Description
Wrap a phase difference with an explicit half-cycle tie.
Numerical grids and sampled modes require explicit coordinate, boundary and sign conventions. A staggered location, minimum-image gap or Nyquist label is one component of a discretization rather than a complete field solve or unique physical interpretation.
Wrap a phase difference with an explicit half-cycle tie.
When to use this tool
Use Wave Packet Phase Unwrapping Tie when checking the stated grid-coordinate, periodic-image or sampled-mode convention.
How to use the tool and how it works
- Enter phaseDifference, tiePositive. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read principalDifference, tied. Inspect tied before interpreting the associated values.
Wrap a phase difference with an explicit half-cycle tie. Reduce modulo 2*pi, use the shorter signed representative and choose +pi or -pi at exact equality according to tiePositive; return tied.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| phaseDifference | Phase Difference | Required. Finite number. |
| tiePositive | Tie Positive | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| principalDifference | Principal Difference | Required. Finite number. |
| tied | Exact reduced difference equals pi, without a tolerance. | Required. Boolean. |
{
"input": {
"phaseDifference": 3.141592653589793,
"tiePositive": false
},
"output": {
"principalDifference": -3.141592653589793,
"tied": true
}
}Limitations and assumptions
- Angles are radians; exact equality has no tolerance and a single principal difference does not unwrap a complete phase series.
- 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 complete mesh, transform convention and boundary conditions for a consistent numerical simulation or physical interpretation.
References
Similar or alternative tools
- Computational Physics: Spectral Mode Nyquist Sign
Map a Fourier index to a signed mode.
- Spectral Derivative One Mode Factor
Return one Fourier derivative factor under an explicit complex convention.