This document provides an overview of different techniques for representing 3D objects in 2D drawings through various types of projections and perspectives. It discusses cylindrical and conic projections, first angle projection which uses three standard views, oblique projection which distorts sides, axonometric projections including isometric views, two-point and single-point perspective, techniques for dimensioning drawings, understanding scale and units of measurement, and provides an introduction to the International System of Units.

1. GRAPHIC
EXPRESSION
Lesson 2. 1st term

2. Perspective in drawings
• We use projection drawings to represent 3D
objects in two dimensions (our paper)
• There are two types of projections:
Cylindrical (Orthogonal)
Conic
•No distorsion
•Vanishing point (VP) far away
•Objects are distorted in the
same way our eyes see them
•Vanishing point close
(x, y, z)
VP
VP

3. First angle projection
• Cylindrical projection composed of three
views (taken from very far away) of the
object:
front
side
top

4. First angle projection:
result
front
top
side

5. Oblique projection
• We represent one of
the faces (mathing
with X and Y axis) in
true dimension and
the others are
distorted.
Y
Z
X

6. Representing objects in
oblique projection
We have to consider the X, Y and
Z axis.
We first draw the front face of
the figure (X and Y axis
Then we draw the sides
corresponding with the z axis
with a reduction coefficient of
1/2
We finally close the figure
with the lines corresponding
to the back of the figure
Y
Z
X

7. Axonometric projection
_ Isometric projection
• Axonometric projection shows an object from the corner so
we see its three sides
• Objects seem distorted because the same scale is used for
all features
• One axis is drawn vertical and the others are at an angle.
120º
120º
120º
Isometric projection

8. Drawing objects in
isometric projection
We draw according the axis at 120º
angles
We first draw a figure’s corner
120º
120º
120º
Second we draw the lines which
correspond to the sides next to the
corner, corresponding with Z axis
Then we draw the lines corresponding
to the left and rigth corners
We first draw a figure’s corner
Isometric projection

9. Two point perspective
Draw an horizontal line across the page
and mark two vanishing points: VP1 and VP2
 Draw one corner of the box: vertical line
Draw the construction lines from the top
and the botton of the corner to the
vanishing point
 Draw two vertical lines corresponding to
the left and rigth corners. They go from
the top to the botton lines
Draw the last construction lines from the
top and the botton of the other corners
Complete the box using the construction
lines
VP1
VP 2

10. Single point perspective
First draw the front of the cube. Then
add a vanishing point (X)
Draw thin construction lines from each
corner to the vanishing point
Draw the lines which correspond to the
back of the figure
Draw the rest of the figure over the
segments of the construction lines
VP

11. Dimensioning
• To dimension means “to indicate the real
size of an object in its drawing”
70
25
50
45

12. Scale
• Scale is a quotient/relationship beetween
the size of an object’s drawing and the
real size of this object.
Scale=Drawing size/real size: 1:n or n:1
It is written as entire number, one of it is 1.
Amplification
scale: 2:1 (n:1)
Reduction
scale: 1:2
Real scale: 1:1

13. Magnitudes and units
• Magnitude is a physical
property which we can
measure / determine /
quantify: i.e: length,
mass,…
• Units are the symbols
which go after a number
and identify the
magnitude we refer to

14. Types of magnitudes
• Fundamental: we can express or determine
them with a direct measurement: there
are seven: mass (M), length (L), time (t)
• Derived (derivadas): they are obtained by
combining the fundamental magnitudes:
force, volume, surface…

15. Metric system
• A metric system is a unit system where bigger
and smaller quantities are easier to convert. In a
metric system, units of the same magnitude are
transformed into powers of 10.
106
1000
100
mega
kilo
M
K
10
0.1
0.01
0.001 10-6
hecto dam
deci
centi
mili
micro
H
d
c
m
µ
D
1

16. The international system
(S.I.)
• It is a metric system where units are
Type
Funda-
magnitude
Unit
Length
Meter (m)
Mass
Kilogram (kg)
mental
Time
Second (s)
Temperature
Kelvin (K)
Derived
Force
Newton (N=kgm/s2
Energy
Joule (J=Kgm2/s2
Power
Watt (J/s)

17. Conversion coefficients
• For different reasons, magnitudes can be
expressed into different units. To convert
those units we multiply them by conversion
coefficients: They are quotients where we
write the units we want to convert and their
mathematical relationship. i.e
52km
1000
1
m
Km
52000
m
1. We identify how many different magnitudes we have: 1
(length) and add the same number of coeff. (1)
2. We write the former unit in the denominator and the new as
the numerator
3. Before the unit, we add a “1” before the bigger unit and before
the smaller, the number of smaller units contained in the bigger .
4. We simplify and multiply, obtaining the result