Descriptive geometry

The descriptive geometry is before a a whole method to solve in a graphic way on paper of the problems of intersections and shades between definite volumes and surfaces in a geometrical way in space with three dimensions.

These problems are for a share those which were posed in the trades of the size of the stones and of the frame (example of the staircases Débillardé S, etc). The descriptive geometry was theorized by Gaspard Monge but the methods of projection were former for him.

It thus consists in representing one or more objects of space with 3 dimensions in a minimum of orthogonal projections to raise ambiguity and to preserve of it, for the problem arising, the maximum of useful properties (conservation of Angle S and Length S).

The choice of the plans of projection is thus function of the problem arising and two plans can be enough. A certain number of conventions are necessary to make readable a layout of geometry descriptive:

• the frontal projection which is an orthogonal projection of a front view, is in top of the sheet.
• the flat projection of the sight of top on the horizontal level is in bottom of the sheet.
• two projections are separated by the line from ground , an horizontal line representing the intersection of the two plans of projection in space.
• the points of two projections are paired by lines of recall illustrated by fine features (or reds).
• the objects are regarded as opaque solids. The edges seen are in continuous black feature and the hidden edges are into dotted.

The “drawing géométral” that draftsmanship is the well-known is implementation a direct of the descriptive geometry with close but a little different conventions.

Representation of an intersection between two volumes

The intersection of two volumes (for example an emerging drilling surfaces some or two welded parts) often follows a “complex” curve. The drawing of this curve requires to locate the points on two projections: the point belongs to two volumes, one of the sights will give its dimension, the other sight its distance. The construction of this curve, will be made " point by point " , with the method of the auxiliary plan.

External bond

• Course of descriptive geometry of the School of architecture of Nancy

• A. Javary, Treated descriptive geometry , 1881 (on Gallica):
• Cones and cylinders, sphere and surfaces of the second degree
• the straight line, the plan, the polyhedrons