Descriptive Geometry :Line's projection
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Transcript of Descriptive Geometry :Line's projection
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