Design & colour
2D point transformation
Scale, rotate and translate a point set with a comparison plot and CSV export.
A clear answer. Here’s how.
For 2–1,000 points, subtracts the pivot, applies independent X/Y scales, rotates counter-clockwise, restores the pivot, then adds translation. Negative scales reflect axes and zero scales collapse a dimension. Export includes original and transformed coordinates. This is Cartesian geometry; screen Y-down coordinate systems reverse the visual rotation convention. Coordinates and translation use the same unit.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Point CSV
X,Y 0,0 4,0 4,3 0,3
- X scale
- 1
- Y scale
- 1
- Counter-clockwise rotation (degrees)
- 30
- Pivot X
- 0
- Pivot Y
- 0
- Translation X
- 1
- Translation Y
- 2
Example result
| Original X | Original Y | Transformed X | Transformed Y |
|---|---|---|---|
| 0 | 0 | 1 | 2 |
| 4 | 0 | 4.46410161514 | 4 |
| 4 | 3 | 2.96410161514 | 6.59807621135 |
| 0 | 3 | -0.5 | 4.59807621135 |
Subtract pivot, scale X/Y, rotate counter-clockwise, restore pivot, then translate. Zero scale is allowed.