Engi 1504 – Graphics
Lecture 6: Descriptive Geometry
 Properties of lines
 Properties of planes
 Auxiliary planes
 Midterm hints
 Class assignment 6
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet
1
Points and Lines
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The point is the basic building block for an
object.
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet
2
Points and Lines

Standard notation
– AF is the view of point A on the frontal plane
– The height, width, and depth are specified with
reference to the reference (folding lines)
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet
3
Points and Lines

Note:
– The distance behind a plane (say the front plane) is seen in all
other adjacent views.
– If the distance to point A from the folding line is known in one
adjacent view, point A can be located in another adjacent view
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet
4
Lines
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A line is made up of two points
3 views of line AB are shown
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet
5
Lines
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Vertical line – shows as a
point in top view, parallel
to front and right side
planes
Horizontal – infinite
positions, but all points
must have equal elevation
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet
6
Lines
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Inclined line – parallel to
front or right plane.
Always parallel to one
plane and inclined to the
others
Oblique line – inclined to
all principal planes
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet
7
Auxiliary Planes
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The length of a line can only be measured if it
is seen in true length
Recall: A line can be seen true length if
projected onto a plane parallel to it
So to find the true length of a line we draw an
auxiliary folding line parallel to it.
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet
8
Auxiliary Planes
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Consider the front and
top view of oblique line
ab

We can draw an
auxiliary plane parallel to
either line aFbF or aHbH
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet
9
Auxiliary Planes
H
1

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TL
Auxiliary plane
parallel to line
aHbH
The line is
perpendicular to
horizontal (top)
view
H1
H2
H2
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet 10
Point View of a line
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Recall: A line can be seen as a point if
projected onto a plane perpendicular to it
So an auxiliary plane perpendicular to a line
that shows true length will show as a point.
Note: to show line as a point, need a view
that shows true length first.
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet 11
Point View of a line

Course: Engineering Graphics 1504
Memorial University of Newfoundland
D3
aobo
O

Recall: A line can be seen
as a point if projected onto a
plane perpendicular to it
So an auxiliary plane
perpendicular to a line that D
shows true length will show 3
as a point.
Note: to show line as a
point, need a view that
shows true length first.
A

Sheet 12
Slope of a line
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The slope (or grade) of a line is the inclination
of the line with the horizontal
Slope can be measured in a view that shows
vertical height and the line in true length
So we draw a folding line in the horizontal
(top) view.
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet 13
Slope of a line
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So we need an
auxiliary view (folded
from the top view), that
shows the line as true
length
Slope is the angle
between the true length
line and a line parallel
to the folding line
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet 14
Direction of a line
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Bearing
The direction of a line (given
as a compass reading) is
seen only in the top view.
Think of holding a compass.
A bearing is measured from
either north or south, with
north usually at top of page
Azimuth is measured from
north and specified as an
angle from 0-360º
Azimuth
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet 15
Summary
Find true length of a line:
1.
Place an auxiliary view parallel to the line and project two points
on the line onto the auxiliary view
Find point view of a line:
1.
2.
Need a true length line first
Locate an auxiliary view perpendicular to the true length line and
project endpoints
Find slope of a line
1.
2.
Need a true length line and an edge view of the horizontal
Find an auxiliary view (folded off the top view) that will show true
length
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet 16
Summary Continued …
Things to remember about lines:

If a line is parallel to a folding line, it will appear true length in
the adjacent view

Bearing and azimuth are seen only in the plan (top) view

If two lines intersect, the intersection point will correspond in
all views

The shortest distance between two lines is seen where one of
the lines appears as a point

Perpendicular lines appear perpendicular in any view in which
one or both of the lines appear in true length

A line will appear true length in any view folded off a point
view of the line.
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet 17
Break Time
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Take 5 minute break
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet 18
Midterm Hints and Topics
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Midterm exam is November 2nd
Lectures 1-5 are covered (Chapters 1-4 in text)
Review your assignments
Review visualization exercises
Practice as many problems as you can
Contact me if you are stuck. My office hours are 1-2
pm on Tuesdays and 9-10am on Thursdays
Student Questions?
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet 19
Class Assignment #6
Point A is 15 m behind the frontal plane and
30 m below the horizontal plane. Point B is 33
m behind the frontal plane and 12 m below
the horizontal plane. The line AB bears N 65º
E. Using an appropriate scale draw a point
view of line AB.
Course: Engineering Graphics 1504
Memorial University of Newfoundland
Sheet 20