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The line in the dihedral system
A line is defined in dihedral by its two projections. Its traces are the points where it crosses the projection planes: the horizontal trace H, where it cuts the horizontal plane, and the vertical trace V, where it cuts the vertical one. Those two traces determine the line, and almost every exercise in this block starts from them.
What you need to know
- Draw a line through two given points and name its projections r′ and r″.
- Find the traces H and V and place them correctly: on the ground line, with the other projection on it.
- Tell apart horizontal, frontal, profile, ground-line-parallel lines and lines through it.
- Recognise which quadrants a line crosses from where its traces fall.
How it is solved
- Project both points: each with its height (elevation) and its distance (plan).
- Join the matching projections: r′ with r′ and r″ with r″.
- Where a projection crosses the ground line is the trace of that plane; carry it up or down to the other projection.
- Check the result: the horizontal trace has height 0 and the vertical one, distance 0.
How it appears in the exam
It usually appears as the starting point of another exercise: “given line r defined by points A and B…”. If the line is a profile line, the usual two projections are not enough: the points must be taken to the third projection to fix it.
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