Bow-Tie Width Predictor Fancy Shapes

Measure sampled central dark-band span on aligned waist brightness profile under caller threshold, rather than predict a bow-tie from cut dimensions; unresolved band edges are only observed sample brackets, not optical causation.

Description

A measured central dark band can be located on an aligned brightness profile.

A measured central dark band can be located on an aligned brightness profile. Sampled edge locations provide only an observed span, not a prediction from cut dimensions.^[1]

When to use Bow-Tie Width Predictor Fancy Shapes

Use this tool to measure sampled central dark-band span on aligned waist brightness profile under caller threshold, rather than predict a bow-tie from cut dimensions; unresolved band edges are only observed sample brackets, not optical causation.

Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.

How to use Bow-Tie Width Predictor Fancy Shapes and understand its results

Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.
Enter measuredAcrossWaistPositionsMm, measuredNormalizedBrightness, callerDarkBrightnessUpperThreshold using the field table and calculation rules, then run the tool.
Read observedCentralDarkBandWidthMm, centralDarkBandObserved. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
measuredAcrossWaistPositionsMm	Measured across waist positions mm	list of number	Required
measuredNormalizedBrightness	Measured normalized brightness	list of number	Required
callerDarkBrightnessUpperThreshold	Caller dark brightness upper threshold	number	Required

Use increasing waist positions in mm with a sample exactly at zero, normalized brightness and threshold in [0,1]. Darkness is strictly below threshold. Grow the contiguous central dark run and return its sampled width and flag; a bright center returns zero and false.

Paired lists must be nonempty and have equal lengths. Each sequence checked for increasing order must contain at least two strictly increasing values.

observed width=last contiguous dark sample position−first contiguous dark sample position

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
observedCentralDarkBandWidthMm	Observed central dark band width mm	number
centralDarkBandObserved	Central dark band observed	boolean

json

{
  "input": {
    "measuredAcrossWaistPositionsMm": [
      -2,
      -1,
      0,
      1,
      2
    ],
    "measuredNormalizedBrightness": [
      1,
      0.2,
      0.1,
      0.2,
      1
    ],
    "callerDarkBrightnessUpperThreshold": 0.3
  },
  "output": {
    "observedCentralDarkBandWidthMm": 2,
    "centralDarkBandObserved": true
  }
}

Limitations and assumptions

A single central dark sample can return width zero with true. Band edges are not interpolated, and optical cause is not inferred.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.

Alternative or Complementary methods

Use Optical Symmetry Score: Audit aligned image brightness asymmetry about declared horizontal/vertical mirror axes, normalized to total flux; unlike paired physical outline error, illumination/registration remain confounders and no automatic alignment. For a complementary task, use Contrast Pattern Grade Estimator: Grade measured spatial RMS luminance contrast under caller independent bands and physical patch areas; differs from temporal scintillation, no laboratory cut grade or perceptual preference is inferred.

References

Bow-Tie Width Predictor Fancy Shapes — tool.io

Similar or alternative tools

Optical Symmetry Score
Audit aligned image brightness asymmetry about declared horizontal/vertical mirror axes, normalized to total flux; unlike paired physical outline error, illumination/registration remain confounders and no automatic alignment.
Contrast Pattern Grade Estimator
Grade measured spatial RMS luminance contrast under caller independent bands and physical patch areas; differs from temporal scintillation, no laboratory cut grade or perceptual preference is inferred.