Description
Normalize their dot, clamp its cosine to [-1, 1], and return π-acos(cosine) as internalRadians.
Solid-geometry formulas assume particular shapes and measurement directions. Axial height, slant length, filled-volume centroid, and surface centroid are different quantities even when they describe the same object.
Normalize their dot, clamp its cosine to [-1, 1], and return π-acos(cosine) as internalRadians.
When to use this tool
Use Prism Dihedral Normal Dot Term when you need a local dimension, area, or centroid term for the stated ideal solid.
How to use the tool and how it works
- Enter firstNormal, secondNormal. 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 cosine, internalRadians. Use the output convention below.
Require nonzero three-component normals with a finite positive norm product. Normalize their dot, clamp its cosine to [-1, 1], and return π-acos(cosine) as internalRadians.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstNormal | Outward face normal with nonzero norm. | Required. Array of finite number; maximum items 256. |
| secondNormal | Other outward face normal with nonzero norm. | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| cosine | Cosine | Required. Finite number. |
| internalRadians | π minus the angle between outward normals. | Required. Finite number. |
{
"input": {
"firstNormal": [
1,
0,
0
],
"secondNormal": [
0,
1,
0
]
},
"output": {
"cosine": 0,
"internalRadians": 1.5707963267948966
}
}Limitations and assumptions
- The internal-angle interpretation assumes consistently outward face normals; the tool does not infer face orientation, verify a prism, or resolve an arbitrary angle convention.
- 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 a complete solid model for clipping, oblique shapes, or nonuniform material. Confirm radius, height, and centroid conventions before applying an ideal-shape identity.
References
Similar or alternative tools
- Tetrahedron Face Normal Orientation
Cross B-A with C-A, dot with opposite-A, reverse the normal only for a positive dot, and return signedDot, outwardNormal, and degenerate for exact zero.
- Ellipse Parametric Normal Unit Vector
Form [cos/a, sin/b] and normalize it for the outward normal.