How a six-line world file maps pixels
A world file stores the affine coefficients in the unintuitive line order A, D, B, E, C, F. The map equations are X = A·column + B·row + C and Y = D·column + E·row + F. A and D form the transformed pixel-column axis; B and E form the pixel-row axis. C and F locate the center of the upper-left pixel.
Pixel centers versus outer corners
The upper-left pixel center is (0, 0), but its outside upper-left edge is (-0.5, -0.5). For a raster W pixels wide and H pixels high, the outer opposite edge is (W−0.5, H−0.5). Confusing centers with edges shifts an axis-aligned raster by half a pixel in both directions. This tool calculates and labels both conventions instead of silently mixing them.
Rotation, skew, scale, and orientation
Rotation terms are not automatically errors. The two basis-vector lengths give pixel-axis scale, their dot product gives the angle between them, and the determinant reports signed area scaling and invertibility. Non-orthogonal axes mean skew. A conventional north-up, axis-aligned world file generally has positive A, negative E, and zero B and D, but other orientations can be intentional.
Validation boundary
This is an affine sidecar preflight, not authoritative georeferencing or CRS validation. It does not read embedded GeoTIFF tags, reproject coordinates, resolve or verify EPSG definitions, apply WKT axis-order semantics, calculate control-point accuracy from more than three points, inspect raster content, identify the correct datum, prove file pairing, or certify spatial accuracy. The PRJ parser is a bounded metadata inventory, not an OGC WKT conformance engine.
Frequently asked questions
Why is the world-file line order A, D, B, E, C, F?
It is the established sidecar storage order, even though the coefficients are commonly grouped as A, B, C and D, E, F in the two affine equations. The coefficient table makes that mapping explicit.
Can the generated bounds file preserve rotation?
No. Four axis-aligned outer bounds do not define a rotated footprint. Bounds mode deliberately generates a north-up transform. Use three non-collinear pixel-center control points to generate a general affine transform.
Does a valid PRJ guarantee correct placement?
No. The PRJ can be valid but belong to another dataset, use an unexpected axis convention, or describe a different datum or unit. This page never fetches external CRS definitions or reprojects coordinates.
Authoritative references
Esri’s world-file documentation defines the six coefficients, stored order, affine equations, and upper-left pixel-center meaning. GDAL’s geotransform tutorial documents the related corner-based six-coefficient convention. The OGC CRS WKT standard is the authority for coordinate-reference-system WKT.
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