# Stage 6h: bi-harmonic membrane over the located flap sphere. Melting (06g) barely dented
# the fold — layered flaps are locally smooth and resist neighbour-averaging. Replace instead:
# excise the sphere, solve the rim-anchored membrane (same method that healed the gusset).
#   blender --background --python 06h_flap_membrane.py -- <in.blend> <out.blend> <cx> <cy> <cz> <r>
import bpy, sys, time
import numpy as np

argv = sys.argv[sys.argv.index("--") + 1:]
BLEND, OUT = argv[0], argv[1]
CTR = np.array([float(argv[2]), float(argv[3]), float(argv[4])])
R = float(argv[5])
t0 = time.time()


def log(m):
    print(f"[flap {time.time()-t0:6.1f}s] {m}", flush=True)


bpy.ops.wm.open_mainfile(filepath=BLEND)
ob = max([o for o in bpy.data.objects if o.type == 'MESH'],
         key=lambda o: len(o.data.vertices))
me = ob.data
n_v = len(me.vertices)
co = np.empty(n_v * 3)
me.vertices.foreach_get("co", co)
co = co.reshape(-1, 3)

n_e = len(me.edges)
ev0 = np.empty(n_e * 2, dtype=np.int32)
me.edges.foreach_get("vertices", ev0)
ev0 = ev0.reshape(-1, 2)


def grow_edges(mask, rings, ev):
    m = mask.copy()
    for _ in range(rings):
        hit = m[ev[:, 0]] | m[ev[:, 1]]
        m2 = m.copy()
        m2[ev[:, 0]] |= hit
        m2[ev[:, 1]] |= hit
        m = m2
    return m


sph = np.linalg.norm(co - CTR, axis=1) < R
free_m = grow_edges(sph, 1, ev0)
collar = grow_edges(free_m, 2, ev0) & ~free_m
S = np.nonzero(free_m | collar)[0]
in_S = np.zeros(n_v, dtype=bool)
in_S[S] = True
glb = np.full(n_v, -1, dtype=np.int64)
glb[S] = np.arange(len(S))
se = ev0[in_S[ev0].all(axis=1)]
a_ = glb[se[:, 0]]
b_ = glb[se[:, 1]]
deg = np.zeros(len(S))
np.add.at(deg, a_, 1.0)
np.add.at(deg, b_, 1.0)
free = free_m[S]
log(f"sphere {sph.sum()} -> free {free.sum()}, collar {(~free).sum()}")


def Ls(X):
    out = deg[:, None] * X
    np.add.at(out, a_, -X[b_])
    np.add.at(out, b_, -X[a_])
    return out


def A_op(U):
    X = np.zeros((len(S), 3))
    X[free] = U
    return Ls(Ls(X))[free]


Xc = np.zeros((len(S), 3))
Xc[~free] = co[S[~free]]
rhs = -Ls(Ls(Xc))[free]
U = co[S[free]].copy()
r = rhs - A_op(U)
p = r.copy()
rs = (r * r).sum()
rs0 = rs
for it in range(120000):
    Ap = A_op(p)
    al = rs / max((p * Ap).sum(), 1e-30)
    U += al * p
    r -= al * Ap
    rs2 = (r * r).sum()
    if rs2 < 1e-18 or rs2 < rs0 * 1e-14:
        break
    p = r + (rs2 / rs) * p
    rs = rs2
co_new = co.copy()
co_new[S[free]] = U
d = np.linalg.norm(co_new - co, axis=1)
log(f"membrane: {free.sum()} verts (CG {it} iters, rel {rs2/max(rs0,1e-30):.2e}), "
    f"max move {d.max():.4f}")

me.vertices.foreach_set("co", co_new.reshape(-1))
me.update()
if me.has_custom_normals:
    vn = np.empty(n_v * 3, dtype=np.float32)
    me.vertices.foreach_get("normal", vn)
    me.normals_split_custom_set_from_vertices(vn.reshape(-1, 3))
bpy.context.preferences.filepaths.save_version = 0  # no .blend1 autosave
bpy.ops.wm.save_as_mainfile(filepath=OUT)
log(f"WROTE {OUT}")
print("FLAP_DONE")