1. How to solve missing view problems and other mysteries of 3D worlds
Lab 3--Developing visual 3D skills:
How to solve missing view problems and other mysteries of 3D worlds
<Lab3-F2012-HowTo-missviewMissline-v3.pptx>

2. Objectives for the lab Learn how to Do simple isometric drawings1
Do simple multiview drawings
And overall -- develop visualizing skills so that you can
move back & forth among isometric ( & other pictorial) & multiview drawings to develop your ideas
1 Lecture 4 will provide additional detail about isometric drawings, as part of “pictorial” projections.

3. Developing Visualizing Skills 1/7
Important to develop skills for
Looking at multiview and visualizing the object (or drawing a pictorial such as an isometric)
Looking at the object and being able to sketch a multiview
Text: shows several ways to develop these skills:
Projection studies: look at examples of combined multiview & iso (Recommended: study text fig 5-104, make sure you see the correspondence between iso and each ortho view)
Build sample physical models
Try these

4. Adjacent Areas: Developing Visualizing Skills 2/7
Adjacent areas: (key concept) surfaces which are next to each other.
Visible line: intersection between 2 planes; so …
Boundary between surfaces shows as a line indicating a change in planes
No 2 adjacent areas can lie in same plane (i.e. if there is a line, the 2 adjacent planes must not be co-planar)
Try to apply this notion: given a top view, sketch several possible objects
You Try It: sketch a possible 3-view OR isometric that has the top view shown:
Pick 1 or 2 samples of student’s work (3-view or iso) and sketch on board (or sketch in ppt) 4

5. Adjacent Areas: Developing Visualizing Skills 3/7
The problem: do 3-view or iso that matches the given top view:
Possible solutions:
What was yours?

6. Developing Visualizing Skills 4/7
One Technique:
Surface Labeling:
You did this in Lab.
Analysis by Solids and by Surfaces are similar
Vertex Labeling:
Can help as check in multiview drawing

7. Similar Shapes: Developing Visualizing Skills 5/7
apply rules 5 & 6: a surface will keep its basic configuration in all views (except of course on edge); so …
e.g. If it looks like an ‘ell’ in one view, it’ll look like an ell in ALL views
“Ell”
“U”
Inverted “T” 7

8. Convention: Arrangement of Orthographic Views
Remember the glass box: projecting the object onto its faces and unfolding the faces results in the view placement shown:
… and this is the STANDARD view arrangement;
you must follow this in all multiview drawings
Top View
Depth
Width
NB: distance between Top/Front & Front/Side is arbitrary; you can adjust it. It corresponds to the size of the Glass Box compared to the overall object size.
BUT Top/Front MUST be aligned! Same for F/Side
Note placement & alignment of views. Remind students a)of reasons for this convention and b)they must follow it for all their home work and exam problems.
Crucial to have correct placement, alignment: without it, cannot tell what part of each view goes with what other part!
Note : The following can be seen from the slide:
T & F: same width, aligned vertically
F & R: same height, aligned horizontally
T & R: same depth
Right Side View
Front View
Height 8

9. Developing Visualizing Skills 6/7
Another technique: Missing Line exercises
What’s missing from this multiview?

10. Developing Visualizing Skills 7/7
How to: Missing View exercises

11. Projection Between Views
Given two views of any point, the same point in any other orthographic view can be found
A 45º mitre line is used to locate points and transfer depth dimensions between top and side views
Why does this work?
See slide 17:
reflecting thru 45 deg line is equiv to rotation of 90 deg!
So reflection is like swinging camera 90 deg or
Rotating R side of glass box 90 deg
Why does this work? See slide 17: reflecting thru 45 deg line is equiv to rotation of 90 deg!
So reflection is like swinging camera 90 deg or rotating R side of glass box 90 deg

12. Align Bounding Boxes of each View
WIDTH
DEPTH
TOP
WIDTH
DEPTH
Miter line at 45°
HEIGHT
HEIGHT
FRONT
RIGHT

13. Sketch Features – View Projection
TOP
Miter line at 45°
FRONT
RIGHT

14. Line “Order” 1. Visible 2. Hidden 3. Center Draw lines in this order:
From Bertoline: Figure 2.38 / Pg 42
In technical drawing, it is important that hidden features be represented, so that the reader of the drawing can clearly understand the object.
Thus we need hidden lines to show that those features do exist, but just are hidden in that particular view.
We also need center lines to understand how the features defined in the 2D views translate into 3D.
NOTE: hidden lines & center lines are used only on Orthographic projection drawings, never on isometric drawings
Q: Do we need a convention for what line to show if two lines fall on top of each other?
A: Yes! Otherwise features which are more important (eg: visible lines) would be overridden by less important features (eg: hidden lines) and the resulting drawing would be interpreted inaccurately.
2. Hidden
3. Center 14

15. Add missing view in indicated location. (is there a missing line?)

16. Add missing view in indicated location. (is there a missing line?)
… don’t forget the missing line!
1 what is overall containing bounding brick? You can tell the W & D from top, W H from front!
2. What are basic components? Small block on large, chamfer on lg block. So do next level bbox
3. What are details?
a) divide into top & bottom
b) “notch out” top to small block
c) chamfer side of base

17. Add missing view in indicated location.
1 what is overall containing bounding brick? You can tell the W D from top, and W H from front!
2. What are basic components? An “Ell” shape. So do next level bbox
3. What are details?
a) corner off bottom
b) notch out of bottom
c) notch out of back of Ell
d) corner off back of Ell
4. Add these

18. Add missing view in indicated location.
1 what is overall containing bounding brick? You can tell the W D from top, and W H from front!
2. What are basic components? An “Ell” shape. So do next level bbox
3. What are details?
a) corner off bottom
b) notch out of bottom
c) notch out of back of Ell
d) corner off back of Ell
4. Add these

19. Add missing view in indicated location.
Do bounding box
Basic shape: 2 slabs about same thickness
Details
vertical slab smaller, off-center
vert slab: notched

20. Add missing view in indicated location.
Do bounding box
Basic shape: 2 slabs about same thickness
Details
vertical slab smaller, off-center
vert slab: notched

21. In doing this lab, you’ll have learned --
How to do an orthographic projection:
Plan views, front views and side views
Combining P, F and S into multiview drawings
How to do an isometric drawing
How to use all of this in solving visualization problems like missing view and missing line
Start to develop skills to think and work in 3D, to be able to move back and forth among these views in order to develop your ideas, and to understand those of others

22. That’s all!