Description
Compare oriented versus unoriented bench axis/normal angles.
Oral laboratory and research records use specimen labels, model coordinates, material quantities, event times, and device identifiers. A matching label or dimensional clearance answers a narrower question than verified anatomy, traceability, or clinical suitability. Source identity, reference frames, and measurement units must remain explicit.
Compare oriented versus unoriented bench axis/normal angles.
When to use this tool
Use Dental Guide Bench Hole Axis Angle Term when you need this specimen-record, device-label, timing, material, or model-geometry check.
How to use the tool and how it works
- Enter axis, guideNormal. 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 angleRadians, acuteAngleRadians. Use the output convention below.
Require nonzero three-component axis and guideNormal. Divide their dot product by the product of their hypot norms, clamp that cosine to [-1,1], and return its acos as angleRadians; acuteAngleRadians uses the cosine's absolute value.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| axis | Axis | Required. Array of finite number; maximum items 256. |
| guideNormal | Guide Normal | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| angleRadians | Angle Radians | Required. Finite number. |
| acuteAngleRadians | Angle of the unoriented axis to the normal, between zero and pi/2. | Required. Finite number. |
{
"input": {
"axis": [
0,
0,
2
],
"guideNormal": [
0,
0,
-1
]
},
"output": {
"angleRadians": 3.141592653589793,
"acuteAngleRadians": 0
}
}Limitations and assumptions
- The second angle treats axis direction as unoriented. This is a supplied-vector geometry check, not a guide-placement or clinical validation; tiny or huge vectors can cause underflow/overflow and a result error because the raw dot/norm product is not scaled.
- 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 authenticated records and the intended laboratory or measurement protocol for the full task. Verify source labels, coordinate frames, calibration, and the limits of the supplied physical model.
References
Similar or alternative tools
- Jaw Model Plane Offset Coordinate Term
Translate a supplied oriented plane along its unit normal and report point distances.
- Optical Axis Reference Gap
For suppliedReferenceGap within zero through 90 degrees reduce secondAxisDegrees-firstAxisDegrees modulo 180 and return unorientedGap=min(wrapped,180-wrapped) and residual=unorientedGap-suppliedReferenceGap.