Description
Return only the perpendicular component magnitude relative to a supplied nonzero axis.
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.
Return only the perpendicular component magnitude relative to a supplied nonzero axis.
When to use this tool
Use Vector Axis Rejection Length 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 vector, axis. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read perpendicularLength. Use the output convention below.
Require aligned vector and nonempty nonzero axis. Normalize the axis after scaling by its largest absolute component, subtract the vector's projection on that unit axis, and return the perpendicular residual's Euclidean length.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vector | Vector | Required. Array of Finite number.; maximum items 256. |
| axis | Axis | Required. Array of Finite number.; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| perpendicularLength | Perpendicular Length | Required. Finite number. |
{
"input": {
"vector": [
3,
4
],
"axis": [
1,
0
]
},
"output": {
"perpendicularLength": 4
}
}Limitations and assumptions
- This is distance from a vector to the axis direction through the origin, not point-to-line distance with an offset. Floating-point cancellation can affect very small rejection lengths.
- 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 Axis Angle Infinitesimal Step
Return the first-order active Rodrigues rotation v+angle*(unitAxis cross v), with angle in radians.
- Vector Fixed Axis Rotation Quarter Turn
Rotate a three-component vector around x, y, or z by an integer number of quarter turns using signed swaps.