Placenta Previa — 2D Margin Shear-Field Model

This is the 2D counterpart to the 3D placenta previa simulator. Rather than moving a placenta through a 3D uterus and reading one shear-stress scalar at its margin, this version treats the margin as a curved rim of a disc and computes each rim point's own true geometric distance to the internal os. Pushing that per-point distance through the same coverage and shear formulas as the 3D model yields a full shear-stress field along the margin instead of a single number: because a disc's curvature means every point away from the single closest one is strictly farther from the os, the field-averaged bleed rate is always at or below the 3D model's single-point estimate for the same edge distance — the field spreads risk across the rim instead of concentrating it all at the one point the 3D model samples, which is the anatomically more realistic picture of a curved placental margin. Spiral-artery inflow on the opposite hemisphere still follows the same Poiseuille r⁴ relation, so the two models can be compared side by side.