# Diédrico System: Third straight projection

The main projections of the line on the dihedral plans (horizontal and vertical planes) possible to determine other new planes orthogonal projections on.

We'll see how generically determine a new projection from two. Later we will consider your application to study the so-called “auxiliary projections”, influencing their usefulness in solving various problems.

In particular, the so-called most often used “third projection” which is carried out on a plane orthogonal to the preceding plane profile called. The three planes ( Horizontal, H, Vertical, V.. and Profile, P) determine a trirectangular trihedral, in which are the three coordinates (x,and,z) allowing spatial information to restore it represented (projected).

Projecting onto a plane, the only coordinate that has not projected in this projection is perpendicular to this plane.

If we project onto the horizontal plane (XY) the Z coordinate of the Temperature on the vertical projection, but also on the profile corresponding to the plane.

We see that two orthogonal planes share a coordinate that can be used to obtain the new projection.

Given two planes orthogonal projections : How can we get the third projection?

To start we get the representation that we will set the first point, P to Q, in the third projection. The other point we will fix it by the dimensions to be maintained on.

We have seen that the projections are linked by reference lines. The new projections, P”’ and Q”’ the line, third projection, will be found in the corresponding reference lines, therefore remain the same “z” or from the horizontal dimension.

A embroidery, the value of “remoteness”, coordinate “and“, from the vertical plane, V.., is maintained in the third projection, thereby allowing the identification of points searched.

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