Graded point
SŠ7 minOne view and a number beside it – the third dimension is written, not drawn.
Graded points
The height IS the third dimension. It is not drawn – it is written beside the point.
The line AB
- Plan length d
- 6.04
- Rise Δh
- 3.00
- Interval i
- 2.01
- Slope s
- 0.50
- Slope in %
- 49.7%
- Slope angle
- 26.41°
- True length
- 6.75
Interval and slope are reciprocals. A bigger interval means a GENTLER line, not a steeper one.
The plane ABC
- Plane interval
- 1.79
- Slope
- 0.56
- Slope angle
- 29.14°
A plane’s contours are parallel and evenly spaced – their spacing IS the plane’s interval. Raise one point’s height and watch them close up.
Show
Spatial view
Theory
Elevation projection has a single image plane – the horizontal π₁. A point is projected onto it and its height is simply written next to the view as a number, the kóta. Hence the notation A(3): at the position A₁ there is a point 3 units above the image plane.
This is not a simplification but a complete description: the pair (plan position, height) fixes a point in space just as uniquely as a pair of views does in Monge projection. The third dimension is carried by a number instead of a second picture.
That is why it is the projection of maps, terrain and earthworks. A contour map IS an elevation drawing: each line is the set of points sharing one height. A negative height means a point below the image plane – the floor of an excavation, say.
Step-by-step construction
Practice
Build the construction yourself
What is the next step?
1 / 5Choose the step that comes next. The drawing only advances on a correct choice.
Check your understanding
How many image planes does elevation projection use?
What does the notation A(3) mean?
What does a negative height mean?
Downloadable material
A PDF for this lesson is in preparation.
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