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Figure 3.13

Special case is a profile line. The general solution evidently fails; the solution demands profile
projection.
In general, a straight line is uniquely determined by its two traces. The only exception is the
case in which M and N fall together as a single point on the axis x. The required line can then be
any line which passes through this point; in order to determine the line, some other condition must
be given (e.g., another point).
Some special lines have no all traces.

3.6 TRUE-LENGTH OF LINE SEGMENT

In general, a projection of line segment is not equal to true-length of line segment. Segment
АВ is inclined to all planes of projection, therefore segment projections will be less him.
Let's consider a rectangular triangle ABB 1. A horizontal projection /A 1B 1/ it will be equal to
a leg of a triangle ABB 1.To define size of the second leg of a triangle we will look at a face-to-
face plane of projections. The projection to a face-to-face plane, /B xB 1/ is equal to full size of the
second leg of a triangle ABB 1. We will in addition be convinced of it when we will consider
private position of straight lines in space. Now running forward, pay your attention, that the leg of a
triangle ABB 1 is perpendicular a horizontal plane of projections and is parallel to a face-to-face
plane of projections. In general case full size of the second leg of a triangle is /B xB 21 - A xA 2/.
Thus, knowing two legs of a triangle of a rectangular triangle, we can find its hypotenuse.
Having the complex drawing of a straight line of the general position where any of projections of a
piece of this straight line is not equal to full size of a piece, we can find its full size.
The length of line segment AB may be determined from the right triangle ABB 1 in which one
cathetus is equal to the projection of this line segment AB on projection plane (in this case on П 1)
A 1B 1 and another cathetus is equal to difference of the distances from the projection plane to the
end points of line segment (Fig. 3.14). Angle (in this case α) in this triangle determines the slope
angle of the line segment AB to the projection plane (in this case on П 1).

Figure 3.14

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