Representation Systems

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 three-dimensional 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 three-dimensional 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 DegreesGONAL= angle

• PARALLEL ORTHOGRAPHIC PROJECTIONS – Used in technical drawings

• OBLIQUE PROJECTIONS

• CONIC projection F

CLASSIFICATION OF THE REPRESENTATION SYSTEMS

Representation Systems

DIEDRIC .- Uses parallel orthographic projections

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

VERTICAL PLANE

HORIZONTAL PLANE

GROUND LINE

FIRST QUADRANTSECOND

QUADRANT

FOURTH QUADRANTTHIRD

QUADRANT

Representation of an object

Vert.projection

Horizontal projection

Observer

a´

a

Example of projection

Elevation or Front view

Plan or top viiew

Left side viewRepresentation

of the views ofan object

ISOMETRIC PERSPECTIVE

• In general, perspectives aim to represent three-dimensional 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.

o

Z

XY

How to pass from diedric system to isometric

Front view

Plan

Left sideview

o

Z

XY

Front view

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 vanishing point.

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.)

Horizon line

Ground line

Height of the point of view

Distance points

Vanishing point

Area where we place the objects that we want to draw from top view

Example: Drawing a chessboard in one point perspective(P.V.)

Horizon line

Ground line

V.P.

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