◦ Are the group of rules and geometric methods to define the shape of three dimensional objects on a plane. ◦ They give us information about the measurement and proportion of the represented object. ◦ They use projections to depict 3D objects into 2D representations on a plane.

Type of projection PROJECTION SYSTEMS Orthographic Parallel Projection DIMENSIONED DRAWINGS SYSTEM DIHEDRAL SYSTEM AXONOMETRIC SYSTEM ISOMETRIC DIMETRIC TRIMETRIC Oblique Parallel Projection CAVALIER PERSPECTIVE Central Projection ONE POINT PERSPECTIVE TWO POINT PERSPECTIVE THREE POINT PERSPECTIVE

DIHEDRAL SYSTEM Sistema axonométrico. AXONOMETRIC ( CAVALIER PERSPECTIVE ) AXONOMETRIC ( ISOMETRIC ) LINEAR PERSPECTIVE DIMENSIONED DRAWINGS SYSTEM

 It uses a orthographic parallel projection and only one projection plane.  The projection is completed with measures of height accoding to the volumen.  This system does not provide perspective.

 It is a system of reprentation that uses orthographic parallel projections and the projecting rays are all parallel one another and perpendicular to the projection plane. PROJECTION PLANE PROJECTING RAY

ELEMENTS OF THE DIHEDRAL SYSTEM This system is based on two projection planes, perpendicular to each other, called Vertical Plane (PH) and Horizontal Plane ( PH ). Both planes divides the space in four parts or Quadrants. The line of intersection between the two projecting planes is called Fold Line (FL).

For practical purposes, we need to fold the horizontal plane over the vertical plane, so that planes end up unfolded over the same plane which is the paper.

 To obtain the representation of a point in the space over a plane, we need to trace the projection rects, perpendicular to the planes.  A point “A” in the space is represented in capital letter, and its projections are represented with small letters: “a2” is the vertical projection and “a1” is the horizontal projection.  The distance from the point to the vertical plane is called depth. The distance from the point to the horizontal plane is called height.  Height and depth correspond with another projection of the point on the auxiliary profile plane (PP), and it is represented as “a3”.

PV PH PV P P2P2 P2P2 P1P1 P1P1 depth height depth

 The projections or “views” of an object over the projection planes are called : Top view or plan: Projection on the horizontal plane. Front elevation or front view: Projection on the vertical plane. Profile or side view: Projection on the auxiliary plane (right and /or left).

ALZADO FRONT VIEWSIDE VIEW TOP VIEW

The profile or side view gives us additional information about the object. It may represent the right side view,which is shown on the left of the front view. Therefore, the left side view is represented on the right of the front view.

AXONOMETRIC SYSTEM It is a system of reprentation that uses parallel projections and the projecting rays are all parallel one another, perpendicular to the projection plane in some cases, and oblique in one particular case. It consist in three coordinate planes whose intersections forms three axes that arrange the three dimensions on the paper.

TYPES OF AXONOMETRY ISOMETRIC : Is a kind of orthographic axonometry whose axes form equal angles of 120º with each other DIMETRIC: Is a kind of orthographic axonometry whose axes form two equal angles and a different one. TRIMETRIC: Orthographic axonometry whose axes form three different sized angles CAVALIER SYSTEM: It is a type of oblique axonometric system which always shows a right angle between two of its axes.

The representation systems are reversible, that means, it is needed a projection of an object in a certain type of system, to obtain the projections in a particular systemof representation. We need the dihedrical views of a solid in order to obtain its axonometric projections. In that way, we need the axonometric or linear perspective projections of an object, to obatin its dihedrical views

CAVALIER PERSPECTIVE

CUBE AND CIRCUMFERENCE IN CAVALIER PERSPECTIVE

It uses a central projection, so the projection rays come all from a known focus, and the rays converge at that point. It is a system based on the perspective projection of an object on a projection plane. Its main feature are the vanishing lines, which are lines converging towards the vanishing points Linear perspective is the pictorial system which drawings are more likely to the human vision. The projection rays coming from one point is very similar to the eye´s visual rays.

Point of wiew (PV) :it represents the exact place whre the observr is located. Principal ray: perpendicular line from the point of view to the the picture plane. It determines the distance between the picture plane and the point of view. Picture plane: the plane where the projection or drawing appears through the intersection of the visual rays whit it. Principal point (PP) : it is the intersection of the principal ray with the picture plane. Ground plane : it is always perpendicular to the picture plane, and it is the plane where the objects are generally leaning. It represents the floor. The distance between the point of view to the ground plane represents the height of the viewer. Horizon plane : it is a plane parallel to the ground plane and where the point of view is located. Horizon line (HL) : it is the rect intersection of the picture plane with the horizon plane Ground line (GL): it is the rect intersection between the picture plane and the ground plane. Horizon line and ground line are always parallel to each other. Vanishing points : These are points on the horizon where vanishing lines converge towards. Vanishing lines : they are the projectiosn of the lines that intersect on the same vanishing point.

28 ONE POINT PERSPECTIVE: representation of an object whose one side is parallel to the projection plane. There is one single vanishing point. TWO POINT PERSPECTIVE: in this representation the object is set up oblique to the picture plane. It has two vanishing points. THREE POINT PERSPECTIVE: the object is set up oblique to the picture plane and the point of view needs to be shown in a much higher location than the ground plane. It has three vanishing points. Three- point

 It offers the front perspective of an object over a vertical plane placed between the object and the point of view.  The object has one side parallel to the projection.

 It offers the oblique perspective of an object over a vertical plane placed between the object and the point of view.  The object has not any side parallel to the projection plane.

TWO POINT PERSPECTIVE

VANISHING POINT

TWO VANISHING POINTS PF and PF’

The representation systems are reversible. In order to draw a linear perspective, we need the solid´s projections in any other system or representation. In this case, dihedrical projections are given to construct a two point perspective.

PV To find the Distance point´s location for a One Point Perspective, trace an arc with the distance from the Principal point PP to the Point of view PV. This arc cuts the horizon line at D and D’. Other than the vanishing points, we need two more points, called DISTANCE POINTS. These help us to find the correct lenght of the object sides belonging to depth.

To find the distance points on a Two Point Perspective, trace a 30º and 60º lines from PV to the horizon line, and they cross it at F and F’, distance points for this perspective.

“Rue a Pontoise” by Maurice Utrillo This landscape could also be described as a cityscape. The artist uses linear perspective in his painting, making the horizontal lines join together at the vanishing point.

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