Pearl Shape Symmetry Rater
Audit centered pearl outline through principal second-moment axes and radial RMS residual, distinct from paired mirror errors; sampling must be comparable, not a pearl shape/market grade or 3D reconstruction.
Description
Pearl outline shape can be described by principal second-moment axes and radial variation.
Pearl outline shape can be described by principal second-moment axes and radial variation. A centered two-dimensional sample provides a shape proxy, not a full three-dimensional reconstruction.1
Audit centered pearl outline through principal second-moment axes and radial RMS residual, distinct from paired mirror errors; sampling must be comparable, not a pearl shape/market grade or 3D reconstruction.
When to use Pearl Shape Symmetry Rater
Use this tool to audit centered pearl outline through principal second-moment axes and radial RMS residual, distinct from paired mirror errors; sampling must be comparable, not a pearl shape/market grade or 3D reconstruction.
Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.
How to use Pearl Shape Symmetry Rater 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 centeredPearlOutlinePointsMm using the field table and calculation rules, then run the tool.
- Read principalOutlineAxisRatio, rmsRadialDeviationFraction. 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 |
|---|---|---|---|
| centeredPearlOutlinePointsMm | Centered pearl outline points mm | list of list of number | Required |
Supply at least three centered 2D outline points in mm. Enforce sample-centroid centering within the relative 10⁻⁹ norm check, require positive minor variance and mean radius, and return principal axis ratio plus normalized radial RMS.
axis ratio=sqrt(larger second-moment eigenvalue/smaller); radial deviation=RMS(radius−mean radius)/mean radius Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| principalOutlineAxisRatio | Principal outline axis ratio | number |
| rmsRadialDeviationFraction | Rms radial deviation fraction | number |
{
"input": {
"centeredPearlOutlinePointsMm": [
[
1,
0
],
[
-1,
0
],
[
0,
1
],
[
0,
-1
]
]
},
"output": {
"principalOutlineAxisRatio": 1,
"rmsRadialDeviationFraction": 0
}
}Limitations and assumptions
Sampling and alignment affect the result. The metrics do not assign a pearl market or laboratory shape grade.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Matrices are limited to 128 rows and 128 entries per row; other numeric lists are limited to 100,000 entries. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Outline Deviation Symmetry Check: Audit corresponding measured outline points about caller already-aligned mirror axis, preserving pair deviations; no automatic alignment, mineral shape ideal or inferred optical symmetry. For a complementary task, use Pearl Size Millimeter Sieve Classifier: Classify measured pearl diameter with caller sieve bands and boundary uncertainty, preserving multiple possible sizes; no invented exact size at ambiguous screen boundary.
References
-
Pearl Shape Symmetry Rater — tool.io
Similar or alternative tools
- Outline Deviation Symmetry Check
Audit corresponding measured outline points about caller already-aligned mirror axis, preserving pair deviations; no automatic alignment, mineral shape ideal or inferred optical symmetry.
- Pearl Size Millimeter Sieve Classifier
Classify measured pearl diameter with caller sieve bands and boundary uncertainty, preserving multiple possible sizes; no invented exact size at ambiguous screen boundary.