CHAPTER 2

PROJECTION OF LINES

1. A straight line’s projection is still a straight line

2. How to construct a line

3. The traces line

4. Line’s position corresponding to projection planes

1. Projection of a straight line is still a line, but in special cases, it shows a point view

2. How to construct a line:

Two given points → construct a line

A point on a line

Principles:

1. If a point is known to be on a line, the projections of the point will appear on all the views

of the line;

2. The proportion which a point divides a line keeps the same after projection

If a point M belong to a line, then the point projection are situated on the same name

projections of a line: dmdmDM ;; .

3. The traces line

The traces line means the points where line is intersected with the projection plans.

The point where line intersect the horizontal projection plan call horizontal trace. Is

denoted by H. H is a point on horizontal plane, so will coincide with the horizontal

projection, h. The vertical projection hI is situated on OX axis and the profile projection , hII

is situated on OY axis.

The point where line intersect the vertical projection plan call vertical trace. Is

denoted by V. V is a point on vertical plane, so will coincide with the vertical projection, vI.

The horizontal projection v is situated on OX axis and the profile projection , vII is situated

on OZ axis.

The point where line intersects the profile projection plan call profile trace. Is denoted

by W. W is a point on profile plane, so will coincide with the profile projection, wII.

To represent the vertical trace in plan we’ll proceed as follow:

- dI is intersect with OX axis and the result is hI

- from hI point we’ll draw the perpendicular line on OX axis until when this will

intersect the horizontal line projection in h point which represent the horizontal trace

of line.

To represent the horizontal trace in plan proceed as follow

- d is intersect with OX axis and the result is v point

- from v point we’ll draw the perpendicular line on OX axis until when this will intersect

the vertical projection line in vI point which represent the vertical trace of line.

To represent the profile trace in plan proceed as follow:

- dI is intersect with OZ axis and the result is wI point

- from wI point we’ll draw the parallel line with OX axis until when this will intersect the

profile projection line in wII point which represent the profile trace of line.

4. Line’s position corresponding to projection planes

Lines-located at special position

1. Inclined lines: parallel with one of the principal planes of projection, and inclined to the

other two projection planes.

a. Horizontal lines

b. Profile line

c. Frontal lines

2. Principal lines/normal lines: perpendicular to one of the principal plane of

projection

a. Horizontal principal line/H-normal line

b. Profile principal line/W(P) -normal line

c. Frontal principal line/V-normal line

3. Lines affiliate to projection plans or projection axes

1. Inclined lines: parallel with one of the principal planes of projection, and inclined to

the other two projection plans.

a. Horizontal line

The horizontal line is the line which is parallel with horizontal plan of projection. All points

located on this line have the same Z.

The characteristics of this line are ：

b. Frontal line

The frontal line is the line which is parallel with vertical plan of projection. All points located

on this line have the same Y, so ab OX.

The characteristics of this line are:

c. Profile line

The profile line is the line which is parallel with the profile plan of projection. All points

located on this line have the same X. The projections d and d’ are perpendicular in the

same point on the OX axis.

The characteristics of this line are

Table 1. The lines parallel with one of the principal planes of projection

2. Principal lines/normal lines: perpendicular to one of the principal plane of

3. projection

2. Principal lines/normal lines: perpendicular to one of the principal plane of

projection

Horizontal principal line

H-normal line

H-normal line is the line which is perpendicular on the horizontal plan of projection

The characteristics of this line are

Frontal principal line

V-normal line

V-normal line is the line which is perpendicular on the vertical plan of projection.

The characteristics of this line are

W/P-normal line

W/P-normal line is the line which is perpendicular on the profile plan of projection.

Characteristics:

Table 2. The lines perpendicular to one of the principal plane of projection

3. Lines affiliate to projection planes or projection axes

Lines in planes of projection

lines in [V]

Lines affiliate to planes of projection

horizontal principal lines in V (N- normal lines in V)

Lines on projection axes

line on OX

Oblique line

Characteristics：

All projections are foreshortened

All projections are inclined to projection axes

True angles a, β, γ can’t be obtained directly