Description
Combine three scalar coordinates under supplied affine weights whose sum is approximately one.
A vector is an ordered set of components in a chosen basis. Its norm measures magnitude, while dot products, projections, and coordinate transformations describe different relationships. Component order, angle units, normalization, and numerical tolerances determine the meaning of a computed result.
Combine three scalar coordinates under supplied affine weights whose sum is approximately one.
When to use this tool
Use Vector Three Point Barycentric Coordinate Term when you need the particular coordinate operation, derivative, residual, or domain check under a known basis convention.
How to use the tool and how it works
- Enter first, second, third, weights. 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 coordinate. Use the output convention below.
Require exactly three weights whose sum differs from one by at most 1e-12. Return coordinate=first*weights[0]+second*weights[1]+third*weights[2].1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Finite number. |
| second | Second | Required. Finite number. |
| third | Third | Required. Finite number. |
| weights | Three affine weights summing to one within 1e-12; negative values permitted. | Required. Array of Finite number.; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| coordinate | Coordinate | Required. Finite number. |
{
"input": {
"first": 2,
"second": 6,
"third": 10,
"weights": [
0.25,
0.5,
0.25
]
},
"output": {
"coordinate": 6
}
}Limitations and assumptions
- Weights may be negative, so the result is an affine coordinate and need not lie inside a triangle. Only one scalar coordinate is combined; weights are not solved from geometric points or normalized automatically.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- 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
Choose a complete vector or matrix operation when a single component or residual is insufficient. For sensitive near-zero or near-singular cases, inspect numerical conditioning and use an appropriate precision and tolerance.
References
Similar or alternative tools
- Vector Three Point Affine Dependence Residual
Calculate the vector residual for a supplied point's affine relation to two other points at a fixed parameter.
- Homogeneous Point Weight Flag
Classify a supplied homogeneous weight; other coordinates must separately define a nonzero projective tuple.