6.5 DESCRIPTIVE GEOMETRY The Descriptive Geometry turns 3D into 2D so that we can draw volumes or spaces over a flat surface. This type of geometry is based in the concept of Projection.

PROJECTION The projection of a point is the resulting intersection point of a projective ray through the point with a projection plane, called picture plane. The intersection A’, is the image of point A on the plane.

ELEMENTS OF A PROJECTION   

Focus of projection: point of view where the projection lines called “projection rays” come from. (V) Picture or projection plane: Plane where an object is projected to obtain its flat repesentation. Projection ray : straight line whose origin is in the focus of projection. It goes through a point of the object and intersects with the projection plane. Rays are always projecting elements such as points, lines or objects over the projection plane.

PROJECTION PLANE

PROJECTION RAY

OBJECT FOCUS

PROJECTION

3

TYPES OF PROJECTIONS There are two types : • Parallel Projection: whose rays come from the infinite or an unknown focus and they are all parallel. This projection is classified in Orthographic and Oblique parallel projection depending on which angle side the rays intersect the picture plane. • Central or Perspective Projection: whose projecting rays come all from one point or focus.

ORTHOGRAPHIC PROJECTION

OBLIQUE PROJECTION

CCENTRAL PROJECTION

PARALLEL PROJECTION  The focus of projection is unknown, that is, it is located in

the infinite, so the projection rays are all parallel.  The image or the projection has the same measurement as the object itself in the space. Parallel projections can be:

ORTHOGHAPHIC

OBLIQUE

ORTHOGRAPHIC PROJECTION  The projection rays fall perpedicularly upon the projection

plane, forming a 90º angle with the plane.

OBLIQUE PROJECTION The projection rays fall obliquely upon the projection plane, forming an angle with the plane different to 90º.

CENTRAL OR PERSPECTIVE PROJECTION  The focus of projection is known, that is, it is located somewhere in

the space, so the projection rays converge all at that point, called “point of view”.  The image or projection has never the same measurement as the object itself in the space.It depends on the distances between the focus, object and the projection plane.