Schwarz-Christoffel Conformal Mapping
Mapping upper half-plane to polygons — angle-preserving transformations
Target polygon
Square
Triangle
Pentagon
L-shape
Strip
Grid lines:
12
Animation speed:
0.5
Morph t:
1.00
▶ Animate morph
Schwarz-Christoffel:
f(z) = C ∫ Π(z−aₖ)^(αₖ−1) dz
Maps upper half-plane to a polygon with interior angles παₖ. Pre-images aₖ are mapped to polygon vertices.
Conformal:
angles are preserved locally — rectangular grid becomes a "warped" grid fitting exactly inside the polygon.