Description
Audit exact or caller-tolerance antipodal angular transitions where shortest direction is ambiguous; no motion-direction inference from sparse samples.
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.
Audit exact or caller-tolerance antipodal angular transitions where shortest direction is ambiguous; no motion-direction inference from sparse samples.
When to use this tool
Use this tool to audit exact or caller-tolerance antipodal angular transitions where shortest direction is ambiguous; no motion-direction inference from sparse samples.
How to use the tool and how it works
- Enter turns, tolerance using the input definitions below.
- Run the operation. Resolve malformed-input errors before interpreting the result.
- Read result.ambiguousSteps. Interpret signs, units, ordering and null values using the rules below.
For each consecutive pair calculate its shortest signed turn increment. Return the later sample index when ||increment|−1/2|≤tolerance, with tolerance in [0,1/2].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. |
| tolerance | Nonnegative antipodal ambiguity tolerance in turns, from 0 through 1/2. | Finite number satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.ambiguousSteps | Later original sample indexes of transitions within tolerance of an antipodal half turn. |
{
"input": {
"turns": [
0,
0.5,
0.6
],
"tolerance": 0
},
"output": {
"result": {
"ambiguousSteps": [
1
]
}
}
}Limitations and assumptions
- Ambiguity is a sampling observation; no direction is recovered. At tolerance 1/2 every consecutive step is included.
- 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 Sector Boundary Distance
Compute circular turn distance to the nearest equal-sector boundary, not the sector center or a linear clock endpoint.
- Turn Sector Center
Return the normalized center turn of an explicit zero-based equal angular sector; origin is a caller coordinate.