Description
Return the sign of arc minus half the supplied full turn and an exact-equality halfway flag.
Spherical geography models Earth with one radius and angular coordinates. Surface arcs, polar heights, circle radii, and area fractions are different derived quantities; an ideal spherical result does not include ellipsoid or terrain effects.
Return the sign of arc minus half the supplied full turn and an exact-equality halfway flag.
When to use this tool
Use Great Circle Arc Halfway Sign when you need a stated spherical geographic term or angular conversion.
How to use the tool and how it works
- Enter arcRadians, fullTurnRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read relativeSign, halfway. Inspect halfway before interpreting the associated values.
Require positive fullTurnRadians and arcRadians between zero and that full turn. Return the sign of arc minus half the supplied full turn and an exact-equality halfway flag.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| arcRadians | Arc Radians | Required. Finite number; minimum 0. |
| fullTurnRadians | Full Turn Radians | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| relativeSign | Relative Sign | Required. Safe integer. |
| halfway | Halfway | Required. Boolean. |
{
"input": {
"arcRadians": 3,
"fullTurnRadians": 6
},
"output": {
"relativeSign": 0,
"halfway": true
}
}Limitations and assumptions
- The caller supplies the full-turn value rather than the tool fixing it to 2π. relativeSign is -1, 0, or +1; this is a comparison, not an arc-distance or path calculation.
- 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 ellipsoidal geodesy or a suitable terrain model when spherical assumptions are inadequate. Keep angular units, physical length units, latitude definition, and reference radius explicit.
References
Similar or alternative tools
- Spherical Distance Central Angle Reference
Return that central angle in radians and its fraction of a full 2π turn.
- Longitude Arc Complement
Return the smaller of their absolute difference and its 360-degree complement as shortArcDegrees, and 360 minus that result as longArcDegrees.