Description
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.
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.
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.
When to use this tool
Use Tetrahedron Face Normal Orientation 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 a, b, c, opposite. 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 signedDot, outwardNormal, degenerate. Inspect degenerate before interpreting the associated values.
Require four three-dimensional points. 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.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| a | A | Required. Array of finite number; maximum items 256. |
| b | B | Required. Array of finite number; maximum items 256. |
| c | C | Required. Array of finite number; maximum items 256. |
| opposite | Opposite | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| signedDot | Signed Dot | Required. Finite number. |
| outwardNormal | Outward Normal | Required. Array of finite number; maximum items 256. |
| degenerate | Degenerate | Required. Boolean. |
{
"input": {
"a": [
0,
0,
0
],
"b": [
1,
0,
0
],
"c": [
0,
1,
0
],
"opposite": [
0,
0,
1
]
},
"output": {
"signedDot": 1,
"outwardNormal": [
0,
0,
-1
],
"degenerate": false
}
}Limitations and assumptions
- The normal is not unit length and the dot has cubic-length units; zero includes coplanar or degenerate geometry and does not define a unique outward side. No tolerance or full tetrahedron-quality check is applied.
- 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 Oriented Volume Single Term
Return coordinate × cofactor/6 as volumeContribution.
- Prism Dihedral Normal Dot Term
Normalize their dot, clamp its cosine to [-1, 1], and return π-acos(cosine) as internalRadians.