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Questioned Document Baseline Slope Term Tool

Two-point baseline slope with radians measured in the supplied image-axis orientation, without handwriting attribution.

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Description

Return Δy/Δx as slope and atan2(Δy,Δx) as directed angle in radians.

Forensic measurement calculations require a known calibration, geometric model and uncertainty convention. A converted length, ratio or residual describes the supplied measurements; it does not establish common origin, identity or evidentiary strength.

Return Δy/Δx as slope and atan2(Δy,Δx) as directed angle in radians.

When to use this tool

Use Questioned Document Baseline Slope Term when you need an explicit image or physical-measurement term.

How to use the tool and how it works

  1. Enter firstX, firstY, secondX, secondY. Use the units and conventions below.
  2. Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
  3. Read slope, angleRadians. Use the output convention below.

Require distinct x coordinates. Return Δy/Δx as slope and atan2(Δy,Δx) as directed angle in radians.1

Input fieldMeaning and unitsAccepted input
firstXFirst XRequired. Finite number.
firstYFirst YRequired. Finite number.
secondXSecond XRequired. Finite number.
secondYSecond YRequired. Finite number.
Output fieldInterpretationReturned shape
slopeSlopeRequired. Finite number.
angleRadiansAngle Radians Unit: rad.Required. Finite number.
json
{
  "input": {
    "firstX": 0,
    "firstY": 1,
    "secondX": 10,
    "secondY": 3
  },
  "output": {
    "slope": 0.2,
    "angleRadians": 0.19739555984988078
  }
}

Limitations and assumptions

  • All coordinates share a scale. Directed angle can differ by π for reversed points; no handwriting identity, baseline fit, or evidentiary conclusion is inferred.
  • Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
  • Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Use the validated measurement method and original evidence for interpretation. Include calibration, geometry, uncertainty and the full evidentiary context rather than turning a numerical match into an identification.

References

  1. Calculation and input contract: forensic-science/questioned-document-baseline-slope-term — tool.io

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