Description
Cross-check supplied squared distance against a coordinate-difference norm.
Distance calculations require a metric, coordinate convention, unit basis and tie policy. Selecting the nearer endpoint differs from computing distance to the full segment. A circular shortest-angle difference also needs an explicit choice between equally short positive and negative half turns.
Cross-check supplied squared distance against a coordinate-difference norm.
When to use this tool
Use Vector Distance Squared Norm Crosscheck when you already have coordinateDifferences, suppliedSquaredDistance and need to cross-check supplied squared distance against a coordinate-difference norm.
How to use the tool and how it works
- Enter coordinateDifferences, suppliedSquaredDistance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read calculatedSquaredDistance, residual. Use the output convention below.
Require suppliedSquaredDistance>=0; calculate norm=Math.hypot(...coordinateDifferences), squared=norm*norm, residual=suppliedSquaredDistance-squared.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coordinateDifferences | Coordinate Differences | Required. Array of finite number; maximum items 256. |
| suppliedSquaredDistance | Supplied Squared Distance | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| calculatedSquaredDistance | Square of Math.hypot over supplied coordinate differences; can overflow despite a finite norm. | Required. Finite number. |
| residual | Residual | Required. Finite number. |
{
"input": {
"coordinateDifferences": [
3,
4
],
"suppliedSquaredDistance": 26
},
"output": {
"calculatedSquaredDistance": 25,
"residual": 1
}
}Limitations and assumptions
- An empty difference vector gives zero norm. Squaring can overflow and cause rejection even when the norm is finite; no tolerance, metric selection or geometric relationship is inferred.
- 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
Use the actual coordinates and intended metric when geometric distance is required. Preserve reference normalization and angular tie conventions in the full calculation; supplied endpoint distances or squared-norm residuals do not establish the underlying geometry.
References
Similar or alternative tools
- Morphogenesis Reference Landmark Distance
Calculate Euclidean distance between supplied matching coordinate arrays.
- Normalized Distance Reference Change
Compare one supplied distance normalized by two positive references.