Description
Sum supplied signedTurnsRadians and divide by 2π for winding.
Polygon formulas combine edge, angle, and area contributions under a stated shape model. A single shoelace term or turning-angle ratio is only part of a full polygon computation and does not independently validate its boundary.
Sum supplied signedTurnsRadians and divide by 2π for winding.
When to use this tool
Use Polygon Boundary Turn Sum when you need a polygon dimension, angle, or local accumulation term.
How to use the tool and how it works
- Enter signedTurnsRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read turnSumRadians, winding. Use the output convention below.
Sum supplied signedTurnsRadians and divide by 2π for winding.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| signedTurnsRadians | Signed Turns Radians | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| turnSumRadians | Turn Sum Radians | Required. Finite number. |
| winding | Winding | Required. Finite number. |
{
"input": {
"signedTurnsRadians": [
1.5707963267948966,
1.5707963267948966,
1.5707963267948966,
1.5707963267948966
]
},
"output": {
"turnSumRadians": 6.283185307179586,
"winding": 1
}
}Limitations and assumptions
- Turns are assumed already correctly measured and oriented; winding is not rounded and the tool does not inspect vertices, closure, self-intersections, or enforce an integer 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
Evaluate the complete ordered boundary for area, winding, and validity. Use a general polygon method when regularity, simplicity, convexity, or uniform shape assumptions do not hold.
References
Similar or alternative tools
- Polygon Signed Area Edge Term
Return (firstX × secondY-secondX × firstY)/2 as signedAreaContribution.
- Regular Polygon Apothem Radius Ratio
Require sides 3-1000000 and return cos(π/sides).