Description
Return planar local turning sign.
Differential-calculus formulas relate supplied local values and derivatives under explicit coordinate and unit conventions. A tangent term, curvature expression or directional derivative assumes the required differentiability and regularity; substituting numerical derivatives does not verify those hypotheses for an actual function.
Return planar local turning sign.
When to use this tool
Use Parametric Curve Local Turning Sign when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter dx, dy, ddx, ddy. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read cross, sign. Use the output convention below.
Return planar local turning sign. Require nonzero velocity (dx,dy); cross = dx*ddy-dy*ddx, sign = sign(cross).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| dx | Dx | Required. Finite number. |
| dy | Dy | Required. Finite number. |
| ddx | Ddx | Required. Finite number. |
| ddy | Ddy | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| cross | Cross | Required. Finite number. |
| sign | Sign | Required. Safe integer. |
{
"input": {
"dx": 1,
"dy": 0,
"ddx": 0,
"ddy": 2
},
"output": {
"cross": 2,
"sign": 1
}
}Limitations and assumptions
- Orientation depends on coordinate convention and parametrization; no curve, global winding or geometric validity is checked.
- 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
Differentiate or validate the complete function and its domain first; use suitable symbolic or numerical methods and check regularity and coordinate conventions for the intended interpretation.
References
Similar or alternative tools
- Parametric Curve Osculating Radius
Return osculating radius from speed and cross-product magnitude.
- Parametric Curvature Numerator At Point
Return the signed and absolute planar curvature numerator.