DESCRIPTIVE GEOMETRY
What is descriptive geometry?
• The construction of the majority of the
objects around us (houses, motorcycles,
televisions, telephones, computers, etc.)
requires that these objects to be
previously defined (design process) and
subsequently represented with exact
precision on plans (objective description of
the form).
Think about objects that require
a design
• Are these objects two-dimensional?
• How can we draw a three-dimensional
object in a paper (2D)?
• Descriptive geometry makes it possible
to objectively represent objects and
elements that pertain to the threedimensional space on two-dimensional
supports.
• So, do you think that descriptive geometry
affects our lives?
• In what way?
• Talk in groups of four people.
• We can represent objects by the
representation systems.
• Representation systems are graphic
languages to link elements in 3D to
elements in 2D and vice versa. They are a
very important part of descriptive
geometry.
• These languages are universal. They can
be understood all over the world.
• Representation systems are based on the
projections of the geometrical threedimensional elements on plans. The
projections vary according to the
representation system.
• It is as if we take a photo of the object and
we print it out.
TYPES OF PROJECTIONS
• We can project the objects in different
ways:
• ORTHOGONAL PROJECTION
• OBLIQUE PROJECTIONS
• CONIC PROJECTIONS
IN GREEK
ORTHO= 90 Degrees
GONAL= angle
• PARALLEL ORTHOGRAPHIC
PROJECTIONS
– Used in technical drawings
• OBLIQUE PROJECTIONS
• CONIC projection
F
CLASSIFICATION OF THE
REPRESENTATION SYSTEMS
DIEDRIC .- Uses parallel orthographic
projections
Representation
Systems
AXONOMETRIC: Uses parallel
orthographic projections. (ISOMETRIC is
the variation of the axonometric system
that we are going to use)
CAVALIER PERSPECTIVE.- Uses oblique
parallel projections
CONIC: Uses conic projections
This is an example of how an object is
represented in each system
DIEDRIC SYSTEM
• (1746 –1818) was
a French mathematician,
a revolutionary, and the
inventor of descriptive
geometry, the theoretical
basis on which technical
drawing is based. During
the French Revolution he
served as a minister of
the Marine and was
involved in the
reformation of the French
educational system,
founding the École
Polytechnique.
Gaspar Monge
Representation
of an object
Vert.projection
Observer
Horizontal projection
a´
a
Example of projection
Representation
of the views of
an object
Elevation or
Front view
Plan
or top
viiew
Left side
view
ISOMETRIC PERSPECTIVE
• In general, perspectives aim to represent threedimensional objects in a single view or
projection ,allowing the viewer to clearly see
how the object is in reality.
ISOMETRIC PERSPECTIVE
• This system is composed of
three planes forming a
trihedral (XOY, YOZ and
ZOX), which is projected,
forming the same angle, onto
the drawing plane. This gives
us the isometric perspective.
In other words, it is the
corner of a cube.
Y
Z
o
X
How to pass from
diedric system to isometric
Z
Front view
Left side
view
o
Plan
Y
X
One point perspective
• With conic perspective we can draw reality
the way we see it.
• It is just the way that a camera captures
reality.
• Conic perspective is a method that gives
us the sensation of distance and depth in
a flat support.
• It is an optical illusion.
One point perspective
• First rule:
– When we look at a group of parallel lines that
escape and we want to draw them, we do not
draw them parallel, but instead we draw them
meeting at one point.
– We call this point the
.
RICHARD
ESTES: "Bridge"
Basic elements in linear perspective
• Point of view : It is the observer’s eye.
• Horizon line: The height of this line coincides
with the height of the point of view.
• Ground line: It is a theoretical line that help us to
draw the figures. The distance between the
horizon line and the ground line is the height of
the observer.
• Vanishing point: It is always on the horizon line.
• Distance points: They are the vanishing points of
the lines that form 45º with the representation
plane
(P.V.)
Distance points
Horizon line
Height of
the point of view
Vanishing point
Ground line
Example: Drawing a chessboard in one point perspective
(P.V.)
V.P.
Horizon line
Ground line
Example of how to rise an object
(P.V.)
Horizon line
Ground line
Summary
• Descriptive geometry represents 3D objects in a paper
(2D)
• The four systems of representation are:
– DIEDRIC SYSTEM for technical drawings
– ISOMETRIC SYSTEM give us an idea of how the object is in 3D
(perspective of the object)
– CAVALIER SYSTEM the same
– LINEAR PERSPECTIVE (CONIC PERSPECTIVE) is a
perspective of the object as we see it