Description
Construct a right-handed axis-angle quaternion for an explicit model rotation.
Dental model and device records use coordinate frames, image scale, dimensions, force references, and observation schedules. A projection, gap, ratio, or metadata order checks a particular supplied representation. These local calculations do not establish a treatment plan or the clinical suitability of a device.
Construct a right-handed axis-angle quaternion for an explicit model rotation.
When to use this tool
Use Tooth Model Rotation Quaternion Component Term when you need this particular model geometry, device budget, observation share, or record comparison.
How to use the tool and how it works
- Enter axis, angleRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read w, x, y, z. Use the output convention below.
Require a three-component axis with positive hypot norm. Return quaternion w=cos(angleRadians/2) and vector components=(axis/norm)*sin(angleRadians/2).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| axis | Nonzero three-component axis; extreme norm overflow is not stabilized. | Required. Array of finite number; maximum items 256. |
| angleRadians | Signed angle in radians. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| w | W | Required. Finite number. |
| x | X | Required. Finite number. |
| y | Y | Required. Finite number. |
| z | Z | Required. Finite number. |
{
"input": {
"axis": [
0,
0,
2
],
"angleRadians": 3.141592653589793
},
"output": {
"w": 6.123233995736766e-17,
"x": 0,
"y": 0,
"z": 1
}
}Limitations and assumptions
- The output is one axis-angle quaternion and does not rotate a scan or plan treatment. Extremely large finite axis components can overflow the norm and return zero vector components, so a unit quaternion is not guaranteed at numeric extremes; coordinate handedness remains supplied.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Use a validated measurement or device model and appropriate source records for the full task. Check coordinate systems, calibration, geometric assumptions, and observation denominators before interpreting the term.
References
Similar or alternative tools
- Occlusal Plane Normal Component
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