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Elevation laws and the composition of a planar curve with one.
A road or rail centreline is authored as two independent laws: a planar
layout carrying the transition spirals, and a vertical profile giving
height as a function of distance along that layout. The 3D centreline is
their composition. This module holds the vertical half and the pairing;
the planar half is an ordinary Curve2.
§Height is a function of PLAN distance, not 3D arc length
The vertical profile a surveyor writes is indexed by chainage measured on
the horizontal layout, so height_at takes plan distance. The two differ
whenever the grade is non-zero, because ds3 = sqrt(1 + g^2) ds_plan.
Over a 120 m curve at a 2% entry grade the 3D length exceeds the plan
length by 12.5 mm, which reads the profile 0.35 mm off if the distances
are confused. That is small but it is a systematic misreading, not noise,
and it compounds along a chain of segments.
Naming the convention here means a consumer never has to guess which distance a law is written in.
Structs§
- Elevated3
- A planar curve carrying an independent elevation law.
Enums§
- Elevation
Law - Height as a function of distance along the plan.