Have You Ever Seen

This House Plan Before ?

• Plan

• Elevation

• Orthogonal Projection

CHAPTER 10

10. 1 ORTHOGONAL PROJECTION

A. Identify orthogonal projections

The orthogonal projection of an object onto a plane is the image formed

on the plane by normals from the object to the plane

A. Identify orthogonal projections

In the diagram 1, theoutline of the cuboid as seen from above isprojected onto the horizontal plane. Thus, the rectangle ABCD is the orthogonal projection of the cuboid onto the horizontal plane.

DIAGRAM 1

A

B C

D

Object

Horizontal plane

Orthogonalprojection

B. Drawing Orthogonal Projections

Step 1 : From the corners of the object, draw normals to the plane given

Step 2 : Join up the feet of the normals on the planeto get the orthogonalprojection of the object

Object

Horizontal plane

Orthogonalprojection

EXAMPLE Orthogonal projection of the object onto vertical plane

Vertical plane

DC

E F

A B

DC

X

EXAMPLE Orthogonal projection of the object onto vertical plane as viewed from x

E F

A B

EXAMPLE Orthogonal projection of the object ontothe horizontal plane

Horizontal plane

EXAMPLE Orthogonal projection of the object onto the horizontal plane

Horizontalplane

C Determining the difference between an object and its orthogonal projection

A B

D C

P Q

RS

A/P B/Q

D/S C/R

The edges of an object and theirorthogonal projections onto a planeare equal if the edges of the object are parallel to that plane.

The edge, AB of the object is equal to the edge of the orthogonal projection of AB and, so on, since the edges, AB, BC, an AD are parallel to the horizontal plane.

C Determining the difference between an object and its orthogonal projection

A B

D C

P Q

RS

A/P B/Q

D/S C/R

When viewed from above, the corner, P, is beneath the corner, A. Thus , the orthogonalprojection of this corner is labelled as A/P. For similar reasons, the orthogonal projection of corner Bis labelled as B/Q and so on.

DC

E F

A B

D C

X

A/E B/F

C Determining the difference between an object and its orthogonal projection

Edge AD of the object and theorthogonal projection of AD ontoa plane are different in length,since edge AD is not parallel to the vertical plane.

Edge DE of the object and theorthogonal projection of DE ontoa plane are equal in length,since edge DE is parallel to the vertical plane.

ADrawing the plan of a solid object

The orthogonal projection of an object onto the horizontal plane is

calleda plan

In drawing the plan of a solid object, the followinglines are used:

solid lines are used to show the visible edges of the object

dashed lines are used to show the hidden edges of the object

thin light lines, called projection lines, are used to connect the plan and the elevations

EXAMPLE PLAN

EXAMPLE PLAN

EXAMPLE PLAN

EXAMPLE PLAN

EXAMPLE PLAN

EXAMPLE PLAN

B Drawing the front and side elevations of a solid object

The orthogonal projection of an object onto a the vertical plane is called an elevation. The orthogonal projection of an object, as seen from the front, onto the vertical plane, is called the front elevation whereas, the orthogonal projectionof an object, as seen from the side, onto the vertical planeis called the side elevation.

In drawing the elevation of a solid object, the following lines are used:

solid lines are used to show the visible edges of the object

dashed lines are used to show the hidden edges of the object

thin light lines, called projection lines, are used to connect the plan and the elevations

EXAMPLE ELEVATION

EXAMPLE ELEVATION

X

Y

EXAMPLE ELEVATION

X

EXAMPLE ELEVATION

EXAMPLE ELEVATION

Y

EXAMPLE ELEVATION

EXAMPLE ELEVATION

EXAMPLE ELEVATION

EXAMPLE ELEVATION

EXAMPLE ELEVATION

EXAMPLE ELEVATION

(a) Plan M L

E/F

H/G

Q/P

K/J

L/R

E

F

N

K

J

R

Q

H

G

PM/N

(a) Plan

E

F

M

N

L

K

J

R

Q

H

G

P

(a) Plan

E

F

M

N

L

K

J

R

Q

H

G

P

(a) Plan

C

(b) Elevation viewed from C

(b) Elevation viewed from C

C

(b) Elevation viewed from C

(d) Elevation viewed from D

D

(d) Elevation viewed from D

D

(d) Elevation viewed from D

FG

HE

DI

J

K B

C

AL

2 cm

4 cm

4 cm

4 cm

8 cm

5 cm

PLAN

FG

HE

DI

J

K B

C

AL

2 cm

4 cm

4 cm

4 cm

8 cm

5 cm

PLAN

FG

HE

DI

J

K B

C

AL

2 cm

4 cm

4 cm

4 cm

8 cm

5 cm

PLAN

K/L B/A

H/G E/F

J/I C/D

M

FG

HE

DI

J

KB

C

AL

2 cm

4 cm

4 cm

X

Q N

4 cm

5 cm

4 cm

6 cm

ELEVATION-VIEWED FROM X

J/K C/B

P

N

G/L F/A M

P/Q

H/I E/D

Y

M

FG

HE

DI

J

KB

C

AL

2 cm

4 cm

4 cm

Q N

4 cm

5 cm

4 cm

6 cm

ELEVATION-VIEWED FROM Y

PLAN

G

ELEVATION-VIEWED FROM G

H

ORTHOGRAPHIC PROJECTION

RQP

N

M

N

Step 1: Relocate the width and depth measurements of the entire

object. Draw surfaces M and N

Step 2: Project the top view of the object onto the front view.

Relocate the height measurement on the entire object. Then, draw

surfaces P and R

Step 3: Project the top and front views on the object onto the right

side view. Draw the height and depth of the entire object. Draw

surfaces N and Q

Solid With Inclined Surfaces

Example 1

THIRD ANGLE PROJECTION

Top view

Left side view Front view

The three views when an object is projected onto the vertical, horizontal and additional vertical planes at third angle projections.

Example 2

Top view

Left side view Front view

STEP 1

Construct projection line from top view to left side view.

STEP 2

Construct projection line from front view to left side view.

STEP 3

Draw the left side view.

Example 3

Question:

Construct a left side view of the object shown above.