Representation systems

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).

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.

We can project the objects in different ways:

•          ORTHOGONAL PROJECTION

•          OBLIQUE PROJECTIONS

•          CONIC PROJECTIONS

( IN GREEK, ORTHO= 90 Degrees, GONAL= angle) 

CLASSIFICATION OF THE REPRESENTATION SYSTEMS

 

 

 Diedric System:

Isometric Perspective

         This system is composed of three planes forming a trihedral, which is projected, forming the same angle, onto the drawing plane. This gives us the isometric perspective. 

Conic 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.

•          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. 

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

One point perspective

 

Two points perspective (Dos puntos de fuga)

 

 

 

NEXT PROJECT: 

Design the classroom with one point perspective. Some examples: 

QUADRILATERALS

A quadrilateral is a polygon with four sides. It has:

• Four sides (edges)
• Four vertices (corners)
• The interior angles add up to 360 degrees
• Two diagonals: a diagonal of a quadrilateral is a line segment whose end-points are opposite vertices of the quadrilateral. In picture below, ABCD is a quadrilateral, AC, BD are the two diagonals.

We name a quadrilateral by naming the four vertices in consecutive order. So we can name the quadrilateral as ABCD.

TYPES OF QUADRILATERALS

1. Parallelograms (paralelogramos)

A parallelogram is a quadrilateral where both pairs of opposite sides are parallel. Also opposite angles are equal.

Types of parallelograms

 Square
 All sides equal, all angles 90°, the diagonals are equal and perpendicular.

 Rectangle
Opposite sides equal, all angles 90°, the diagonals are congruent but they are not perpendicular. 

Rhombus
Opposite sides parallel and equal, the diagonals are not equal but they are perpendicular.

Rhomboid
A rhomboid has opposite sides that are parallel and equal.

2. Trapezium (Trapecios- trapezoid US)

A trapezium is a quadrilateral with a pair of parallel sides.

The pair of parallel sides (SR||PQ) are called the bases of the trapezium, and the non-parallel sides (PS,QR) form the legs of the trapezium. The distance between the bases or the trapezium is called the height or the altitude. 

Types of trapeziums

If we have two right angles and two parallel sides, then we have an

rectangle trapezium

 

If the two legs of the trapezium are congruent to each other, then we have an isoceles trapezium

If the four sides or the trapezium have different lengths, then we have a scalene trapezium

 

3. Trapezoid (trapezoide)

A trapezoid (trapezium in US) is a quadrilateral with NO parallel sides

You can find a overview abour quadrilaterals here: