Description
For nonnegative radius and abs(angleRadians)<=2*pi return arcLength=radius*abs(angle), chordLength=2*radius*sin(abs(angle)/2), and excess=arcLength-chordLength.
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.
For nonnegative radius and abs(angleRadians)<=2*pi return arcLength=radius*abs(angle), chordLength=2*radius*sin(abs(angle)/2), and excess=arcLength-chordLength.
When to use this tool
Use Arch Model Segment Curve Chord 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 radius, angleRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read arcLength, chordLength, excess. Use the output convention below.
For nonnegative radius and abs(angleRadians)<=2*pi return arcLength=radius*abs(angle), chordLength=2*radius*sin(abs(angle)/2), and excess=arcLength-chordLength.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radius | Radius | Required. Finite number; minimum 0. |
| angleRadians | Signed central angle with magnitude at most 2*pi. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| arcLength | Arc Length | Required. Finite number. |
| chordLength | Chord Length | Required. Finite number. |
| excess | Nonnegative modeled arc-minus-chord length, subject to numeric rounding. | Required. Finite number. |
{
"input": {
"radius": 10,
"angleRadians": 3.141592653589793
},
"output": {
"arcLength": 31.41592653589793,
"chordLength": 20,
"excess": 11.415926535897931
}
}Limitations and assumptions
- Angle is radians and the segment is assumed circular. A full turn approaches a zero chord numerically; no arch fitting, tooth positions, or clinical space analysis is performed.
- 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 Landmark Chord Length
Measure a supplied planar research landmark chord without treatment planning.
- Arch Curve Reference Gap
Compare summed observed and reference arch-segment lengths and return their signed and relative gaps.