geoprimsField-grade geospatial math

Slope stake (catch point)

Where a road template's cut or fill slope meets existing ground on one side, its offset and the cut or fill to the shoulder, found by iteration and written in stake notation.

Experimental: not yet fully verified. How results are checked

25ft

Set the stake at 25 ft from the centerline: C 4.5 / 25.0 R.

Cut or fill
Cut or fill
Stake notation
Ground elevation at the catch point
Provenance
Computed by
survey.earthwork.slope-stake 1.0.0, core 0.1.0
Model
Design line from the shoulder: grade + (x − w)/s_cut in cut, grade − (x − w)/s_fill in fill; ground linear between the points given; the catch point solves ground(x) = design(x) by Brent's method to 1e-6 of the unit (Ghilani & Wolf 2021, ch. 26)
Accuracy
The iteration converges far inside 0.01 of the unit; the answer is as good as the ground points and the template
Notes
1 shown with the answer
Cites
Ghilani, C. D., and Wolf, P. R., Pearson, Elementary Surveying: An Introduction to Geomatics

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How we got thisFormula, worked example, sources, and proof

Model: Design line from the shoulder: grade + (x − w)/s_cut in cut, grade − (x − w)/s_fill in fill; ground linear between the points given; the catch point solves ground(x) = design(x) by Brent's method to 1e-6 of the unit (Ghilani & Wolf 2021, ch. 26)

Accuracy: The iteration converges far inside 0.01 of the unit; the answer is as good as the ground points and the template

Worked example: A cut on ground rising 10% to the right. Source: add-survey-suite catch-point scenario on planar ground. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Cut slope
2
Fill slope
3
Grade elevation
100 ft
Existing ground
0 ft, 102 ft 60 ft, 108 ft
Half width
16 ft
Side
right

You get

Catch point offset
25 ft
Cut or fill
4.5 ft
Cut or fill
cut
Stake notation
C 4.5 / 25.0 R
Ground elevation at the catch point
104.5 ft

Review: Not yet independently reviewed by a licensed surveyor.

Last verified: 2026-09-23, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.0, core 0.1.0. See this tool in the verification report.

Changes

Checked against: 6 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.