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"""Sunken plateaus: Kerguelen-type continental crust that never rose. Outline,
surface and volcanic field are functions of position and the plateau's config (deterministic per name), so the world
build, the seabed pass and the viewer agree at any resolution."""
from __future__ import annotations
import numpy as np
from .graph import distance_to
from .noise import fbm, name_seed
from .sphere import east_north, gc_dist_km, great_circle_point, latlon_to_xyz, tangent_dir, xyz_to_latlon
from .zones import smootherstep
EDGE_WARP = 0.15 # outline radius ± 15 % (fractal noise): bays and lobes, like a small continent
MARGIN_KM = 150.0 # the surface blends down to the surrounding sea floor over this distance inside the outline
RELIEF_M = 400.0 # internal relief (ridges, basins)
HIDDEN_MAX_M = -550.0 # hidden plateaus: every cell at least this deep (checked at −500 m after erosion's re-solve)
SITE_RULES = (("land", 400.0), ("a plate boundary", 150.0), ("the trench", 200.0)) # km from the outline
def semi_axes(p: dict):
"""(long, short) semi-axes (km) of the plateau's ellipse: π·a·b = area_km2, a / b = elongation."""
e = float(p.get("elongation", 1.0))
b = float(np.sqrt(p["area_km2"] / (np.pi * e)))
return e * b, b
def _near(xyz, p, radius_km, pad_km=0.0):
a, _ = semi_axes(p)
lim = min(np.pi, (a * (1.0 + EDGE_WARP) / (1.0 - EDGE_WARP) + pad_km) / radius_km)
return xyz @ latlon_to_xyz(*p["center"]) > np.cos(lim)
def rho(xyz, p: dict, seed: int, radius_km: float):
"""Normalised radius of points: 0 at the centre, < 1 inside the noise-warped elliptical outline."""
xyz = np.asarray(xyz, dtype=np.float64)
c = latlon_to_xyz(*p["center"])
e, n = east_north(c[None])
ang = np.arccos(np.clip(xyz @ c, -1.0, 1.0)) * radius_km # km from the centre along the surface
t = tangent_dir(np.broadcast_to(c, xyz.shape), xyz)
x, y = ang * (t @ e[0]), ang * (t @ n[0]) # east, north (azimuthal equidistant)
az = np.radians(p.get("azimuth_deg", 0.0))
along, across = x * np.sin(az) + y * np.cos(az), x * np.cos(az) - y * np.sin(az)
a, b = semi_axes(p)
r = np.sqrt((along / a) ** 2 + (across / b) ** 2)
w = np.clip(2.0 * fbm(xyz, name_seed(seed, p["name"]), 4, 25.0), -1.0, 1.0)
return r / (1.0 + EDGE_WARP * w)
def cell_ids(xyz, plateaus: list, seed: int, radius_km: float):
"""Plateau index per point (−1 outside every plateau)."""
xyz = np.asarray(xyz, dtype=np.float64)
ids = np.full(len(xyz), -1, np.int16)
for k, p in enumerate(plateaus):
idx = np.flatnonzero(_near(xyz, p, radius_km))
if len(idx):
ids[idx[rho(xyz[idx], p, seed, radius_km) < 1.0]] = k
return ids
def _place(rng, p, seed, radius_km, origin, max_km, inside=0.85, tries=30):
"""A random point within max_km of origin inside the outline (rho < inside); None if none is found."""
e, n = east_north(origin[None])
for _ in range(tries):
az, dist = rng.uniform(0.0, 2.0 * np.pi), rng.uniform(0.0, max_km)
q = great_circle_point(origin, np.sin(az) * e[0] + np.cos(az) * n[0], dist, radius_km)
if rho(q[None], p, seed, radius_km)[0] < inside:
return q
return None
def _ll(q):
lat, lon = xyz_to_latlon(np.asarray(q, dtype=np.float64))
return round(float(lat), 4), round(float(lon), 4)
def features(p: dict, seed: int, radius_km: float) -> dict:
"""The plateau's volcanic field at world scale (deterministic per name): its own hotspot point, 6–20 cones and
1–3 calderas (none when vent = 0); island plateaus lift 3–6 of the cones to +0.6…+1.5 km."""
rng = np.random.default_rng(name_seed(seed, p["name"]) + 7)
c = latlon_to_xyz(*p["center"])
_, b = semi_axes(p)
vent = float(p.get("vent", 1.0))
hot = _place(rng, p, seed, radius_km, c, 0.3 * b)
hot = c if hot is None else hot
cones, calderas = [], []
if vent > 0:
for _ in range(int(rng.integers(6, 21))):
q = _place(rng, p, seed, radius_km, hot, 0.6 * b)
r_km, h = float(rng.uniform(15.0, 40.0)), float(rng.uniform(500.0, 2000.0)) * vent
if q is not None:
lat, lon = _ll(q)
cones.append({"lat": lat, "lon": lon, "radius_km": r_km, "height_m": h, "island": False})
for _ in range(int(rng.integers(1, 4))):
q = _place(rng, p, seed, radius_km, hot, 0.5 * b)
r_km = float(rng.uniform(20.0, 50.0))
if q is not None:
lat, lon = _ll(q)
calderas.append({"lat": lat, "lon": lon, "radius_km": r_km, "rim_m": 300.0 * vent,
"floor_m": -400.0 * vent})
if p.get("islands", False) and cones:
k = min(len(cones), int(rng.integers(3, 7)))
for i in rng.choice(len(cones), size=k, replace=False):
cones[int(i)].update(island=True, peak_m=float(rng.uniform(600.0, 1500.0)),
radius_km=float(rng.uniform(40.0, 70.0)))
return {"name": p["name"], "center": [float(v) for v in p["center"]], "hotspot": list(_ll(hot)),
"cones": cones, "calderas": calderas}
def surface(xyz, p: dict, feat: dict, seed: int, radius_km: float, z_floor):
"""Heights of points inside the outline: the plateau top (depth across top_m by low-frequency noise, ± RELIEF_M)
plus its cones and calderas, blended down to z_floor over MARGIN_KM inside the edge."""
xyz = np.asarray(xyz, dtype=np.float64)
s = name_seed(seed, p["name"])
t = np.clip(0.5 + 1.5 * fbm(xyz, s + 1, 3, 8.0), 0.0, 1.0)
top0, top1 = p["top_m"]
z = -(top0 + (top1 - top0) * t) + RELIEF_M * np.clip(2.5 * fbm(xyz, s + 2, 5, 40.0), -1.0, 1.0)
for c in feat["cones"]:
if not c["island"]:
d = gc_dist_km(xyz, latlon_to_xyz(c["lat"], c["lon"]), radius_km)
z = z + c["height_m"] * np.clip(1.0 - d / c["radius_km"], 0.0, 1.0) ** 1.5
for c in feat["calderas"]:
d = gc_dist_km(xyz, latlon_to_xyz(c["lat"], c["lon"]), radius_km)
r = c["radius_km"]
z = z + c["rim_m"] * np.exp(-((d - r) / (0.25 * r)) ** 2) + c["floor_m"] * (1.0 - smootherstep(d / r))
_, b = semi_axes(p)
w = smootherstep((1.0 - rho(xyz, p, seed, radius_km)) * b / MARGIN_KM)
return np.asarray(z_floor, dtype=np.float64) + (z - z_floor) * w
def islands(xyz, feat: dict, radius_km: float, z):
"""Island cones lift the ground to their peak_m (small volcanic islands); only raises."""
z = np.asarray(z, dtype=np.float64)
for c in feat["cones"]:
if c["island"]:
d = gc_dist_km(np.asarray(xyz, dtype=np.float64), latlon_to_xyz(c["lat"], c["lon"]), radius_km)
f = np.clip(d / c["radius_km"], 0.0, 1.0)
z = np.where(d < c["radius_km"], np.maximum(z, c["peak_m"] - (c["peak_m"] - z) * f ** 1.2), z)
return z
def apply(g, z, plateaus: list, plateau_id, seed: int):
"""Grid heights with the plateaus set (after the world's sea-level solve): surfaces and volcanic fields; hidden
plateaus clamped to HIDDEN_MAX_M; islands, each island's nearest cell raised to its peak (so every resolution
keeps it)."""
z = np.asarray(z, dtype=np.float64).copy()
R = g.radius_km
for k, p in enumerate(plateaus):
idx = np.flatnonzero(np.asarray(plateau_id) == k)
if len(idx) == 0:
continue
feat = features(p, seed, R)
zk = surface(g.xyz[idx], p, feat, seed, R, z[idx])
if p.get("islands", False):
z[idx] = islands(g.xyz[idx], feat, R, zk)
for c in feat["cones"]:
if c["island"]:
i = g.cell_index(c["lat"], c["lon"])
z[i] = max(z[i], c["peak_m"])
else:
z[idx] = np.minimum(zk, HIDDEN_MAX_M)
return z
def site_report(g, data: dict, plateaus: list) -> list:
"""Plateaus that no longer fit their site on this world, as warnings: outline ≥ 400 km from land,
≥ 150 km from plate boundaries, ≥ 200 km from the sketch's trench. Reported, never moved."""
ids = np.asarray(data["plateau_id"])
masks = {"land": ~np.asarray(data["ocean"]) & (ids < 0), "a plate boundary": np.asarray(data["bnd_type"]) > 0,
"the trench": np.asarray(data.get("sk_trench", np.zeros(g.n))) > 0.5}
out = []
for what, lim in SITE_RULES:
if not masks[what].any():
continue
d = distance_to(g, masks[what])
for k, p in enumerate(plateaus):
m = ids == k
if m.any() and float(d[m].min()) < lim:
out.append(f"plateau {p['name']}: {float(d[m].min()):.0f} km from {what} (rule ≥ {lim:.0f} km)")
return out
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