Engineering Communications GL2 Geometric modelling Projection Systems Lecture presentations available on WWW: http://www.mame.mu.oz.au/~mcg/EngCom

A graphic is a representation on a 2-D surface of a 3-D scene An artist may attempt to create a ‘realistic’ image. Note the use of perspective. In fact, there are distortions in this picture, and it does not create the same projection on the retina as a real scene would.

Meaning may be communicated better by deliberate distortion

In engineering graphics: a variety of types of distorted images are available to communicate meaning strict rules apply to the construction and interpretation of these images a universal language of graphic communication is thus achieved

Perspective projection Projection plane 2-D projection View point 3-D object Projection rays Perspective projection Engineering graphics are obtained by projection from the 3-D object to the viewing surface (the projection plane)

Types of projection Perspective projection is rarely used in manual drawing Rather, we us a variety of orthographic projections, for which the projection rays are parallel

View point at  Projection plane 2-D projection Parallel projection rays 3-D object In orthographic projection, the projection rays are parallel (view point at infinity)

Perspective projection is useful for ‘non technical’ communications Perspective renderings for marketing, etc. are readily obtained with computer-aided drawing (CAD) systems

Projection techniques Bertoline, et al. Fig. 9.2 Projection techniques Orthogonal (multiview) Axonometric Oblique Perspective

Categories of orthographic projection Projectors Principal plane of object

Third-angle orthogonal projection Top view Top horizontal plane Glass projection box First quadrant Third quadrant Left side view Front vertical plane Front view Left profile plane

Third-angle orthogonal projection horizontal plane vertical plane left profile plane horizontal plane width depth depth behind vertical plane top (plan) view depth depth behind vertical plane height below horizontal plane height left side view front view left profile plane vertical plane

Axonometric projection Lines of sight perpendicular to projection plane Principal axes all inclined to projection plane TRIMETRIC DIMETRIC ISOMETRIC A C C A C B B B A y z x y z x y z x Example: A=120º B=130º C=110º x:y:z = 1 : 0.808 : 0.938 Example: A=C=131.5º B=97º x : y : z = 0.5 : 1 : 1 Always: A = B = C = 120º x : y : z = 1 : 1 : 1

Isometric projection X Y Z isometric projection A B projection plane  0.816  b C A = B = C = 120° a = b = 30° Scale ratios = (2/3) = 0.816 X : Y : Z = 1 : 1 : 1 For an isometric drawing, scale = FS on each axis

Oblique projection  Full scale Scale = cot Full scale Principal object face parallel to projection plane

Varieties of oblique projection Cavalier Cabinet General

Isometric sketch T-square Set square depth height width Top view Front view Side view T-square Set square

Projections of a cube compared ... Full scale Full scale Oblique (Cabinet) Half scale Isometric 45º Full scale 30º 60º Full scale radius = 1 semi-minor axis = (1/2) semi-major axis = (3/2)

Introduction to Cartesio software (download from EngCom homepage)

Follow up Read Bertoline: Do problems from Bertoline: § 4.5: Introduction to Projections § 8.1: Projection Theory § 8.2: Multiview Projection Planes § 8.3:Advantages of Multiview Drawings Do problems from Bertoline: Probs 4.2(6)(47), 4.3(2)(6) Check the EngCom web site