Description
Audit explicit finite coefficient arity and linear determinant, no invertibility tolerance inferred.
A planar affine transform combines a linear map and translation. This family stores [a,b,c,d,e,f], mapping [x,y] to [a×x+c×y+e,b×x+d×y+f]. Positions include translation; displacements use only the linear block, and normal covectors use its inverse transpose. Composition order changes the result.
Audit explicit finite coefficient arity and linear determinant, no invertibility tolerance inferred.
When to use this tool
Use this tool to audit explicit finite coefficient arity and linear determinant, no invertibility tolerance inferred.
How to use the tool and how it works
- Enter coefficients using the input definitions below.
- Run the operation. Resolve malformed-input errors before interpreting the result.
- Read result.valid, result.determinant. Interpret signs, units, ordering and null values using the rules below.
Return valid when the coefficient list has exactly six finite values. For that length return determinant = a×d−b×c; otherwise determinant is null.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coefficients | Finite coefficient list to audit or convert; the operation specifies whether six values are required or checked. | Dense list of at most 128 finite numbers, subject to the stated integer/shape rules. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.valid | Whether the supplied finite list has six coefficients, without an invertibility requirement. |
| result.determinant | a×d−b×c for a six-value list, otherwise null. |
{
"input": {
"coefficients": [
2,
0,
0,
3,
4,
5
]
},
"output": {
"result": {
"valid": true,
"determinant": 6
}
}
}Limitations and assumptions
- A zero determinant does not make valid false: the flag checks layout/finite values, not invertibility, conditioning or affine fit quality.
- Matrices have six finite coefficients. Point/vector inputs have two components within ±1,000,000,000; rectangle bounds are likewise bounded and ordered. Coordinate units and axis directions are caller-defined. No conditioning threshold is inferred for inversion.
- Every declared top-level input is required and unknown fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
- Numeric outputs must be finite and within the absolute safe-integer magnitude; exact larger integers use decimal text. Source positions are zero-based UTF-16 offsets and span ends are exclusive unless a different convention is explicitly stated.
Alternative or Complementary methods
Check coefficient layout and application order when exchanging matrices. Use point, displacement or normal operations according to the quantity being transformed, and a separate conditioning analysis for numerically sensitive inverses.
References
Similar or alternative tools
- Affine Six Coefficient Layout Converter
Convert SVG-style compact coefficients to a 2x3 row-major six-element layout, not an arbitrary matrix transpose.
- Affine Matrix About Anchor Transform
Move the linear transform’s origin to an explicit anchor, preserving existing translation.