GL2:1

Engineering Communications GL2

Geometric modellingProjection Systems

• Lecture presentations available on WWW:

http://www.mame.mu.oz.au/~mcg/EngCom

GL2:2

A graphic is a representationon 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.

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Meaning may be communicated better by deliberate distortion

GL2:4

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

GL2:5

Projection plane

3-D objectView point

Projection rays

2-D projection

Engineering graphics are obtained by projection from the 3-D object to the viewing surface (the projection plane)

Perspectiveprojection

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• Perspective projection is rarely used in manual drawing

Types ofprojection

• Rather, we us a variety of orthographic projections, for which the projection rays are parallel

GL2:7

Projection plane

3-D object

Viewpointat

In orthographic projection, the projection rays are parallel (view point at infinity)

Parallel projection rays

2-D projection

GL2:8Perspective projection is useful for ‘non technical’ communications

Perspective renderings for marketing, etc. are readily obtained with computer-aided drawing (CAD) systems

GL2:9

Ber

toli

ne, e

t al.

Fig

. 9.2

Projection techniques

Orthogonal (multiview) Axonometric

Oblique Perspective

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Parallel top ro jectio n p lane

Normal top ro jectio n p lane

Orthogonal

Inclined top ro jectio n p lane

Normal top ro jectio n p lane

Axonometric

Parallel top ro jectio n p lane

Inclined top ro jectio n p lane

Oblique

Orthographic pro jectio n( P aralle l p ro jecto rs )

Categories of orthographic projection

Principalplane ofobject

Projectors

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Top horizontal plane

Frontvertical plane

Left profile plane

Third-angle orthogonal projection

Top view

Front view

Leftsideview

Glass projection box

First quadrant

Third quadrant

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Third-angle orthogonal projection

vertical plane

horizontal plane

left profile plane

leftsideview

depth

horizontal plane

vertical plane

leftprofile

plane

depth behindvertical plane

height belowhorizontal plane

top (plan)

view

width

heightfrontview

depth depth behindvertical plane

GL2:13

DIMETRIC

A

CTRIMETRIC

Axonometric projection• Lines of sight perpendicular to projection

plane• Principal axes all inclined to projection

plane

A

C

B

Example:A=120º B=130º C=110ºx:y:z = 1 : 0.808 : 0.938

B

Example:A=C=131.5º B=97º x : y : z = 0.5 : 1 : 1

xyz

ISOMETRIC

A

C

B

Always:A = B = C = 120ºx : y : z = 1 : 1 : 1

xy

z

xyz

GL2:14

projection plane

Isometric projection

isometric projection

A = B = C = 120°

A B

C

= = 30°

X Y

Z

Scale ratios = (2/3) = 0.816X : Y : Z = 1 : 1 : 1

For an isometric drawing, scale = FS on each axis

0.816

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Scale = cot

Oblique projection

Full scale

Full scale

Principal object face parallel to projection plane

GL2:16

Cavalier

Cabinet

General

Varieties of oblique projection

GL2:17Isometric sketch

T-square

Set square

dep

thh

eig

ht

width

Top view

Front viewSide view

depth

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45º

60º

Full scale

Full scale

Full

scale

Full scale

Half s

cale

radius = 1

semi-major axis = (3/2)

semi-minor axis = (1/2)

Isometric

Oblique (Cabinet)

Projections of a cube compared ...

30º30º

GL2:19

Introduction to Cartesio software(download from EngCom homepage)

GL2:20

Follow up• Read 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