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Coordinate Maps

Visualize how transformations deform space. See grid lines, unit shapes, and the Jacobian at any point. Compose multiple maps.

Transformations

Display

Examples

horiz. lines
vert. lines
circle

How This Tool Works

Define a coordinate transformation as a pair of component functions (or triple, for 3D). The tool applies the map to a grid, unit circle, or unit square and visualizes how the input space deforms under the transformation.

Jacobian Matrix

Click any point on the output grid to see the Jacobian matrix evaluated there. The determinant is computed automatically, showing the local area scaling factor and whether orientation is preserved or reversed.

Composable Maps

Chain multiple transformations together to visualize compositions. Built-in presets include rotations, scaling, shear, complex squaring, polar coordinates, inversions, cylindrical maps, and twist deformations.