Matrix Transformation Lab
See how 2D scale, rotation, shear and translation transform a shape, compare operation order and export coordinates and the combined matrix.
Explore a preset, then edit the controls. Results update when you leave a field or select an option.
A worked example
A 90° counterclockwise rotation maps (1, 0) to (0, 1). Translating before rotating usually produces a different position from translating afterward.
Scope and practical limits
2–100 vertices. Scaling is bounded to ±100, shear ±10 and translation ±10,000. Affine 2D transforms only, without perspective or 3D meshes.
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Using Matrix Transformation Lab
See how 2D scale, rotation, shear and translation transform a shape, compare operation order and export coordinates and the combined matrix.
- Choose a preset to see a worked example, then edit the labeled values.
- Inspect the live chart and result summary. Read any warnings about assumptions or unsupported inputs.
- Review the calculation table, which shows 50 rows per page. Exports contain all available result rows.
- Export the chart as SVG or PNG and the data as CSV or JSON. Save a project to reopen your inputs later.
Example
A 90° counterclockwise rotation maps (1, 0) to (0, 1). Translating before rotating usually produces a different position from translating afterward.
Questions & answers
Which operation runs first?
The leftmost named operation runs first. The combined 3×3 matrix uses column vectors, so matrix multiplication accumulates in the reverse written product order.
What does a zero determinant mean?
The shape has collapsed along at least one dimension. Such a transform cannot be inverted. Negative determinants reverse orientation.
Can I keep editing later?
Save project downloads the inputs and options as JSON. Open project restores that file. Undo and redo remain available during this tab session.
Are images and data exports free?
Yes. Chart SVG/PNG and data CSV/JSON exports do not require an account. Specialized exports are shown beside the result when supported.
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