under development and marked in Table 1.
•
More realistic 3D model views with shaded
Idesawa, M., (1973), A System to Generate a Solid
Figure from Three View, Bulletin of the JSME,
16(92):621-52
Markowsky, G., Wesley, M.A., (1980) Fleshing Out
Wire Frames, IBM Journal of Research and
Development, Vol. 24, No.5, pp 582-587
Varley, P., Martin, R., (2007) Sketch input of 3D
Models, Current Direction, International Conference on
Computer Vision Theory and Applications VISAPP07,
Proceedings of the Second International Conference on
Computer Vision Theory and Applications, Barcelona,
Spain, March 2007
images. There is also a need to overlap with the
multiviews (as glass box animation) so that the
matching of the 3D model and the orthographic
views are clearly visible.
•
Deployment of the software to a web interface
increasing accessibility so that it can be used
without direct installation.
After the software development is finished, it
needs to be introduced in the course and tested by the
students. Further studies will be performed and the
Vesselov, N.A., Golovin, S.I., (2007) A review of
methods for computer-aided reconstruction of solid
models by their orthographic views, Moscow
University
Computational
Mathematics
and
Cybernetics 31(3): 128-132
Wang, W., Grinstein, G.G., A Survey of 3D Solid
Reconstruction from 2D Projection Line Drawings,
Computer Graphics Forum 12(2):137
Wesley, M.A., Markowsky, G., (1981) Fleshing Out
Projections, IBM Journal of Research and
Development, Vol.25, No.6, pp.934-954
software may be refined to assure an increase in student
performance and understanding.
IX. VI. References
Company, P., Contero C., Piquer, A., Aleixos, N.,
Consesa, J., Naya, F., (2004) Educational software for
teaching drawing-based conceptual design skills,
Computer Applications in Engineering Education
12(4):257-268
Company, P., Piquer, A., Contero, M., Naya, F., (2005)
A Survey on Geometrical Reconstruction as a Core
63rd Annual ASEE/EDGD Mid-Year Conference Proceedings, Berkeley, California – January 4-7, 2009