Unit 1.Systems of Representation

ART & DRAWING UNIT 1: SYSTEM OF REPRESENTATION.

UNIT 1: SYSTEMS OF REPRESENTATION

OUTLINE

ASPECTOS LINGSTICOS

VOCABULARY

1. SYSTEM OF REPRESENTATION. TYPES OF PROJECTIONS: A. ORTOGONAL B. OBLIQUE C. CENTRAL 2. DIEDRIC SYSTEM. ELEMENTS AND PROJECTIONS 3. AXONOMETRIC SYSTEM ELEMENTS AND PROJECTIONS 4. VOCABULARY

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Carmen Castillo

I.E.S. FERNANDO III EL SANTO / PROYECTO BILINGE

A.N.L.: ART AND DRAWING

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ART & DRAWING UNIT 1: SYSTEM OF REPRESENTATION.1. SYSTEMS OF REPRESENTATION. Systems of representation are ways to represent three dimensional figures or objects on a plane surface by using what we call projections. We can find different systems depending on the type of projection we use. But does it mean to project? To project is, for example, to project a point (a dot) through a straight line until we get to a plane (a plane surface). The point where the straight line touches the plane is the projection of the point. TYPES OF PROJECTIONS A. ORTOGONAL PROJECTIONS When the direction of the projection is perpendicular to the plane. We find the ortogonal projections in: -Diedric System -Axonometric System -System of contour maps (planos acotados)

B. OBLIQUE PROJECTIONS Definition: When the direction of the projection is oblique to the plane. In the System of Projections in Cavalier Perspective we find one oblique direction of projection. The Y axis is projected into an oblique direction to the plane. C. CENTRAL PROJECTIONS This is when the directions of projection come from one point called centre of projection. We find these types of projections in the Conic System.

http://www.dibujotecnico.com/saladeestudios/teoria/gdescriptiva/sistemas/sistemas.aspCarmen Castillo



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2. DIEDRIC SYSTEM This was developed by the French painter and military Mathematician Gaspard Monge. Its main function is to represent three dimensional objects on a plane by using perpendicular projections. ELEMENTS OF THE SYSTEM -The planes: horizontal plane (PH) and vertical plane (PV). -The earth line (LT) -Ortogonal projections -The element to be projected.

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ART & DRAWING UNIT 1: SYSTEM OF REPRESENTATION.PROJECTION OF A POINT We need to consider two planes, PV and PH, and a point. For example, point A has got two projections, one on each one of these planes. To get the vertical projection of PV, we have to trace a straight line that passes by point A until it touches PV at one point called a. To get the horizontal projection of PH, we have to trace a straight line that passes by point A until it touches PH at one point called a. The measurement between A (the point on the 3D space) and its projection on PV (a), is called distance. The measurement between A (the point on the 3D space) and its projection on PH (a), is called height/elevation. (EXAMPLE)

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ABATIMIENTO (REVOLUTION) OF THE HORIZONTAL PLANE To revolve a plane is to put one plane on to another one resulting in only one plane, and called a twodimensional surface. It is as if the PH plane could turn round and LT could act as a turning round axis. So, after the resolution, we obtain just one plane. (EXAMPLE)


PROJECTION OF STRAIGHT LINES To represent lines, we need first to project two points belonging to that line. After joining them together we will have the projection of the line. (EXAMPLE)

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http://www.edutecne.utn.edu.ar/sistemas-representacion/SISTEMAS_de_REPRESENTACION.pdf

PROJECTION OF PLANES To represent planes, we have to draw the straight lines that result from the intersection between those and both PV and PH. These straight lines are called traces. The vertical trace on PV and the horizontal trace on PH. (EXAMPLE)

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AXONOMETRIC SYSTEM We find this in three variations depending on the type of triangle (triangle of the traces) that results from the intersection between the plane of projection and the axis of the system. -Isometric -Dimetric -Trimetric

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A. ISOMETRIC This is when the triangle of the traces is an equilateral (its sides and angles are equal). First, we have to draw the triangle and second, we draw the axis. Once the triangle has been drawn, we can get the axis by tracing at least two bisections of two angles from the equilateral triangle. These axis are considered the projections of the axis from the space.(EXAMPLE) B. DIMETRIC This is when the triangle is an isosceles (two sides and two angles are equal and the side and angle left are different. Once the triangle has been drawn, we can get the axis by tracing the two bisections; the ones with the different angles. (EXAMPLE) C. TRIMETRIC This is when the triangle has got different sides and angles. Once the triangle has been drawn, we can get the axis by tracing the three bisections. (EXAMPLE)

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ELEMENTS OF THE SYSTEM -Axes: x, y and z. These axes are three straight lines that cut themselves in point O, the centre of the system. -Point O: the origin or centre of the system. -The planes where we project on to: xoy, xoz and yoz. The axes cut each two into a 90 angle. When these axes are projected on the plane, the angles between them change. So this way in Isometric we will have 120 between each axis.

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PROJECTION OF A POINT A point has got three projections: -a on plane xoz. -a on plane xoy. -a on plane yoz. -Point A is considered the main projection. (EXAMPLE). The directions of projection are straight lines on these planes. So we can get the projections of a point just by tracing straight lines passing through point A. (EXAMPLE)

PROJECTION OF A STRAIGHT LINE (EXAMPLE) The straight line from the previous example. To get the projection of that line we first must get the projections of the points where this line cuts the planes. In this case we have got points A and B. Each point has got three projections on each one of the planes. We can get them by tracing perpendicular straight lines on the planes that pass by point A. PROJECTION OF FIGURES Steps to be followed to draw a cube with 4cm side while applying a reduced scale of 4/5. - Draw an equilateral triangle using free measurement. - Trace a pair of bisections in two of its angles to get the centre and the axis of the system in isometric. - Make the revolution of axis x and y: a) Trace the perpendicular bisector (mediatriz) to the base side of the triangle of the traces. b) Draw a semi circumference, taking as a centre the point where the mediatriz cuts the side of the triangle. So, where this arch cuts the perpendicular we have got the revolved point O. Now we just need to join point O with the extremes of the segment (side of the triangle). c) Now we can put the real measurements in the revolved axis to get the reduced new measurement. (EXAMPLE)

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ART & DRAWING UNIT 1: SYSTEM OF REPRESENTATION.1. VOCABULARY VocabularyA B C D Different adjectivo Distance nombre Divide E Equivalent F H I M N Number sust. O Ones P Pair sust. Q R Representation nombre S Same adjetivo System sust. T To Add verbo. To Check v. To Divide v. To Put verbo To Remove verbo Top W /d/ /t ek/ /di'va d / /p t/ /r 'mu:v/ /top/ Sumar Comprobar Dividir Poner Quitar Arriba /se m/ /'s st m/ Mismo Sistema /'repr zen'te n/ Representacin /per / Par /w ns/ Unidades /'n mb r / Nmero / 'kw v l nt/ Equivalente /'d fr nt/ /'d st ns/ /d 'va d / Diferente Distancia Dividir

Pronunciation

Translation

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Unit 1.Systems of Representation