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Figure 4.28

In Fig. 4.29 the oblique plane ABC and the line l are given in both the horizontal and frontal
projections. A frontal-projecting plane Δ, coincidental with and containing the given line l, appears
as an edge in the frontal projection. The intersection of the given plane ABC and the frontal-
projecting cutting plane Δ containing l is the line 1 2. The lines l and 1 2 both lie in the frontal-
projecting cutting plane Δ and intersect each other at point K in the horizontal projection. Since
point K is on line l, it is also on plane ABC because line 1 2 is on plane ABC. Therefore point K is
the required point, being common to both the line l and the given plane ABC. It can now be
projected to the related projection. Use careful visualization to determine what portion of the line
should be visible in each projection.

Figure 4.29

If line 1 2 had appeared parallel to l in the horizontal projection, it would behave indicated
that the line l was parallel to plane ABC and therefore it would have no point of intersection with
the given plane.

4.10 DETERMINING THE VISIBILITY OF LINES ON THE PROJECTIONS

To determine which line of an apparent intersection of two lines is more distant to the
horizontal projection, project the exact crossover point of the lines to the adjoining frontal
projection.
In the adjoining frontal projection, determine which of the lines is more distant to the axis x.
This line is above of the other line in the horizontal projection and is visible in this projection.
To determine which line of an apparent intersection of two lines is more distant to the frontal
projection, project the exact crossover point of the lines to the adjoining horizontal projection.
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