Description
Normalize a supplied nonzero level-set gradient.
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.
Normalize a supplied nonzero level-set gradient.
When to use this tool
Use Implicit Levelset Gradient Normalizer when evaluating the stated implicit-derivative or level-set term from supplied partial derivatives.
How to use the tool and how it works
- Enter gradient. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read normal, magnitude. Use the output convention below.
Normalize a supplied nonzero level-set gradient. Compute magnitude = hypot(gradient), require it positive and return normal = gradient/magnitude.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| gradient | Gradient | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| normal | Normal | Required. Array of finite number; maximum items 256. |
| magnitude | Magnitude | Required. Finite number. |
{
"input": {
"gradient": [
3,
4
]
},
"output": {
"normal": [
0.6,
0.8
],
"magnitude": 5
}
}Limitations and assumptions
- The normal points along the supplied gradient; no surface, outward direction or actual differentiability 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
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 Second Partial Diagonal Term
Return a second derivative for a supplied implicit planar curve.
- Implicit Curve Vertical Tangent Flag
Classify exact zero patterns of two implicit partials.