Description
Check gradient/direction orthogonality and a regular-level flag.
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.
Check gradient/direction orthogonality and a regular-level flag.
When to use this tool
Use Gradient Level Set Tangent Orthogonality when evaluating the stated local differential-calculus identity from supplied values.
How to use the tool and how it works
- Enter gradient, direction, tolerance. Follow any array-alignment requirements below. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read dotProduct, withinTolerance, regularLevel. Inspect withinTolerance, regularLevel before interpreting the associated values.
Check gradient/direction orthogonality and a regular-level flag. Require aligned nonempty vectors and tolerance >= 0; dotProduct is their dot product, withinTolerance tests absolute dot, regularLevel means any gradient component nonzero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| gradient | Gradient | Required. Array of finite number; maximum items 256. |
| direction | Direction | Required. Array of finite number; maximum items 256. |
| tolerance | Nonnegative caller-selected comparison tolerance, in matching units. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| dotProduct | Dot Product | Required. Finite number. |
| withinTolerance | Within Tolerance | Required. Boolean. |
| regularLevel | Whether the supplied gradient is nonzero; orthogonality can hold with a zero gradient. | Required. Boolean. |
{
"input": {
"gradient": [
2,
3
],
"direction": [
3,
-2
],
"tolerance": 0
},
"output": {
"dotProduct": 0,
"withinTolerance": true,
"regularLevel": true
}
}Limitations and assumptions
- Direction need not be unit length; zero gradient can pass orthogonality while regularLevel is false and no tangent space is established.
- 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
- Multivariable Directional Derivative Contribution
Return coordinate contributions to a unit-direction derivative.
- Implicit Curve Vertical Tangent Flag Tool
Exact first-derivative tests for a supplied planar implicit curve gradient.