Triangulation, trilateration, graphical intersection

Triangulation is a method of horizontal control survey in which control stations are fixed at the vertices of a chain or net of triangles. One side (the base line) is measured very accurately, all the angles of the triangles are measured, and the lengths of the other sides are computed with the sine rule.

Trilateration is the method in which the lengths of all the sides of the triangles are measured directly with an EDM (electromagnetic distance measuring) instrument, and the angles are computed from the sides using the cosine rule.

Graphical intersection in plane tabling

Graphical intersection is the plane table method in which a point is located by drawing rays to it from two plotted stations at the ends of a base line, and marking the point at the intersection of the rays. No distance to the point needs to be measured.

1. Set the table at A, level it, centre and orient it; plot a and the base line ab to scale.
2. Sight the point P from a and draw the ray.
3. Shift to B, orient the table by back-sighting along ba, sight P and draw the ray from b.
4. The two rays meet at p, the plotted position of P. A third ray from another station checks it.

            p
          / |  \
        /   |    \
      a ---------- b

Graphical intersection is the same idea as triangulation (the point is fixed by two angles from a known base), done graphically instead of by computation.