Description
Unwrap supplied turn observations using shortest signed consecutive increments; exact half-turn ties go positive and larger actual motion cannot be recovered.
A turn is one full revolution, equal to 360 degrees or 2π radians. Circular coordinates wrap modulo one, so a shortest signed change can differ from direct subtraction. Sector indexes partition the circle, while unwrapping observations requires a direction convention for exact half-turn ties.
Unwrap supplied turn observations using shortest signed consecutive increments; exact half-turn ties go positive and larger actual motion cannot be recovered.
When to use this tool
Use this tool to unwrap supplied turn observations using shortest signed consecutive increments; exact half-turn ties go positive and larger actual motion cannot be recovered.
How to use the tool and how it works
- Enter turns using the input definitions below.
- Run the operation. Resolve malformed-input errors before interpreting the result.
- Read result.unwrapped. Interpret signs, units, ordering and null values using the rules below.
Preserve the first turn observation. For each consecutive pair normalize its difference to [0,1), choose d when d≤1/2 or d−1 otherwise, and accumulate those shortest signed increments. Empty input returns an empty trace.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| turns | Ordered signed angular observations in turns; repeated samples are retained. | Dense list of at most 128 finite numbers, subject to the stated integer/shape rules. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.unwrapped | Observed turns accumulated using shortest signed increments, preserving the first value. |
{
"input": {
"turns": [
0.9,
0.1,
0.3
]
},
"output": {
"result": {
"unwrapped": [
0.9,
1.1,
1.3
]
}
}
}Limitations and assumptions
- Exact half-turn ties choose positive motion. Sparse samples cannot reveal extra revolutions or the actual direction of motion beyond a half turn.
- All angle observations, origins, distances and tolerances here use turns, not radians or degrees. Floating comparisons can affect values extremely close to a wrap boundary.
- Every declared top-level input is required and unknown fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
- Numeric outputs must be finite and within the absolute safe-integer magnitude; exact larger integers use decimal text. Source positions are zero-based UTF-16 offsets and span ends are exclusive unless a different convention is explicitly stated.
Alternative or Complementary methods
Keep angular units and origin consistent. Use the ambiguity audit before relying on shortest-step unwrapping; extra revolutions and motion between sparse observations need other evidence.
References
Similar or alternative tools
- Turn Direction Ambiguity Audit
Audit exact or caller-tolerance antipodal angular transitions where shortest direction is ambiguous; no motion-direction inference from sparse samples.
- Turn Sector Boundary Distance
Compute circular turn distance to the nearest equal-sector boundary, not the sector center or a linear clock endpoint.