The same Biot–Savart kernel that drives the 2D heatmap evaluates a full volumetric H-field on grids up to 100 × 100 × 100. Switch render mode without re-solving — the tensor is shared.
The 3d_volume render mode draws nested isosurfaces of |H| so the geometry of the field becomes legible at a glance. Adjust the threshold with a slider; the surface re-meshes against the cached H-tensor without a second solver call.
Underneath every visualisation is a vectorised voxel grid evaluated via Biot–Savart on NumPy. The 2D plane caps at 500 × 500; the 3D volume at 100 × 100 × 100. LOD levels 0 / 1 / 2 cut grid density in halves and quarters for a 4× speed-up.
The vector_field mode overlays downsampled arrow glyphs on the same tensor — direction at a glance, magnitude through opacity. Density factors of 2 to 4 keep the canvas readable on large coils.
