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Descriptive geometry: the dihedral system explained

The concepts you need for Technical Drawing and engineering graphics, from projections to true lengths, with a 3D editor to see every construction from both sides.

1. What the dihedral system is

Descriptive geometry turns a three-dimensional object into flat drawings that can be measured. The dihedral system uses two perpendicular planes: the horizontal plane (PH) and the vertical plane (PV). Their intersection is the ground line (LT). Every point becomes two projections: the plan (below the ground line) and the elevation (above it).

2. A point: three numbers, two projections

A point is fixed by x along the ground line, y (offset from the vertical plane) and z (height above the horizontal plane). The plan is drawn at (x, y) and the elevation at (x, z), always on the same vertical line.

3. Lines and their traces

A line is drawn by joining the projections of two of its points. Its horizontal trace H is where it meets the horizontal plane; the vertical trace V is where it meets the vertical plane. A line parallel to one plane has only one trace.

4. Planes and their traces

A plane is normally given by its two traces, α1 and α2, which meet on the ground line. It can also be defined by three points, a point and a line, or two parallel lines.

5. True length: rotations and changes of plane

A segment is only seen in true length when it is parallel to the projection plane. Rotating a plane down onto the horizontal plane, or adding a new projection plane parallel to the element, shows true lengths and angles without distortion.

6. Intersections, distances and angles

To cut a line with a plane, contain the line in an auxiliary projecting plane and use the intersection line. Distances and angles are measured in true magnitude, never on a projection that is not in true length.

Practise it

Diédrico Studio draws the 3D model and its two projections at the same time: rotate the model, move a point and watch both views change with it.

Open the editorSolved exercises