Description
Move the linear transform’s origin to an explicit anchor, preserving existing translation.
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.
Move the linear transform’s origin to an explicit anchor, preserving existing translation.
When to use this tool
Use this tool to move the linear transform’s origin to an explicit anchor, preserving existing translation.
How to use the tool and how it works
- Enter matrix, anchor using the input definitions below.
- Run the operation. Resolve malformed-input errors before interpreting the result.
- Read result.matrix. Interpret signs, units, ordering and null values using the rules below.
For anchor h and linear block L, preserve L and replace translation t with t+h−Lh. Equivalently, apply the original transform around the supplied anchor while retaining its existing translation.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| matrix | Six finite coefficients [a,b,c,d,e,f] in the mapping defined above. | Dense list of at most 128 finite numbers, subject to the stated integer/shape rules. |
| anchor | Anchor [x,y] around which to relocate the supplied linear transform, retaining its original translation. | 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.matrix | Resulting six coefficients [a,b,c,d,e,f] under the stated map and composition order. |
{
"input": {
"matrix": [
2,
0,
0,
3,
4,
5
],
"anchor": [
1,
1
]
},
"output": {
"result": {
"matrix": [
2,
0,
0,
3,
3,
3
]
}
}
}Limitations and assumptions
- If original translation is nonzero the anchor maps to anchor+t; this operation does not force it to be a fixed point.
- 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 Displacement Transform
Transform a displacement using only the linear block; translation is intentionally omitted.
- Affine Normal Covector Transform
Transform a normal covector by inverse transpose without unit renormalization; singular linear maps reject.