Strand Length Bead Count

Fit a complete prefix of explicitly ordered variable-diameter beads and gaps around caller clasp length, retaining remainder; not a fixed bead-size lookup or permission to reorder a graduated strand.

Description

A graduated strand has an explicit bead order and may use variable diameters.

A graduated strand has an explicit bead order and may use variable diameters. Fitting a complete prefix preserves that order rather than optimizing by rearranging beads.^[1]

Fit a complete prefix of explicitly ordered variable-diameter beads and gaps around caller clasp length, retaining remainder; not a fixed bead-size lookup or permission to reorder a graduated strand.

When to use Strand Length Bead Count

Use this tool to fit a complete prefix of explicitly ordered variable-diameter beads and gaps around caller clasp length, retaining remainder; not a fixed bead-size lookup or permission to reorder a graduated strand.

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

How to use Strand Length Bead Count 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 orderedBeadDiametersMm, interBeadGapMm, claspOccupiedLengthMm, targetStrandLengthMm using the field table and calculation rules, then run the tool.
Read maximumCompletePrefixBeadCount, occupiedStrandLengthMm, unfilledTargetLengthMm. 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
orderedBeadDiametersMm	Ordered bead diameters mm	list of number	Required
interBeadGapMm	Inter bead gap mm	number	Required
claspOccupiedLengthMm	Clasp occupied length mm	number	Required
targetStrandLengthMm	Target strand length mm	number	Required

Enter positive ordered bead diameters, nonnegative gap/clasp/target lengths in mm, with clasp no longer than target. Add beads in order, inserting gaps only between accepted beads; stop at the first bead that cannot fit. Return count, occupied length and remaining length.

used length=clasp+sum accepted diameters+(accepted count−1) × gap

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

Output field	Meaning	Value type
maximumCompletePrefixBeadCount	Maximum complete prefix bead count	number
occupiedStrandLengthMm	Occupied strand length mm	number
unfilledTargetLengthMm	Unfilled target length mm	number

json

{
  "input": {
    "orderedBeadDiametersMm": [
      10,
      20,
      10
    ],
    "interBeadGapMm": 1,
    "claspOccupiedLengthMm": 10,
    "targetStrandLengthMm": 42
  },
  "output": {
    "maximumCompletePrefixBeadCount": 2,
    "occupiedStrandLengthMm": 41,
    "unfilledTargetLengthMm": 1
  }
}

Limitations and assumptions

The result is a maximum complete prefix, not an arbitrary subset. Cord, knot and curvature allowances must be represented separately.

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.

Alternative or Complementary methods

Use Graduated Strand Weight: Account heterogeneous graduated spherical bead density/count inventory using exact centered-bore napkin-ring volume, not subtracting a full-length cylinder through curved sphere; excludes cord/clasp and non-spherical pearls. 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

Strand Length Bead Count — tool.io

Similar or alternative tools

Graduated Strand Weight
Account heterogeneous graduated spherical bead density/count inventory using exact centered-bore napkin-ring volume, not subtracting a full-length cylinder through curved sphere; excludes cord/clasp and non-spherical pearls.
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.