Description
Return a fixed-radius arc-length envelope.
Spherical geometry distinguishes central angle, surface arc and straight chord. They coincide only in a small-angle limit, and a sphere-radius sensitivity differs from a geodesic calculation on an ellipsoid.
Return a fixed-radius arc-length envelope.
When to use this tool
Use Fixed Radius Angular Gap Halfwidth when checking a stated spherical arc, chord or radius relationship.
How to use the tool and how it works
- Enter radius, angle, angularHalfwidth. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read minimumArc, maximumArc. Use the output convention below.
Return a fixed-radius arc-length envelope. Require nonnegative radius, angle and angularHalfwidth; minimumArc = radius*max(0,angle-halfwidth), maximumArc = radius*(angle+halfwidth).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radius | Radius | Required. Finite number. |
| angle | Angle | Required. Finite number. |
| angularHalfwidth | Angular Halfwidth | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| minimumArc | Minimum Arc | Required. Finite number. |
| maximumArc | Maximum Arc | Required. Finite number. |
{
"input": {
"radius": 2,
"angle": 1,
"angularHalfwidth": 0.25
},
"output": {
"minimumArc": 1.5,
"maximumArc": 2.5
}
}Limitations and assumptions
- Angles are radians; no shortest-arc cap or probabilistic uncertainty interpretation is imposed.
- 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 endpoint coordinates and an appropriate spherical or ellipsoidal geodesic model for real geographic distance.
References
Similar or alternative tools
- Geodesic Radius Relative Distance Scale
Rescale a spherical arc distance for a new radius at fixed central angle.
- Angular Chord Relative Error From Angle
Return the relative arc-to-chord shortfall.