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Figure 7.18

The line of intersection of two surfaces is found by determining a number of points common
to both surfaces and drawing a line or lines through these points in correct order. This direction is
the same for all projections bodies. All critical points of intersection must be founded. The
resulting line of intersection may be straight, curved, or straight and curved. The problem of finding
such a line may be solved by one of two general methods, depending on the type of surfaces
involved. For the purpose of simplifying this discussion of intersections, it should be assumed that
all problems are divided into these two general groups:
- Problems involving two geometric figures, both of which are composed of plane surfaces.
- Problems involving geometric figures which have either single-curved or double-curved
surfaces.
Any practical problem resolves itself into some combination of the geometrical type forms.

7.4 INTERSECTION OF SOLIDS BOUNDED BY PLANE SURFACES
(POLYHEDRONS)

For instance, the procedure for finding the line of intersection of two prisms is the same as
that for finding the line of intersection of a prism and a pyramid; hence, both problems belong in the
same group.
Interpenetration of polyhedrons is polygonal closed line or lines.
Problems of the group are solved by locating the points through which the edges of each of
two geometric shapes pierce the other. These points are vertices of the line of intersection (Fig.
7.19).
There is intersection of two prisms in Figure 7.20. Whenever one of two intersecting plane
surfaces appears as a line in one view, the points through which the lines of the other surfaces
penetrate it usually may be found by inspecting that view.

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