Arch Model Tooth Width Space Balance Term Tool

Description

Audit supplied model widths and explicitly removed widths without choosing a treatment.

Dental models distinguish lengths along a curve, straight landmark distances, signed midline offsets, and supplied material budgets. Each calculation needs an explicit coordinate frame, unit, and reference convention. A geometric term can describe a model without establishing an appropriate treatment or device.

Audit supplied model widths and explicitly removed widths without choosing a treatment.

When to use this tool

Use Arch Model Tooth Width Space Balance Term when you need this model-space, landmark, midline, or material-budget component from supplied dimensions.

How to use the tool and how it works

Enter toothWidths, availableLength, extractionWidths. Keep parallel arrays aligned. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read requiredLength, releasedLength, netRequired, spaceBalance. Use the output convention below.

Require nonnegative toothWidths, extractionWidths, and availableLength, with total extraction widths no greater than total tooth widths. Return requiredLength=sum(toothWidths), releasedLength=sum(extractionWidths), netRequired=required-released, and spaceBalance=availableLength-netRequired.^[1]

Input field	Meaning and units	Accepted input
toothWidths	Tooth Widths	Required. Array of finite number; maximum items 256.
availableLength	Available Length	Required. Finite number; minimum 0.
extractionWidths	Nonnegative hypothetical space-credit lengths; not a treatment recommendation.	Required. Array of finite number; maximum items 256.

Output field	Interpretation	Returned shape
requiredLength	Required Length	Required. Finite number.
releasedLength	Released Length	Required. Finite number.
netRequired	Net Required	Required. Finite number.
spaceBalance	Space Balance	Required. Finite number.

json

{
  "input": {
    "toothWidths": [
      7,
      8,
      9
    ],
    "availableLength": 22,
    "extractionWidths": [
      7
    ]
  },
  "output": {
    "requiredLength": 24,
    "releasedLength": 7,
    "netRequired": 17,
    "spaceBalance": 5
  }
}

Limitations and assumptions

Use one length unit. ExtractionWidths are a supplied hypothetical space credit, not a recommendation to remove teeth; individual tooth identity, arch geometry, clinical constraints, and treatment planning are not assessed.
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 calibrated model measurements and a suitable full geometry or material model when one term is insufficient. Verify units, coordinate frames, shape assumptions, and reference conventions before comparing results.

References

Calculation and input contract: orthodontics/arch-model-tooth-width-space-balance-term — tool.io

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