Description
Calculate slack=radius-otherAbsoluteSum-abs(coordinate) and inside when slack>=0.
A vector is an ordered set of components in a chosen basis. Its norm measures magnitude, while dot products, projections, and coordinate transformations describe different relationships. Component order, angle units, normalization, and numerical tolerances determine the meaning of a computed result.
Calculate slack=radius-otherAbsoluteSum-abs(coordinate) and inside when slack>=0.
When to use this tool
Use Vector L1 Ball Coordinate Slack when you need the particular coordinate operation, derivative, residual, or domain check under a known basis convention.
How to use the tool and how it works
- Enter radius, otherAbsoluteSum, coordinate. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read slack, inside. Inspect inside before interpreting the associated values.
Calculate slack=radius-otherAbsoluteSum-abs(coordinate) and inside when slack>=0. Require nonnegative radius and otherAbsoluteSum.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radius | Radius | Required. Finite number; minimum 0. |
| otherAbsoluteSum | Other Absolute Sum | Required. Finite number; minimum 0. |
| coordinate | Coordinate | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| slack | Slack | Required. Finite number. |
| inside | Inside | Required. Boolean. |
{
"input": {
"radius": 5,
"otherAbsoluteSum": 2,
"coordinate": -1
},
"output": {
"slack": 2,
"inside": true
}
}Limitations and assumptions
- OtherAbsoluteSum must already be the sum for all other coordinates on the same scale. The tool checks one supplied L1-ball budget without inspecting those omitted coordinates or projecting onto the ball.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Choose a complete vector or matrix operation when a single component or residual is insufficient. For sensitive near-zero or near-singular cases, inspect numerical conditioning and use an appropriate precision and tolerance.
References
Similar or alternative tools
- Vector 3d Coordinate Cyclic Permutation
Cyclically reorder three coordinates by an integer shift modulo three.
- Vector Basis Coordinate Unit Scale
Rescale coordinates for independently scaled basis vectors by dividing by each supplied basis scale.