WEBVTT

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One point, two chainages. One straight 1,000 m reference; opposite origins.

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MATHEMATICS · define the relationship and the meaning of each symbol before calculating.

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L = 1,000 m reference length; sf = forward coordinate; sr = reverse coordinate. The slope −1 means each metre forward removes one metre from reverse chainage.

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INPUT · forward coordinate · read the axis units and the numerical values.

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One straight 1,000 m reference; opposite origins.

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OUTPUT · transformed coordinate · read the axis units and the numerical values.

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At sf = 250 m, sr = 750 m. The physical point is unchanged; its coordinate depends on the selected origin.

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CALCULATION · substitute the defined inputs; keep units through each intermediate step.

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Forward reference: sf = 250; L = 1000 metres

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Reverse transform: sr = L − sf = 1000 − 250 = 750 metres

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Round trip: 1000 − 750 = 250 metres

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Misread coordinate: 750 − 250 = 500 metres apparent displacement

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SENSITIVITY · change one declared input · read the axis units and the numerical values.

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L = 995 m: 745 m reverse coordinate. Keep forward coordinate 250 m; shorten the reference length.

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L = 1000 m: 750 m reverse coordinate. Reference coordinate transformation.

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L = 1005 m: 755 m reverse coordinate. Keep forward coordinate 250 m; length grows by 5 m.

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Check: Apply the transform twice and recover the starting coordinate. Verify endpoints 0 and L, transformed interval length, and a located control point away from the midpoint, where an origin reversal can otherwise be missed.

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ONE ROW · Two clean-looking spreadsheets can put the same pothole a hundred metres apart.

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PARAMETER MAP · 12261 evaluated cells. The colour limits stay fixed across every row.

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The central row uses the same 60 km alignment with opposite origins. Rows above and below introduce a declared origin offset δ. Every point moves by the same amount: a constant

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registration error survives even when all reported chainages have three decimal places. The sloping plane is a coordinate transformation, not terrain.

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VALUE LANDSCAPE · Height and colour encode Reverse chainage (km). This is a graph over the two input axes, not automatically a physical pavement shape.

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This affine example assumes the same route geometry and distance basis. Curved alignment revisions, wheelpaths, carriageways and survey dates need explicit identifiers; a subtraction does not reconcile them.

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Match the reference origin and direction before joining observations.