Projections of a line

8 min

The projection of a line is again a line – two projected points suffice.

Not Started
3D – space
x₁₂π₁π₂ABaA₂B₂a₂A₁B₁a₁
Monge drawing
x₁₂π₂π₁A₂B₂a₂A₁B₁a₁

Orbit the space

Hover a₁ or a₂ – the line highlights in space and in the drawing at once.
2

Theory

The projection of a line is again a line. That single fact is why descriptive geometry is tractable at all: you never project infinitely many points, two are enough.

So the procedure is always the same – pick two points on the line, project them into both image planes and join them in each. You get the front view a₂ and the top view a₁.

Mind what actually determines the line: one view is not enough. A whole projecting plane full of lines shares that one view; only the pair a₁, a₂ picks yours.

3

Step-by-step construction

3D – what happens in space
x₁₂π₁π₂
Drawing – what you draw
x₁₂π₂π₁
1 / 5
4

Practice

Build the construction yourself

3D – what you have
x₁₂π₁π₂
Your drawing
x₁₂π₂π₁

What is the next step?

1 / 4

Choose the step that comes next. The drawing only advances on a correct choice.

Check your understanding

1

What is the projection of a line (in general position)?

2

How many of a line’s points must you project to construct its view?

3

Why is a single view not enough to determine a line in space?

5

Downloadable material

A PDF for this lesson is in preparation.

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