1. University of Warith AL-Anbiya’a
College of Engineering
Air-condition & Refrigeration Department
Desprictive geometry I
First stage
Asst.Lec. Aalaa Mohammed AL-Husseini

2. Traces of Straight line
Intersections of straight line with main projection levels
Horizontal traces of the straight line:
It’s known by the symbol (F) which is represent the intersection point of the straight line with the horizontal plane of projection, so it’s coincide on it’s horizontal projection (F) which mean that the horizontal projection of the horizontal traces (F) always coincide on the horizontal traces (F) of the straight line.
The face projection of the horizontal traces (F) located on the earth line because (F) a point located on the horizontal plane and it’s one point of the straight line points.
The conclusion that (F) is a point from the face projection points

3. How to draw the Horizontal traces of the straight line:
Stretch the face projection of the straight line until intersect the earth line with a point represent (F)
From (F) draw a column up and down which cut the horizontal projection of the straight line at a point (F) which at the same time represents the horizontal traces of the straight line (F)
2. Face traces of the straight line:
It’s known by the symbol (W) which is represent the intersection point of the straight line with the face plane of projection.
The horizontal projection of the face traces (W) located on the earth line .

4. How to draw the face traces of the straight line:
Stretch the horizontal projection of the straight line until intersect the earth line with a point represent (W)
From (W) draw a column up and down which cut the face projection of the straight line at a point (W) which at the same time represents the face traces of the straight line (W).
3. Side traces of the straight line:
It’s known by the symbol (G) which is represent the intersection point of the straight line with the side plane of projection.
The face projection of the side traces (G) located on the vertical folding line .

5. How to draw the side traces of the straight line:
Stretch the face projection of the straight line until intersect the vertical folding line with a point represent (G)
From (G) draw a beam parallel to the earth line which cut the side projection of the straight line at a point (G) which at the same time represents the side traces of the straight line (G).

6. The Real Length of the straight line and it’s slope angles on the main planes of projection
When we study the special cases of the straight line, we easily found the real length of the straight line and it’s slope angles but we don’t touch on the way to find the real length for the straight line in general position. There are many methods to find the real length and the slope angle of the straight line, we will study the following method:
The existence of true length and slope angles by coincidence method

7. The existence of true length and slope angles by coincidence method
The angle of the straight line with it’s horizontal projection can be assumed as (Z1) and the angle of the same line with it’s face projection can be assumed as (Z2), the third angle of the straight line (Z3) with the side projection of the straight line.
Now, we study the method to find the real length of the straight line and it’s slope angles:
The method to find the real length of the straight line and it’s slope angle on the horizontal plane of projection:
Draw the projection of the straight line.
Draw two column on the horizontal projection of the straight line, one from A and the other from B.

8. c. We measure on the column drawn from A dimension equal to a distance of (A) from the horizontal plane of the projection, we get point A after coincide to the horizontal plane , and measure from (B) on the column drawn from it a dimension equal to a distance of (B) from the horizontal plane of the projection, we get point B after coincide to the horizontal plane. Connect between them
d. Measure AB which be the real length and measure the angle between AB and the projection AB which is the angle (Z1).

9. 2. The method to find the real length of the straight line and it’s slope angle on the face plane of projection:
Draw two column on the face projection of the straight line, one from A and the other from B.
b. We measure on the column drawn from A dimension equal to a distance of (A) from the face plane of the projection, we get point A after coincide to the face plane , and measure from (B) on the column drawn from it a dimension equal to a distance of (B) from the face plane of the projection, we get point B after coincide to the face plane. connect between them.
c. Measure AB which be the real length and measure the angle between AB and the projection AB which is the angle (Z2).

10. 3. The method to find the real length of the straight line and it’s slope angle on the side plane of projection:
Draw two column on the side projection of the straight line, one from A and the other from B.
b. We measure on the column drawn from A dimension equal to a distance of (A) from the side plane of the projection, we get point A after coincide to the face plane , and measure from (B) on the column drawn from it a dimension equal to a distance of (B) from the side plane of the projection, we get point B after coincide to the side plane. connect between them.
c. Measure AB which be the real length and measure the angle between AB and the projection AB which is the angle (Z3).

11. Example: find the real length of the straight line AB where A (3,4,5) B (1,6,4) and it’s slope angles on the three planes of projection.

12. Example2: A,B two points in the first angle location
Example2: A,B two points in the first angle location. AB face straight line with (7cm) length and located (4cm) from the face plane of projection. It’s known that point A located (6cm) from the side plane and (3cm) from the horizontal plane. While point B located (6cm) from the side plane.
Represent the straight line AB , measure the slope angles on the planes of projection and find the coordinates of it’s horizontal traces F

13. Thank you For Your Attention