Projections

People have drawn objects for thousands of years, for beauty and for use. A drawing records information about a thing, shares it with others, and helps you think about it. That is why engineers rely on drawings for buildings and machines. An engineering drawing must be detailed enough for someone to build the object from it.

A net is one way to put a solid on paper, but it is hard to picture the solid from a net without cutting and folding it.

The other way is projection. Take a point P in space and a flat surface (a plane) M. Drop a line from P that meets the plane at O. If OP is perpendicular to the plane, meaning ∠POX = 90° for any line OX drawn on the plane, then O is the projection of P.

Do this for every point of an object, and all those points together make the projection of the object. Think of the cartoon hole again: if the object went straight (perpendicularly) through the plane, the hole it left would be its projection.

But one projection is not enough, because it does not tell you which object made it. Very different lines can give the same projection, and so can very different cuboids. Whatever lay in the direction you were not looking from is lost.

So engineers use three projections, onto three planes at right angles to each other: the vertical plane in front of the object, the horizontal plane below it, and the side plane next to it.

The projection on the vertical plane is the front view. On the horizontal plane it is the top view. On the side plane it is the side view. These are the 'profiles' you imagined earlier in the chapter, made exact.

With all three views most of the guesswork disappears. With practice you can picture the solid straight from the three drawings, which is exactly what a workshop has to do.