Description
Return shorter and complementary angular gaps.
A periodic coordinate identifies values separated by a whole cycle. Minimum-image gaps require a wrapping interval and an explicit half-cycle tie convention; signed direction and unsigned separation answer different questions.
Return shorter and complementary angular gaps.
When to use this tool
Use Angle Complement Geodesic Gap when checking one explicit periodic-coordinate or gap convention.
How to use the tool and how it works
- Enter angleRadians, periodRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read shorter, complement. Use the output convention below.
Return shorter and complementary angular gaps. Require positive periodRadians and angleRadians in [0,period]; shorter = min(angle,period-angle), complement = period-angle.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| angleRadians | Angle Radians | Required. Finite number; minimum 0. |
| periodRadians | Period Radians | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| shorter | Shorter | Required. Finite number. |
| complement | Complement | Required. Finite number. |
{
"input": {
"angleRadians": 1,
"periodRadians": 6
},
"output": {
"shorter": 1,
"complement": 5
}
}Limitations and assumptions
- The period is caller-defined and need not equal 2*pi; no endpoints are inferred.
- 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 a complete periodic geometry model when multiple axes, seam-crossing intervals or path winding matter.
References
Similar or alternative tools
- Distance: Periodic Axis Minimum Image Gap
Return a signed minimum-image gap on one periodic axis.
- Periodic Box Wrap One Axis
Wrap a coordinate into a declared periodic box and return its image index.