Description
Return squared separation from two radii and their included angle.
Coordinate distance formulas need compatible lengths and explicit angular units. Straight-line separation, its squared value and travel along a surface are distinct quantities even when they share endpoints.
Return squared separation from two radii and their included angle.
When to use this tool
Use Distance: Polar Radius Angle Distance Term when computing the stated planar or cylindrical coordinate separation.
How to use the tool and how it works
- Enter firstRadius, secondRadius, angleDegrees. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Return squared separation from two radii and their included angle. Require nonnegative radii and angleDegrees in [0,180]; compute (r1-r2)²+4*r1*r2*sin(angle/2)² after conversion to radians.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstRadius | First Radius | Required. Finite number. |
| secondRadius | Second Radius | Required. Finite number. |
| angleDegrees | Included angle in degrees, from 0 through 180. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Returned object; expand its named members below. | Required. Object. |
| result.squaredDistance | Squared separation, in squared length units; take a root separately for distance. | Calculated result member: number. |
{
"input": {
"firstRadius": 2,
"secondRadius": 2,
"angleDegrees": 60
},
"output": {
"result": {
"squaredDistance": 4
}
}
}Limitations and assumptions
- The output has squared length units and is not itself a distance.
- Outputs are nested inside result. 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 the actual spatial geometry and an appropriate surface or network model when travel distance is the question.
References
Similar or alternative tools
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