CATpie: A Python tool for quantifying membrane curvature, area, and geometrically faithful normal-line thickness from molecular dynamics simulations

highlights regions where vertical separation overestimates normal-line spacing due to membrane tilt. CATpie supports atomistic and coarse-grained simulations of planar and undulated bilayers that remain representable as single-valued leaflet height fields z=Z(x,y) over a periodic domain (without overhangs or topological changes), enabling systematic geometric characterisation of membrane simulations.