Description
Compare summed observed and reference arch-segment lengths and return their signed and relative gaps.
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.
Compare summed observed and reference arch-segment lengths and return their signed and relative gaps.
When to use this tool
Use Arch Curve Reference Gap 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 observedSegments, referenceSegments. 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 observedLength, referenceLength, lengthGap, relativeGap. Use the output convention below.
Require aligned nonnegative observedSegments and referenceSegments and a positive sum of referenceSegments. Return both summed lengths, lengthGap=observed-reference, and relativeGap=lengthGap/referenceLength.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| observedSegments | Observed Segments | Required. Array of finite number; maximum items 256. |
| referenceSegments | Reference Segments | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| observedLength | Observed Length | Required. Finite number. |
| referenceLength | Reference Length | Required. Finite number. |
| lengthGap | Length Gap | Required. Finite number. |
| relativeGap | Relative Gap | Required. Finite number. |
{
"input": {
"observedSegments": [
2,
3
],
"referenceSegments": [
2,
2
]
},
"output": {
"observedLength": 5,
"referenceLength": 4,
"lengthGap": 1,
"relativeGap": 0.25
}
}Limitations and assumptions
- Segment lengths need one unit and matching definitions. The tool does not verify correspondence, fit a curve, normalize actual arch shape, or establish a clinical reference.
- 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
Similar or alternative tools
- Arch Model Segment Curve Chord Gap
For nonnegative radius and abs(angleRadians)<=2*pi return arcLength=radius*abs(angle), chordLength=2*radius*sin(abs(angle)/2), and excess=arcLength-chordLength.
- Arch Landmark Chord Length
Measure a supplied planar research landmark chord without treatment planning.