#!/usr/bin/env python3 """R6.2.4 — 3D chest-centric N-anchor multistatic (compose R6.2.2.1 + R6.2.3). See docs/research/sota-2026-05-22/R6_2_4-3d-chest-multistatic.md. R6.2.2.1 (3D N-anchor on body-footprint zones) showed N=5 gives only 49% coverage in 3D vs 97% in 2D -- the 2D-derived knee disappears. R6.2.2.1 predicted: switching to chest-centric zones (R6.2.3) should recover 80%+ in 3D at N=5. This tick tests that prediction. Pure NumPy. """ from __future__ import annotations import argparse import json from pathlib import Path import numpy as np C = 2.998e8 def wavelength_m(freq_ghz: float) -> float: return C / (freq_ghz * 1e9) def in_first_fresnel_3d(p: np.ndarray, tx: np.ndarray, rx: np.ndarray, wavelength: float) -> np.ndarray: r1 = np.linalg.norm(p - tx, axis=1) r2 = np.linalg.norm(p - rx, axis=1) direct = np.linalg.norm(tx - rx) return (r1 + r2) <= (direct + wavelength / 2) def union_coverage_3d(anchors, target_pts, wavelength): if len(anchors) < 2: return 0.0 covered = np.zeros(len(target_pts), dtype=bool) for i in range(len(anchors)): for j in range(i+1, len(anchors)): mask = in_first_fresnel_3d(target_pts, anchors[i], anchors[j], wavelength) covered |= mask return float(covered.mean()) def rasterise_targets_3d(zones, resolution=0.10): pts = [] for name, x0, y0, z0, dx, dy, dz in zones: xs = np.arange(x0, x0 + dx, resolution) ys = np.arange(y0, y0 + dy, resolution) zs = np.arange(z0, z0 + dz, resolution) gx, gy, gz = np.meshgrid(xs, ys, zs, indexing="ij") for x, y, z in zip(gx.ravel(), gy.ravel(), gz.ravel()): pts.append([x, y, z]) return np.array(pts) def candidate_positions_3d(room_w, room_h, room_z, step=0.75): cands = [] for z in [0.8, 1.5, 2.4]: for x in np.arange(0, room_w + 0.001, step): cands.append(np.array([x, 0.0, z])) cands.append(np.array([x, room_h, z])) for y in np.arange(step, room_h, step): cands.append(np.array([0.0, y, z])) cands.append(np.array([room_w, y, z])) for x in np.arange(1.0, room_w, 1.0): for y in np.arange(1.0, room_h, 1.0): cands.append(np.array([x, y, room_z])) return cands def greedy_search(candidates, target_pts, wavelength, n_anchors, n_restarts=4, seed=0): rng = np.random.default_rng(seed) best = {"anchors": [], "score": -1.0} for restart in range(n_restarts): idx0, idx1 = rng.choice(len(candidates), size=2, replace=False) chosen = [candidates[idx0], candidates[idx1]] while len(chosen) < n_anchors: best_marg = -1.0 best_idx = None for k, c in enumerate(candidates): if any(np.allclose(c, a) for a in chosen): continue score = union_coverage_3d(chosen + [c], target_pts, wavelength) if score > best_marg: best_marg = score best_idx = k if best_idx is None: break chosen.append(candidates[best_idx]) final = union_coverage_3d(chosen, target_pts, wavelength) if final > best["score"]: best = {"anchors": [a.tolist() for a in chosen], "score": final} return best def main(): parser = argparse.ArgumentParser() parser.add_argument("--out", default="examples/research-sota/r6_2_4_3d_chest_results.json") parser.add_argument("--n-max", type=int, default=6) parser.add_argument("--restarts", type=int, default=4) args = parser.parse_args() room_w, room_h, room_z = 5.0, 5.0, 2.5 freq = 2.4 lam = wavelength_m(freq) # 3D chest-centric zones (compose R6.2.3's 2D chest with R6.2.1's 3D heights) # Chest of: lying-down (z=0.3-0.5), sitting (z=0.7-1.0), standing (z=1.2-1.5) chest_zones_3d = [ ("bed_chest", 2.2, 0.8, 0.3, 0.6, 0.4, 0.2), # lying chest at z=0.3-0.5 ("chair_chest", 3.7, 3.7, 0.7, 0.4, 0.4, 0.3), # sitting chest z=0.7-1.0 ("standing_chest", 0.5, 3.7, 1.2, 0.6, 0.4, 0.3), # standing chest z=1.2-1.5 ] target_pts = rasterise_targets_3d(chest_zones_3d, resolution=0.10) candidates = candidate_positions_3d(room_w, room_h, room_z, step=0.75) print(f"Room: {room_w}x{room_h}x{room_z} m at {freq} GHz") print(f"CHEST-CENTRIC 3D targets: {len(target_pts)} points across {len(chest_zones_3d)} zones") print(f"Candidates: {len(candidates)} positions (3 wall heights + ceiling)") print() saturation = [] for n in range(2, args.n_max + 1): result = greedy_search(candidates, target_pts, lam, n_anchors=n, n_restarts=args.restarts) heights = [a[2] for a in result["anchors"]] n_low = sum(1 for h in heights if h < 1.0) n_mid = sum(1 for h in heights if 1.0 <= h < 2.0) n_high = sum(1 for h in heights if h >= 2.0) saturation.append({ "n_anchors": n, "coverage": result["score"], "heights": {"low": n_low, "mid": n_mid, "high": n_high}, "anchors": result["anchors"], }) print("=== 3D chest-centric saturation curve ===") print(f"{'N':>3} {'Coverage':>9} {'Marginal':>9} {'Heights L/M/H':>15}") prev = 0.0 for s in saturation: marg = (s["coverage"] - prev) * 100 h = s["heights"] print(f"{s['n_anchors']:>3} {s['coverage']*100:>7.1f}% {marg:>+7.1f} pp {h['low']}/{h['mid']}/{h['high']:>5}") prev = s["coverage"] # Compare to R6.2.2.1 (3D body-centric) at same N print() print("=== R6.2.2.1 prediction validation ===") print(f"R6.2.2.1 said: 'chest-centric should recover N=5 to 80%+ in 3D.'") n5 = next(s for s in saturation if s["n_anchors"] == 5) if n5["coverage"] >= 0.8: print(f"VALIDATED: 3D chest-centric N=5 = {n5['coverage']*100:.1f}% (>= 80% target)") elif n5["coverage"] >= 0.7: print(f"PARTIAL: 3D chest-centric N=5 = {n5['coverage']*100:.1f}% (close to 80% target)") else: print(f"NOT VALIDATED: 3D chest-centric N=5 = {n5['coverage']*100:.1f}% (well below 80%)") print() # Full 4-way comparison print("=== 4-way comparison at N=5 ===") print(f" R6.2.2 (2D body): 96.8%") print(f" R6.2.3 (2D chest): 82.4%") print(f" R6.2.2.1 (3D body): 49.4%") print(f" R6.2.4 (3D chest): {n5['coverage']*100:.1f}% (this tick)") out = { "room": {"width_m": room_w, "depth_m": room_h, "ceiling_m": room_z}, "freq_ghz": freq, "target_zones": [ {"name": n, "x": x0, "y": y0, "z": z0, "dx": dx, "dy": dy, "dz": dz} for n, x0, y0, z0, dx, dy, dz in chest_zones_3d ], "saturation": saturation, "comparison_at_n5": { "r6_2_2_2d_body": 0.968, "r6_2_3_2d_chest": 0.824, "r6_2_2_1_3d_body": 0.494, "r6_2_4_3d_chest": n5["coverage"], }, } Path(args.out).parent.mkdir(parents=True, exist_ok=True) Path(args.out).write_text(json.dumps(out, indent=2)) print(f"\nWrote {args.out}") if __name__ == "__main__": main()