Description
Return coordinate × cofactor/6 as volumeContribution.
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.
Return coordinate × cofactor/6 as volumeContribution.
When to use this tool
Use Tetrahedron Oriented Volume Single 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 coordinate, cofactor. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read volumeContribution. Use the output convention below.
Return coordinate × cofactor/6 as volumeContribution.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coordinate | Coordinate | Required. Finite number. |
| cofactor | Cofactor | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| volumeContribution | Volume Contribution | Required. Finite number. |
{
"input": {
"coordinate": 3,
"cofactor": 8
},
"output": {
"volumeContribution": 4
}
}Limitations and assumptions
- Coordinate and cofactor must belong to the same oriented determinant expansion, with cofactor in squared-length units; a complete signed tetrahedron volume requires the other terms and valid vertex geometry.
- 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 Altitude Volume Term
Return their product divided by three.
- 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.