Description
Classify exact zero patterns of two implicit partials.
An implicit relation defines local derivatives only where its smoothness and nonzero-partial hypotheses apply. Gradient and Hessian components supplied as numbers do not establish that a point lies on the level set or that a regular implicit function exists there.
Classify exact zero patterns of two implicit partials.
When to use this tool
Use Implicit Curve Vertical Tangent Flag when evaluating the stated implicit-derivative or level-set term from supplied partial derivatives.
How to use the tool and how it works
- Enter partialX, partialY. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read verticalTangent, singular, horizontalTangent. Inspect verticalTangent, singular, horizontalTangent before interpreting the associated values.
Classify exact zero patterns of two implicit partials. verticalTangent means partialY zero and partialX nonzero, horizontalTangent the reverse, singular means both zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| partialX | Partial X | Required. Finite number. |
| partialY | Partial Y | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| verticalTangent | Vertical Tangent | Required. Boolean. |
| singular | Singular | Required. Boolean. |
| horizontalTangent | Horizontal Tangent | Required. Boolean. |
{
"input": {
"partialX": 2,
"partialY": 0
},
"output": {
"verticalTangent": true,
"singular": false,
"horizontalTangent": false
}
}Limitations and assumptions
- These local predicates assume a suitable implicit level-set point; no tolerance, actual tangent existence or function regularity 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
Check the original level-set equation, differentiability and the relevant implicit-function hypotheses before interpreting these local derivative formulas.
References
Similar or alternative tools
- Implicit Levelset Gradient Normalizer
Normalize a supplied nonzero level-set gradient.
- Implicit Second Partial Diagonal Term
Return a second derivative for a supplied implicit planar curve.