Description
Return the perpendicular pair (-y,x) for counterclockwise true and (y,-x) otherwise.
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 the perpendicular pair (-y,x) for counterclockwise true and (y,-x) otherwise.
When to use this tool
Use Vector Two Dimensional Perpendicular Orientation Choice 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 x, y, counterclockwise. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read x, y. Use the output convention below.
Return the perpendicular pair (-y,x) for counterclockwise true and (y,-x) otherwise.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | X | Required. Finite number. |
| y | Y | Required. Finite number. |
| counterclockwise | Counterclockwise | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| x | X | Required. Finite number. |
| y | Y | Required. Finite number. |
{
"input": {
"x": 3,
"y": 4,
"counterclockwise": true
},
"output": {
"x": -4,
"y": 3
}
}Limitations and assumptions
- This rotates by a quarter turn in a Cartesian plane without normalizing length. The zero vector is allowed, and screen coordinates with downward-positive y require a separate interpretation of orientation.
- 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 Two Dimensional Polar Angle Sign
Calculate a nonzero planar vector's signed atan2 angle in radians and the angle's sign.
- Vector Tangent Normal Basis Orientation
Classify the orientation of a supplied planar tangent/normal pair from its determinant sign.