Description
Calculate the vector residual for a supplied point's affine relation to two other points at a fixed parameter.
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.
Calculate the vector residual for a supplied point's affine relation to two other points at a fixed parameter.
When to use this tool
Use Vector Three Point Affine Dependence Residual 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, parameter. 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 residual, norm. Use the output convention below.
Require matching first, second, and third vector dimensions. Calculate residual=third-(first+parameter*(second-first)) componentwise and return its Euclidean norm.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Array of Finite number.; maximum items 256. |
| second | Second | Required. Array of Finite number.; maximum items 256. |
| third | Third | Required. Array of Finite number.; maximum items 256. |
| parameter | Parameter | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| residual | Residual | Required. Array of Finite number.; maximum items 256. |
| norm | Norm | Required. Finite number. |
{
"input": {
"first": [
0,
0
],
"second": [
2,
4
],
"third": [
1,
3
],
"parameter": 0.5
},
"output": {
"residual": [
0,
1
],
"norm": 1
}
}Limitations and assumptions
- Parameter is supplied and not fitted or clamped. This measures the residual for that one parameter, not minimum distance to a line, a collinearity proof, or segment containment.
- 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 Affine Combination Weight Residual
Sum weights and return residual=sum-1.
- Vector: Vector Affine Point Direction Tag
Encode a 2D/3D affine point or free direction into homogeneous coordinates with explicit final weight one or zero; no projective division.