Diédrico: Obtención de la proy vertical de una figura conociendo su proy horizontal y el plano

DIHEDRAL SYSTEM: OBTAINING THE VERTICAL PROJECTION OF A FIGURE KNOWING ITS HORIZONTAL PROJECTION AND THE PLANE TO WHICH IT BELONGS For a figure to belong to a plane, its vertices must lie on that plane. In other words, we must obtain the vertical projections of the figure's vertices so that they lie on the plane. The property of a point belonging to a plane is not straightforward. Recall that for a point to belong to a plane, the point must lie on a line that, in turn, lies on the plane. To do this, we draw lines whose horizontal projections pass through the horizontal projections of the points and which lie on the plane. That is, the traces of these lines must lie on the traces of the plane. The simplest method is by drawing frontal or horizontal lines of the plane, but it can also be done using the figure's own edges. From point A1, we draw a line parallel to the ground line until it intersects P1, the horizontal trace of the plane. This point will be the horizontal trace of the frontal line. We obtain the vertical projection of this horizontal trace (which will lie on the ground line). From this vertical projection, we draw a line parallel to the vertical trace of the plane, obtaining the vertical projection of the frontal line that contains point A and is included in point P. From point A1, we draw a perpendicular to the ground line until it intersects the vertical projection of the frontal line, obtaining points A2. To obtain points B2 and C2, we connect B1 and C1, determining on the ground line the horizontal projection of the vertical trace of line B-C and at P1 the horizontal trace of line BC. From these points, we draw perpendiculars to the ground line, obtaining at P2 the vertical trace of line BC and on the ground line itself the vertical projection of the horizontal trace. Connecting these two points gives us the vertical projection of line BC. From B1 and C1, we draw perpendiculars to the ground line until they intersect the vertical projection of BC2, where we obtain B2 and C2. By joining A2, B2, and C2 together, we obtain the required vertical projection of the figure.