Description
Return parametric speed and unit-tangent domain flags.
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 parametric speed and unit-tangent domain flags.
When to use this tool
Use Parametric Speed Zero Domain Flag when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter derivatives. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read speed, zeroSpeed, unitTangentDefined. Inspect zeroSpeed, unitTangentDefined before interpreting the associated values.
Return parametric speed and unit-tangent domain flags. Require nonempty derivative vector; speed = hypot(components), zeroSpeed requires all exactly zero, unitTangentDefined requires any nonzero component.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| derivatives | Derivatives | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| speed | Speed | Required. Finite number. |
| zeroSpeed | Zero Speed | Required. Boolean. |
| unitTangentDefined | Unit Tangent Defined | Required. Boolean. |
{
"input": {
"derivatives": [
0,
0
]
},
"output": {
"speed": 0,
"zeroSpeed": true,
"unitTangentDefined": false
}
}Limitations and assumptions
- These are supplied coordinate derivatives; no tangent vector, curve regularity neighborhood or actual parametrization is verified.
- 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
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