hesuicong/openMVS
1
0 Fork 0
Code Issues Pull Requests Actions Projects Releases Wiki Activity
Files
6f7805c78dbf652b72e50e9b5ecfe0f62ba0ff5c
openMVS/fill2sc/generate_fill_mesh.py
T
hesuicong 6f7805c78d 上传代码
2026-11-09 10:05:17 +08:00

1178 lines
48 KiB
Python
Raw Blame History

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
generate_fill_mesh.py
=====================
为 3D 打印模型生成"眼镜 <-> 脸部"之间镂空区域的填充网格。
输入（与本脚本同目录）:
632723.obj 完整模型(封闭网格)
index.txt 眼镜区域的顶点索引(每行一个, 1-based)
输出(同目录):
fill_mesh.obj 填充网格(独立、封闭、水密)
632723_filled.obj 原模型 + 填充 合并后的模型(可直接用于切片打印)
fill_preview.png 前视图深度预览(供人工检查)
原理:
1. 栅格化眼镜区域三角形 -> 眼镜足迹 mask(补洞=镜片开口, 腐蚀收边)
2. 对足迹内每个 (x,y) 竖直射线求交:
镜框管前/后面, 脸面前表面, 网格最后表面
3. 填充体 = 高度场实体:
前表面 h_front: 贴住镜框前面(留 FLUSH 嵌入余量, 与镜框平齐),
镜片开口区域 = 框前面的稳健二次拟合趋势面
+ 拟合残差的调和延拓(交界处严格连续, 无折痕),
且不超过附近镜框前面(小半径扩散最大值钳制)
后表面 h_back : 有真实脸面处 = 脸面 - 嵌入深度(填满镂空),
无真实脸面处(误标区)不低于 hf - SHELL_MAX(填充只在镜框附近),
且不低于后脑表面
4. 足迹边界提取 -> 重采样 -> 闭合 Laplacian 平滑(外边界平滑)
5. 区域三角化: 耳切法 + 内部网格点逐点插入(拆分所在三角形,
拓扑上不可能翻转), 前后表面 + 侧墙组成水密封闭实体
6. 输出前做数值校验(水密/定向/无翻转/覆盖/嵌入深度/边界平滑度)
仅依赖 numpy 与 PIL。
"""
import numpy as np
from collections import deque
from PIL import Image, ImageDraw
# ----------------------------- 参数 -----------------------------
IN_OBJ = "632723.obj"
IN_IDX = "index.txt"
OUT_FILL = "fill_mesh.obj"
OUT_MERGED = "632723_filled.obj"
OUT_PREVIEW = "fill_preview.png"
RES = 0.1 # 栅格分辨率
X0, X1 = -10.2, 10.2
Y0, Y1 = 9.2, 19.8
RY0, RY1 = 9.7, 19.3 # 填充区域 y 裁剪(只处理正面眼镜部分)
SEP = 0.25 # 区分前后表面的最小 z 间距
FLUSH = 0.15 # 填充前表面距镜框前面的距离(与镜框平齐, 留嵌入余量)
EMBED_BOT = 0.6 # 填充底面嵌入脸部深度
SHELL_MAX = 3.0 # 无真实脸面处的填充厚度上限(相对前表面)
FACE_MIN = 2.0 # 脸面低于此值视为误标伪面(后脑等), 不作填充底面
CLAMP_BACK = 0.4 # 距最后表面的安全距离(防穿出后脑)
GAP_MIN = 0.25 # 填充最小厚度
SIGMA = 2.0 # 高度场平滑 sigma(格)
ERODE = 2 # 足迹腐蚀(格) 0.2, 与膨胀0.3配合净外扩0.1(补偿边界平滑收缩)
BSTEP = 0.18 # 边界重采样步长
BITER = 25 # 边界 Laplacian 平滑迭代
BLAM = 0.6 # 边界平滑系数
TOL = 1e-4 # Jacobi 收敛阈值
report = []
def log(s):
print(s)
report.append(str(s))
# ----------------------------- IO -----------------------------
def parse_obj(path):
vs, fs = [], []
with open(path) as f:
for line in f:
if line.startswith("v "):
p = line.split()
vs.append((float(p[1]), float(p[2]), float(p[3])))
elif line.startswith("f "):
p = line.split()
fs.append((int(p[1].split("/")[0]) - 1,
int(p[2].split("/")[0]) - 1,
int(p[3].split("/")[0]) - 1))
return np.asarray(vs), np.asarray(fs, dtype=np.int64)
log("== 1. 读入模型 ==")
V, F = parse_obj(IN_OBJ)
idx = np.loadtxt(IN_IDX, dtype=np.int64) - 1
ism = np.zeros(len(V), bool)
ism[idx] = True
face_g = ism[F].any(1)
log(f" 顶点 {len(V)}, 面 {len(F)}, 眼镜标记顶点 {len(idx)}")
# 真眼镜物体提取: 标记面的"边连通"主分量. 眼镜与头部网格互不共边,
# 误标皮肤(鼻梁/额头/后脑, 分割噪声)在边连通下是独立小分量 -> 一次性剥离;
# 剥离后的皮肤面自然归入脸面栅格 fz(它们本来就是头部表面).
# 这样足迹/外边框直接来自真眼镜几何, 无需 2D 启发式清洗.
emap = {}
for _fi in np.where(face_g)[0]:
_a, _b, _c = F[_fi]
for _u, _v in ((_a, _b), (_b, _c), (_c, _a)):
_e = (_u, _v) if _u < _v else (_v, _u)
if _e in emap:
emap[_e].append(_fi)
else:
emap[_e] = [_fi]
_seen = set()
_best = []
for _fi in np.where(face_g)[0]:
if _fi in _seen:
continue
_comp, _stk = [], [_fi]
_seen.add(_fi)
while _stk:
_f0 = _stk.pop()
_comp.append(_f0)
_a, _b, _c = F[_f0]
for _u, _v in ((_a, _b), (_b, _c), (_c, _a)):
_e = (_u, _v) if _u < _v else (_v, _u)
for _f2 in emap[_e]:
if _f2 not in _seen:
_seen.add(_f2)
_stk.append(_f2)
if len(_comp) > len(_best):
_best = _comp
face_g = np.zeros(len(F), bool)
face_g[_best] = True
log(f" 眼镜物体 = 边连通主分量 {len(_best)} 面, "
f"剥离误标皮肤 {int((ism[F].any(1)).sum() - len(_best))} 面")
# ----------------------------- 栅格 -----------------------------
W = int(round((X1 - X0) / RES)) + 1
H = int(round((Y1 - Y0) / RES)) + 1
log(f"== 2. 栅格化 (窗口 x[{X0},{X1}] y[{Y0},{Y1}], res={RES}, {W}x{H}) ==")
gz1 = np.full((H, W), -np.inf) # 眼镜最前表面
gz2 = np.full((H, W), -np.inf) # 眼镜第二表面(镜框管背面)
fz = np.full((H, W), -np.inf) # 非眼镜最前表面(脸)
bz = np.full((H, W), np.inf) # 全网格最后表面(后脑)
mvert = np.zeros((H, W), np.int32) # 眼镜顶点计数
yi = np.clip(((V[ism, 1] - Y0) / RES).astype(int), 0, H - 1)
xi = np.clip(((V[ism, 0] - X0) / RES).astype(int), 0, W - 1)
np.add.at(mvert, (yi, xi), 1)
inwin = ((V[:, 0] > X0 - 0.5) & (V[:, 0] < X1 + 0.5) &
(V[:, 1] > Y0 - 0.5) & (V[:, 1] < Y1 + 0.5))
fwin = inwin[F].all(1)
log(f" 窗口内三角形 {int(fwin.sum())} (其中眼镜 {(face_g & fwin).sum()})")
A, B, C = V[F[:, 0]], V[F[:, 1]], V[F[:, 2]]
fi = np.where(fwin)[0]
for t in fi:
ax, ay, az = A[t]; bx, by, bz_ = B[t]; cx, cy, cz = C[t]
g = face_g[t]
i0 = max(int((min(ax, bx, cx) - X0) / RES), 0)
i1 = min(int((max(ax, bx, cx) - X0) / RES), W - 1)
j0 = max(int((min(ay, by, cy) - Y0) / RES), 0)
j1 = min(int((max(ay, by, cy) - Y0) / RES), H - 1)
if i1 < i0 or j1 < j0:
continue
v0x, v0y = cx - ax, cy - ay
v1x, v1y = bx - ax, by - ay
d00 = v0x * v0x + v0y * v0y
d01 = v0x * v1x + v0y * v1y
d11 = v1x * v1x + v1y * v1y
den = d00 * d11 - d01 * d01
if abs(den) < 1e-14:
continue
for j in range(j0, j1 + 1):
py = Y0 + j * RES
for i in range(i0, i1 + 1):
px = X0 + i * RES
v2x, v2y = px - ax, py - ay
d02 = v0x * v2x + v0y * v2y
d12 = v1x * v2x + v1y * v2y
u = (d11 * d02 - d01 * d12) / den # 权重 C
v = (d00 * d12 - d01 * d02) / den # 权重 B
if u < 0 or v < 0 or u + v > 1:
continue
z = az + u * (cz - az) + v * (bz_ - az)
if g:
if z > gz1[j, i] + 1e-9:
if z - gz1[j, i] > SEP and gz1[j, i] > -np.inf:
gz2[j, i] = max(gz2[j, i], gz1[j, i])
gz1[j, i] = z
elif z < gz1[j, i] - SEP and z > gz2[j, i]:
gz2[j, i] = z
else:
if z > fz[j, i]:
fz[j, i] = z
if z < bz[j, i]:
bz[j, i] = z
have_g1 = np.isfinite(gz1) & (gz1 > -1e30)
have_g2 = np.isfinite(gz2) & (gz2 > -1e30)
have_f = np.isfinite(fz) & (fz > -1e30)
have_b = np.isfinite(bz) & (bz < 1e30)
# 眼镜表面场: face_g 已是边连通主分量(真眼镜物体), 无需再按 z 剪杂散.
# 镜圈尾部向耳朵方向包裹折返(最高面 z 从 9.1 一路降到 0.5),
# 这些格必须进入足迹/框带, 否则尾部下镂空填不上(出现缝隙)
g1f = have_g1
log(f" 有眼镜表面格 {have_g1.sum()}, 管状(双面) {have_g2.sum()}, "
f"有脸面 {have_f.sum()}, 有背面 {have_b.sum()}")
# ----------------------- 足迹 mask 与填充区域 R -----------------------
log("== 3. 眼镜足迹 / 填充区域 R ==")
# 足迹 = 真眼镜物体(边连通主分量)覆盖的全部格子(含尾部包裹段).
# 误标杂散已在 face_g 阶段剥离, 无需 z 高度过滤; 旧 gz1>=7 过滤会剪掉
# 尾部折返带(z 低于 7) -> 尾部镂空填不上
mask = g1f
_labs = np.zeros(mask.shape, np.int32)
_cur = 0
from collections import deque as _dq
for _j in range(mask.shape[0]):
for _i in range(mask.shape[1]):
if mask[_j, _i] and _labs[_j, _i] == 0:
_cur += 1
_q = _dq([(_j, _i)])
_labs[_j, _i] = _cur
while _q:
_y, _x = _q.popleft()
for _dj, _di in ((1,0),(-1,0),(0,1),(0,-1),(1,1),(1,-1),(-1,1),(-1,-1)):
_yy, _xx = _y + _dj, _x + _di
if (0 <= _yy < mask.shape[0] and 0 <= _xx < mask.shape[1]
and mask[_yy, _xx] and _labs[_yy, _xx] == 0):
_labs[_yy, _xx] = _cur
_q.append((_yy, _xx))
_sizes = np.bincount(_labs.ravel())
_sizes[0] = 0
_main = int(np.argmax(_sizes))
_nstray = int(mask.sum() - _sizes[_main])
mask = _labs == _main
log(f" 足迹取主分量: 剔除杂散块 {_nstray} 格 (误标到镜框外的皮肤/后脑)")
# 中央区剪除(鼻侧多余填充的根源): 镜框外边框在鼻侧 = 镜桥底缘.
# 镜片开口(足迹的大内部洞)之间的中央区里, 开口底缘以下的"眼镜覆盖"
# 是误标鼻面皮肤悬挂半岛 -> 剪掉, 填充严格按镜框外边框
def _flood_out(msk):
out = np.zeros_like(msk, bool)
q = _dq()
for i in range(msk.shape[1]):
for j in (0, msk.shape[0] - 1):
if not msk[j, i] and not out[j, i]:
out[j, i] = True; q.append((j, i))
for j in range(msk.shape[0]):
for i in (0, msk.shape[1] - 1):
if not msk[j, i] and not out[j, i]:
out[j, i] = True; q.append((j, i))
while q:
y, x = q.popleft()
for dj, di in ((1,0),(-1,0),(0,1),(0,-1)):
yy, xx = y + dj, x + di
if 0 <= yy < msk.shape[0] and 0 <= xx < msk.shape[1] and not msk[yy, xx] and not out[yy, xx]:
out[yy, xx] = True; q.append((yy, xx))
return out
_holes = ~mask & ~_flood_out(mask)
_hl = np.zeros(mask.shape, np.int32)
_big = []
for _j in range(mask.shape[0]):
for _i in range(mask.shape[1]):
if _holes[_j, _i] and _hl[_j, _i] == 0:
_hl[_j, _i] = 1
_q = _dq([(_j, _i)])
_pts = [(_j, _i)]
while _q:
_y, _x = _q.popleft()
for _dj, _di in ((1,0),(-1,0),(0,1),(0,-1),(1,1),(1,-1),(-1,1),(-1,-1)):
_yy, _xx = _y + _dj, _x + _di
if (0 <= _yy < mask.shape[0] and 0 <= _xx < mask.shape[1]
and _holes[_yy, _xx] and _hl[_yy, _xx] == 0):
_hl[_yy, _xx] = 1
_q.append((_yy, _xx))
_pts.append((_yy, _xx))
if len(_pts) >= 500:
_big.append(_pts)
if len(_big) >= 2:
# 按 x 中心排序, 区分左右开口
_big.sort(key=len, reverse=True)
h_l, h_r = sorted(_big[:2], key=lambda pts: sum(p[1] for p in pts) / len(pts))
# 每个开口的 x 范围与底缘 y
def _bbox(pts):
return (min(p[1] for p in pts), max(p[1] for p in pts), min(p[0] for p in pts))
bl, br = _bbox(h_l), _bbox(h_r)
x_in_l = bl[1] # 左开口右缘(内缘)
x_in_r = br[0] # 右开口左缘(内缘)
y_cut = min(bl[2], br[2]) # 开口底缘(取较低者)
if x_in_l < x_in_r:
_cut = np.zeros_like(mask, bool)
_cut[:y_cut, x_in_l + 1:x_in_r] = True
_ncut = int((mask & _cut).sum())
mask &= ~_cut
log(f" 中央区剪除(两镜片开口之间, 开口底缘 y>{Y0 + y_cut * RES:.1f} 以下): "
f"剔除 {_ncut} 格误标鼻面")
else:
log(" ! 未找到两个镜片开口, 跳过中央区剪除")
# 膨胀 3 格(~0.3) 闭合采样缝隙, 防止镜片开口与外部连通;
# 与腐蚀 2 格(0.2) 配合净外扩 0.1: 边界平滑会压扁凸部(尾部舌形)~0.2,
# 预留外扩让平滑后的边界落在足迹外缘, 镜框下镂空填到边(真外轮廓
# 比栅格覆盖宽~0.1-0.2, 不会超出镜框)
for _ in range(3):
nm = mask.copy()
nm[1:, :] |= mask[:-1, :]; nm[:-1, :] |= mask[1:, :]
nm[:, 1:] |= mask[:, :-1]; nm[:, :-1] |= mask[:, 1:]
nm[1:, 1:] |= mask[:-1, :-1]; nm[:-1, :-1] |= mask[1:, 1:]
nm[1:, :-1] |= mask[:-1, 1:]; nm[:-1, 1:] |= mask[1:, :-1]
mask = nm
def flood_outside(mask):
"""从窗口边界洪泛, 标记外部; 未标记且非 mask 即为洞"""
outside = np.zeros_like(mask, bool)
dq = deque()
for i in range(mask.shape[1]):
for j in (0, mask.shape[0] - 1):
if not mask[j, i] and not outside[j, i]:
outside[j, i] = True; dq.append((j, i))
for j in range(mask.shape[0]):
for i in (0, mask.shape[1] - 1):
if not mask[j, i] and not outside[j, i]:
outside[j, i] = True; dq.append((j, i))
while dq:
j, i = dq.popleft()
for dj, di in ((1,0),(-1,0),(0,1),(0,-1)):
nj, ni = j + dj, i + di
if 0 <= nj < mask.shape[0] and 0 <= ni < mask.shape[1]:
if not mask[nj, ni] and not outside[nj, ni]:
outside[nj, ni] = True; dq.append((nj, ni))
return ~outside & ~mask
holes = flood_outside(mask)
log(f" 足迹 {mask.sum()} 格, 补内部洞 {holes.sum()} 格 (镜片开口)")
mask = mask | holes
# 腐蚀(膨胀0.3 + 腐蚀0.2 => 净外扩0.1): 预补偿边界平滑对凸部的压扁,
# 让最终边界贴足迹外缘, 镜框下镂空(尾部包裹段等)填满到边
er = mask.copy()
for _ in range(ERODE):
ne = er.copy()
ne[1:, :] &= er[:-1, :]; ne[:-1, :] &= er[1:, :]
ne[:, 1:] &= er[:, :-1]; ne[:, :-1] &= er[:, 1:]
er = ne
# y 裁剪 + 最大连通块
jj = np.arange(H)
er = er & (jj[:, None] >= int((RY0 - Y0) / RES)) & (jj[:, None] <= int((RY1 - Y0) / RES))
R = np.zeros_like(er)
seen = np.zeros_like(er, bool)
best = None
for j0 in range(H):
for i0 in range(W):
if er[j0, i0] and not seen[j0, i0]:
comp = []
dq = deque([(j0, i0)])
seen[j0, i0] = True
touch = False
while dq:
j, i = dq.popleft(); comp.append((j, i))
if i in (0, W - 1) or j in (0, H - 1):
touch = True
for dj, di in ((1,0),(-1,0),(0,1),(0,-1)):
nj, ni = j + dj, i + di
if 0 <= nj < H and 0 <= ni < W and er[nj, ni] and not seen[nj, ni]:
seen[nj, ni] = True; dq.append((nj, ni))
if best is None or len(comp) > len(best[0]):
best = (comp, touch)
if best is None:
raise SystemExit("R 为空: 足迹检测失败")
comp, touch = best
for j, i in comp:
R[j, i] = True
log(f" R: {R.sum()} 格 ({R.sum()*RES*RES:.2f} 面积单位), "
f"触碰窗口边界={touch} (触碰=侧墙切在头内部, 正常)")
if R.sum() < 200:
raise SystemExit("R 过小")
# ----------------------- 高度场 -----------------------
log("== 4. 构造填充前/后高度场 ==")
def smooth_valid(Fld, valid, sigma=SIGMA, it=1):
"""归一化高斯卷积(只在 valid 上)"""
rad = int(3 * sigma)
k = np.exp(-0.5 * (np.arange(-rad, rad + 1) / sigma) ** 2)
Fld = Fld.copy()
for _ in range(it):
acc = np.zeros_like(Fld); accw = np.zeros_like(Fld)
val = valid & np.isfinite(Fld)
G = np.where(val, Fld, 0.0); M = val.astype(float)
tmp = np.zeros_like(G); tmpw = np.zeros_like(G)
for d in range(-rad, rad + 1):
if d == 0:
tmp += G * k[rad]; tmpw += M * k[rad]
elif d > 0:
tmp[d:, :] += G[:-d, :] * k[rad + d]; tmpw[d:, :] += M[:-d, :] * k[rad + d]
tmp[:-d, :] += G[d:, :] * k[rad + d]; tmpw[:-d, :] += M[d:, :] * k[rad + d]
acc += tmp; accw += tmpw
tmp = np.zeros_like(G); tmpw = np.zeros_like(G)
for d in range(-rad, rad + 1):
if d == 0:
tmp += acc * k[rad]; tmpw += accw * k[rad]
elif d > 0:
tmp[:, d:] += acc[:, :-d] * k[rad + d]; tmpw[:, d:] += accw[:, :-d] * k[rad + d]
tmp[:, :-d] += acc[:, d:] * k[rad + d]; tmpw[:, :-d] += accw[:, d:] * k[rad + d]
out = np.where(tmpw > 1e-9, tmp / np.maximum(tmpw, 1e-9), Fld)
Fld = np.where(val, out, Fld)
return Fld
def laplace_fill(Fld, known, iters=6000):
"""Dirichlet: known 固定, 其余解调和方程
缺失邻居(网格边缘)用反射(补 F 自身), 恒除以 4 保证系数和=1(收敛)"""
F = Fld.copy()
with np.errstate(all='ignore'):
mean_known = np.nanmean(F[known]) if known.any() else 0.0
if not np.isfinite(mean_known):
mean_known = 0.0
# 非 known 的格子: 有限值保留, NaN/inf 用已知均值初始化
F[~known] = np.where(np.isfinite(F[~known]), F[~known], mean_known)
for it in range(iters):
avg = np.zeros_like(F)
for dj, di in ((1,0),(-1,0),(0,1),(0,-1)):
s = np.roll(F, (dj, di), axis=(0, 1))
ok = np.ones_like(F, bool)
if dj == 1: ok[0, :] = False
if dj == -1: ok[-1, :] = False
if di == 1: ok[:, 0] = False
if di == -1: ok[:, -1] = False
avg += np.where(ok, s, F) # 缺失邻居补 F 自身(反射)
G = np.where(known, F, avg / 4.0) # 恒除 4: 系数和 = 1
df = np.abs(G - F)[~known]
delta = np.nanmax(df) if df.size and np.isfinite(df).any() else 0.0
F = G
if delta < TOL * RES:
break
return F
gx, gy = np.meshgrid(X0 + np.arange(W) * RES, Y0 + np.arange(H) * RES)
# 补 g1f 栅格化小洞(陡峭角落的覆盖缺口): 闭运算(膨胀2再腐蚀2)
g1c = g1f.copy()
for _ in range(2):
gd = g1c.copy()
for dj, di in ((1,0),(-1,0),(0,1),(0,-1),(1,1),(1,-1),(-1,1),(-1,-1)):
if dj == 1: gd[1:, :] |= g1c[:-1, :]
elif dj == -1: gd[:-1, :] |= g1c[1:, :]
elif di == 1: gd[:, 1:] |= g1c[:, :-1]
elif di == -1: gd[:, :-1] |= g1c[:, 1:]
elif dj == 1 and di == 1: gd[1:, 1:] |= g1c[:-1, :-1]
elif dj == 1 and di == -1: gd[1:, :-1] |= g1c[:-1, 1:]
elif dj == -1 and di == 1: gd[:-1, 1:] |= g1c[1:, :-1]
else: gd[:-1, :-1] |= g1c[1:, 1:]
g1c = gd
for _ in range(2):
ge = g1c.copy()
for dj, di in ((1,0),(-1,0),(0,1),(0,-1),(1,1),(1,-1),(-1,1),(-1,-1)):
if dj == 1: ge[1:, :] &= g1c[:-1, :]
elif dj == -1: ge[:-1, :] &= g1c[1:, :]
elif di == 1: ge[:, 1:] &= g1c[:, :-1]
elif di == -1: ge[:, :-1] &= g1c[:, 1:]
elif dj == 1 and di == 1: ge[1:, 1:] &= g1c[:-1, :-1]
elif dj == 1 and di == -1: ge[1:, :-1] &= g1c[:-1, 1:]
elif dj == -1 and di == 1: ge[:-1, 1:] &= g1c[1:, :-1]
else: ge[:-1, :-1] &= g1c[1:, 1:]
g1c = ge
g1c |= g1f
# 洞格的 gz1 用邻域最大值填充 —— 仅补两类缺口, 不覆盖正常原值:
# 1) g1c 缺口(栅格化角落缝隙, 原值 -inf);
# 2) 孤立针孔: 原值远低于全部邻居中位数(顶面近水平处三角形投影漏采
# 格心, 射线打到的其实是更低的背面) -> 用邻域最大值顶回真实顶面.
# 尾部包裹段是陡斜坡(有低侧邻居, 单调趋势)不是针孔, 必须保留原值跟随本地框面
gz1f = np.where(g1f, gz1, -np.inf)
_nb = []
for dj, di in ((1,0),(-1,0),(0,1),(0,-1),(1,1),(1,-1),(-1,1),(-1,-1)):
s = np.full_like(gz1, np.nan)
if dj == 1: s[1:, :] = gz1[:-1, :]
elif dj == -1: s[:-1, :] = gz1[1:, :]
elif di == 1: s[:, 1:] = gz1[:, :-1]
elif di == -1: s[:, :-1] = gz1[:, 1:]
elif dj == 1 and di == 1: s[1:, 1:] = gz1[:-1, :-1]
elif dj == 1 and di == -1: s[1:, :-1] = gz1[:-1, 1:]
elif dj == -1 and di == 1: s[:-1, 1:] = gz1[1:, :-1]
else: s[:-1, :-1] = gz1[1:, 1:]
_nb.append(s)
_nb = np.stack(_nb)
_valid_nb = _nb > -1e29
with np.errstate(all='ignore'):
_nbmed = np.nanmedian(np.where(_valid_nb, _nb, np.nan), axis=0)
_pin = g1f & np.isfinite(_nbmed) & (gz1 < _nbmed - 0.4)
gz1d = gz1f.copy()
for _ in range(3):
gf = gz1d.copy()
for dj, di in ((1,0),(-1,0),(0,1),(0,-1),(1,1),(1,-1),(-1,1),(-1,-1)):
s = np.full_like(gz1d, -np.inf)
if dj == 1: s[1:, :] = gz1d[:-1, :]
elif dj == -1: s[:-1, :] = gz1d[1:, :]
elif di == 1: s[:, 1:] = gz1d[:, :-1]
elif di == -1: s[:, :-1] = gz1d[:, 1:]
elif dj == 1 and di == 1: s[1:, 1:] = gz1d[:-1, :-1]
elif dj == 1 and di == -1: s[1:, :-1] = gz1d[:-1, 1:]
elif dj == -1 and di == 1: s[:-1, 1:] = gz1d[1:, :-1]
else: s[:-1, :-1] = gz1d[1:, 1:]
gf = np.maximum(gf, s)
gz1d = gf
gz1f = np.where(g1f & ~_pin, gz1, gz1d)
log(f" 顶面针孔修补: {int(_pin.sum())} 格 (孤立低谷, 用邻域最大值补回顶面)")
nfill = int((g1c & ~g1f & R & (gz1f >= 7.0)).sum())
log(f" 镜框带补栅格化角落缺口: {nfill} 格")
# ---- 镜片开口前表面: 框前面曲面 = 稳健二次拟合 + 残差调和延拓 ----
# zfit = 框前面二次趋势面(IRLS 降权误标/离群格); Rext = 拟合残差的调和延拓
# -> 交界处自动严格连续 (zfit + (gz1 - zfit) = gz1), 内部沿框前面趋势(与框平齐)
def pbasis(x, y):
return np.stack([np.ones_like(x), x, y, x * x, x * y, y * y], 1)
# mfit = 框前面(镜片平面方向)拟合范围: 前面区 z>=7 (框前面实际范围 8~10).
# 尾部包裹段(z 更低的陡斜坡)不参与镜片曲面拟合, 但参与框带钉扎(见 frame_band)
mfit = g1c & R & (gz1f >= 7.0)
# frame_band = 完整框带(含尾部折返段): 前面钉扎到本地最高面 - FLUSH.
# 净外扩+0.1 后, R 最外 ~0.3 带内存在"无栅格覆盖但 gz1f(最大填充)有值"
# 的外缘格(镜框轮廓边). 它们必须归框带: 若按"无覆盖"误入镜片开口,
# 前面拟合面在尾部折返斜坡处会高出包裹面 1~2 (凸出镜框).
_eR = R.copy()
for _ in range(3):
_e = _eR.copy()
for dj, di in ((1,0),(-1,0),(0,1),(0,-1),(1,1),(1,-1),(-1,1),(-1,-1)):
if dj == 1: _e[1:, :] &= _eR[:-1, :]
elif dj == -1: _e[:-1, :] &= _eR[1:, :]
elif di == 1: _e[:, 1:] &= _eR[:, :-1]
elif di == -1: _e[:, :-1] &= _eR[:, 1:]
elif dj == 1 and di == 1: _e[1:, 1:] &= _eR[:-1, :-1]
elif dj == 1 and di == -1: _e[1:, :-1] &= _eR[:-1, 1:]
elif dj == -1 and di == 1: _e[:-1, 1:] &= _eR[1:, :-1]
else: _e[:-1, :-1] &= _eR[1:, 1:]
_eR = _e
outer_band = R & ~_eR
frame_band = (g1c & R) | (outer_band & (gz1f > -1e29))
# 陡斜坡外缘: 最大填充取邻域最高, 在折返坡会高出本地框面 ~1.
# 用 0.3 内真实覆盖格的最小值钳制(保守: 前表面绝不高于本地框面),
# 再轻平滑消除形态学噪声
_mdil = np.where(g1f, gz1, np.inf)
for _ in range(3):
_mn = _mdil.copy()
for dj, di in ((1,0),(-1,0),(0,1),(0,-1),(1,1),(1,-1),(-1,1),(-1,-1)):
s = np.full_like(_mdil, np.inf)
if dj == 1: s[1:, :] = _mdil[:-1, :]
elif dj == -1: s[:-1, :] = _mdil[1:, :]
elif di == 1: s[:, 1:] = _mdil[:, :-1]
elif di == -1: s[:, :-1] = _mdil[:, 1:]
elif dj == 1 and di == 1: s[1:, 1:] = _mdil[:-1, :-1]
elif dj == 1 and di == -1: s[1:, :-1] = _mdil[:-1, 1:]
elif dj == -1 and di == 1: s[:-1, 1:] = _mdil[1:, :-1]
else: s[:-1, :-1] = _mdil[1:, 1:]
_mn = np.minimum(_mn, s)
_mdil = _mn
_fringe = frame_band & ~g1f
gz1f = np.where(_fringe & (_mdil < 1e29), np.minimum(gz1f, _mdil), gz1f)
with np.errstate(all='ignore'):
gz1f = np.where(_fringe, smooth_valid(gz1f, _fringe, sigma=2.0, it=1), gz1f)
xp, yp, zp = gx[mfit], gy[mfit], gz1f[mfit]
wt = np.ones(len(zp))
for _ in range(3):
Aw = pbasis(xp, yp) * wt[:, None]
coef, *_ = np.linalg.lstsq(Aw, zp * wt, rcond=None)
rfit = zp - pbasis(xp, yp) @ coef
wt = 1.0 / (1.0 + (np.abs(rfit) / 0.5) ** 2)
zfit = (pbasis(gx.ravel(), gy.ravel()) @ coef).reshape(H, W)
rf = np.abs((zfit - gz1f)[mfit])
log(f" 框前面拟合(稳健): 残差 mean {rf.mean():.3f}, p90 {np.percentile(rf, 90):.3f}, "
f"max {rf.max():.3f}")
# 残差场边界只用拟合内点: 尾部包裹段(偏离前面平面 1 以上)不参与,
# 其低残差经平滑/调和延拓渗入镜片开口会拉低镜片面
mfit2 = mfit & (np.abs(gz1f - zfit) <= 1.0)
# 残差场: 镜框带上 = gz1 - zfit; 先平滑边界条件(消除格尺度噪声 -> 延拓解光滑),
# 再调和延拓到开口内部
resf = np.full((H, W), np.nan)
resf[mfit2] = gz1f[mfit2] - zfit[mfit2]
resf = smooth_valid(resf, mfit2, sigma=2.5)
Rext = laplace_fill(resf, mfit2)
Rext = np.where(R, Rext, np.nan)
# 前表面: 完整框带(含尾部)贴住本地最高面(FLUSH 嵌入余量, 尾部跟随包裹斜坡);
# 开口 = zfit + Rext - FLUSH
hf = np.full((H, W), np.nan)
hf[frame_band] = gz1f[frame_band] - FLUSH
openf = R & ~frame_band
hfo = np.where(openf, zfit + Rext - FLUSH, np.nan)
# 开口区安全钳制(不得超过 3 格半径内框前沿), 在平滑前施加 -> 折角被平滑柔化
gmax2 = np.where(mfit, gz1f, -np.inf)
for _ in range(3):
gm = gmax2.copy()
for dj, di in ((1,0),(-1,0),(0,1),(0,-1),(1,1),(1,-1),(-1,1),(-1,-1)):
s = np.full_like(gmax2, -np.inf)
if dj == 1: s[1:, :] = gmax2[:-1, :]
elif dj == -1: s[:-1, :] = gmax2[1:, :]
elif di == 1: s[:, 1:] = gmax2[:, :-1]
elif di == -1: s[:, :-1] = gmax2[:, 1:]
elif dj == 1 and di == 1: s[1:, 1:] = gmax2[:-1, :-1]
elif dj == 1 and di == -1: s[1:, :-1] = gmax2[:-1, 1:]
elif dj == -1 and di == 1: s[:-1, 1:] = gmax2[1:, :-1]
else: s[:-1, :-1] = gmax2[1:, 1:]
gm = np.maximum(gm, s)
gmax2 = gm
hfo = np.where(openf & (gmax2 > -1e29), np.minimum(hfo, gmax2 - FLUSH), hfo)
# 开口区整体平滑(镜片表面打印光滑)
hfo = smooth_valid(hfo, openf, sigma=2.0, it=2)
hf = np.where(openf & np.isfinite(hfo), hfo, hf)
# 整体轻度平滑柔化交界折角
hf = smooth_valid(hf, R, sigma=1.5)
# 墙区(R 外缘 4 格): 侧墙顶所在, 需严格嵌入框实体
edge_in = R.copy()
for _ in range(4):
ne = edge_in.copy()
ne[1:, :] &= edge_in[:-1, :]; ne[:-1, :] &= edge_in[1:, :]
ne[:, 1:] &= edge_in[:, :-1]; ne[:, :-1] &= edge_in[:, 1:]
edge_in = ne
wall_zone = R & ~edge_in
# 安全钳制(平滑后仅作用于框带; 开口的钳制已在平滑前施加并被柔化):
# 框带墙区 -> 本地框面 - FLUSH(严格嵌入, 尾部跟随包裹斜坡)
# 框带内部 -> 至多贴到框面 + 0.10(交界平齐, 并集无缝)
hf = np.where(frame_band & wall_zone, np.minimum(hf, gz1f - FLUSH), hf)
hf = np.where(frame_band & ~wall_zone, np.minimum(hf, gz1f + 0.10), hf)
# 交界连续性: 镜片开口格与相邻"平面前框带"格(与镜片面近共面, |gz1f-zfit|<=0.3)
# 的前表面高度差. 陡壁/包裹段格(镜圈管内壁等)与镜片面的台阶是镜框自身几何,
# 并集后不暴露到外表面, 不计入此项
jn, jn_at = 0.0, None
bflat = mfit2 & (gz1f > zfit - 0.3)
for dj, di in ((1,0),(-1,0),(0,1),(0,-1)):
a = np.roll(bflat, (dj, di), axis=(0, 1)) & openf & np.isfinite(hf)
if a.any():
b = np.roll(a, (-dj, -di), axis=(0, 1))
dd = np.abs(np.where(a, hf, 0.0)[a] - np.where(np.isfinite(hf), hf, 0.0)[b])
k = int(np.nanargmax(dd))
if dd[k] > jn:
ja = np.argwhere(a)[k]
jn, jn_at = float(dd[k]), (X0 + ja[1] * RES, Y0 + ja[0] * RES)
log(f" 交界处高度跳变最大 {jn:.3f} @ {jn_at} (平面前框带接缝应<0.3; "
"镜圈圆角处~0.4为镜框自身几何, 并集后不暴露)")
hb = np.full((H, W), np.nan)
# 真实脸面: fz >= FACE_MIN. 低于此值的"脸面"是误标导致的深伪面(后脑/口腔),
# 不能作为填充底面(否则镜桥下会出现十几单位深的伪填充柱)
real_f = have_f & (fz >= FACE_MIN)
hb[real_f] = fz[real_f] - EMBED_BOT
knownb = R & real_f
hb = laplace_fill(hb, knownb)
hb = smooth_valid(hb, R)
# 无真实脸面处(镜桥下/误标区): 填充厚度不超过 hf - SHELL_MAX,
# 保证填充只在镜框附近的 z 范围内; 有真实脸面处仍嵌到脸面(填满镂空)
cap = hf - SHELL_MAX
ncap = int((R & ~real_f & np.isfinite(hb) & (hb < cap)).sum())
hb = np.where(R & ~real_f, np.maximum(hb, cap), hb)
log(f" 厚度上限(无真实脸面处, 距前面>{SHELL_MAX})生效格数: {ncap}")
# 缝隙修补: 平滑可能把底缘底面抬到脸面之前 -> 钳回脸面内(嵌入>=0.25, 并集无缝)
hb = np.where(R & real_f, np.minimum(hb, fz - 0.25), hb)
bzs = smooth_valid(np.where(have_b, bz, np.nan), have_b)
hb = np.where(R, hb, np.nan)
hb = np.where(have_b, np.maximum(hb, bzs + CLAMP_BACK), hb)
hb = np.minimum(hb, hf - GAP_MIN)
# 外扩一格填充 NaN(边界采样用)
for _ in range(60):
nanm = ~np.isfinite(hf)
if not nanm.any(): break
for dj, di in ((1,0),(-1,0),(0,1),(0,-1)):
s = np.roll(np.where(nanm, 0, hf), (dj, di), axis=(0, 1))
ok = ~np.roll(nanm, (dj, di), axis=(0, 1)) & np.isfinite(s)
hf = np.where(nanm & ok, s, hf)
for _ in range(60):
nanm = ~np.isfinite(hb)
if not nanm.any(): break
for dj, di in ((1,0),(-1,0),(0,1),(0,-1)):
s = np.roll(np.where(nanm, 0, hb), (dj, di), axis=(0, 1))
ok = ~np.roll(nanm, (dj, di), axis=(0, 1)) & np.isfinite(s)
hb = np.where(nanm & ok, s, hb)
thickm = np.where(R, hf - hb, np.nan)
log(f" 填充厚度: min {np.nanmin(thickm):.2f}, 中位 {np.nanmedian(thickm):.2f}, "
f"mean {np.nanmean(thickm):.2f}, max {np.nanmax(thickm):.2f}")
# ----------------------- 边界: 提取/平滑 -----------------------
log("== 5. 边界提取与平滑 ==")
# 裂缝边(crack edge)链成回路
edges = {}
def add_edge(a, b):
edges.setdefault(a, []).append(b)
for j in range(H):
for i in range(W):
if not R[j, i]:
continue
if i == 0 or not R[j, i - 1]:
add_edge((i, j), (i, j + 1))
if i == W - 1 or not R[j, i + 1]:
add_edge((i + 1, j + 1), (i + 1, j))
if j == 0 or not R[j - 1, i]:
add_edge((i + 1, j), (i, j))
if j == H - 1 or not R[j + 1, i]:
add_edge((i, j + 1), (i + 1, j + 1))
if not edges:
raise SystemExit("无边界")
start = next(iter(edges))
loop = [start]
cur = edges[start].pop(0)
used = {(start, cur)}
while cur != start:
loop.append(cur)
nxts = [e for e in edges.get(cur, []) if (cur, e) not in used]
if not nxts:
break
nxt = nxts[0]
used.add((cur, nxt))
cur = nxt
P = np.array([[X0 + i * RES, Y0 + j * RES] for (i, j) in loop], float)
area2 = np.sum(P[:, 0] * np.roll(P[:, 1], -1) - np.roll(P[:, 0], -1) * P[:, 1])
if area2 < 0:
P = P[::-1]
log(f" 边界回路 {len(P)} 点, 周长 {np.linalg.norm(np.roll(P,-1,0)-P,axis=1).sum():.2f}")
def resample(P, step):
d = np.linalg.norm(np.roll(P, -1, 0) - P, axis=1)
L = np.concatenate([[0], np.cumsum(d)])
total = L[-1]
n = max(8, int(round(total / step)))
t = np.linspace(0, total, n, endpoint=False)
x = np.interp(t, L, np.concatenate([P[:, 0], P[:1, 0]]))
y = np.interp(t, L, np.concatenate([P[:, 1], P[:1, 1]]))
return np.stack([x, y], 1)
def roughness(P):
d = np.roll(P, -1, 0) - P
a = np.arctan2(d[:, 1], d[:, 0])
da = np.abs((a - np.roll(a, -1) + np.pi) % (2 * np.pi) - np.pi)
return float(da.mean()), float(da.std())
r0 = roughness(P)
B = resample(P, BSTEP)
for _ in range(BITER):
B = (1 - BLAM) * B + BLAM * 0.5 * (np.roll(B, 1, 0) + np.roll(B, -1, 0))
# 面积恢复: 抵消平滑收缩(目标 = R 面积的 97%)
areaR = R.sum() * RES * RES
for _ in range(30):
aB = 0.5 * abs(np.sum(B[:, 0] * np.roll(B[:, 1], -1) - np.roll(B[:, 0], -1) * B[:, 1]))
if aB >= 0.97 * areaR:
break
c = B.mean(0)
s = np.sqrt(0.97 * areaR / max(aB, 1e-9))
s = min(s, 1.05)
B = c + (B - c) * s
B = resample(B, BSTEP)
r1 = roughness(B)
log(f" 边界粗糙度(平均转折角/标准差): 平滑前 {np.degrees(r0[0]):.2f}°/{np.degrees(r0[1]):.2f}° "
f"-> 平滑后 {np.degrees(r1[0]):.2f}°/{np.degrees(r1[1]):.2f}°")
def inside_mask(pts, msk):
ii = np.clip(((pts[:, 0] - X0) / RES).astype(int), 0, W - 1)
jj2 = np.clip(((pts[:, 1] - Y0) / RES).astype(int), 0, H - 1)
return msk[jj2, ii]
bad = ~inside_mask(B, mask)
if bad.any():
c = B.mean(0)
for k in np.where(bad)[0]:
p = B[k]
for s in np.linspace(0.1, 0.9, 30):
q = c + s * (p - c)
if inside_mask(q[None, :], mask)[0]:
B[k] = q
break
for _ in range(10):
B = (1 - BLAM) * B + BLAM * 0.5 * (np.roll(B, 1, 0) + np.roll(B, -1, 0))
B = resample(B, BSTEP)
# 边界须压在镜框带上(存在眼镜表面), 统计覆盖率
bii = np.clip(((B[:, 0] - X0) / RES).astype(int), 0, W - 1)
bjj = np.clip(((B[:, 1] - Y0) / RES).astype(int), 0, H - 1)
nb = np.zeros(len(B), bool)
for dj, di in ((0,0),(1,0),(-1,0),(0,1),(0,-1),(1,1),(1,-1),(-1,1),(-1,-1)):
jj2 = np.clip(bjj + dj, 0, H - 1); ii2 = np.clip(bii + di, 0, W - 1)
nb |= g1f[jj2, ii2]
log(f" 平滑边界 {len(B)} 点, 超出足迹 {int((~inside_mask(B, mask)).sum())}, "
f"压在镜框带上 {nb.mean()*100:.1f}%")
# ----------------------- 区域三角化: 耳切 + 内部点插入 -----------------------
log("== 6. 区域三角化 (耳切法 + 内部网格点插入, 无翻转风险) ==")
Nb = len(B)
def cross3(o, a, b):
return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0])
def ear_clip(P):
"""P 为 CCW 简单多边形, 返回三角形索引列表"""
idx = list(range(len(P)))
tris = []
guard = 0
while len(idx) > 3 and guard < 5000:
guard += 1
m = len(idx)
clipped = False
best_k, best_score = None, None
for k in range(m):
i0, i1, i2 = idx[(k - 1) % m], idx[k], idx[(k + 1) % m]
a, b, c = P[i0], P[i1], P[i2]
cr = cross3(a, b, c)
if cr <= 1e-10:
continue
inside_any = False
for j in idx:
if j in (i0, i1, i2):
continue
p = P[j]
if (cross3(a, b, p) >= -1e-12 and cross3(b, c, p) >= -1e-12
and cross3(c, a, p) >= -1e-12):
inside_any = True
break
if not inside_any:
# 质量分: 面积/边长平方 越大越好
lab = np.hypot(*(np.subtract(b, a))); lac = np.hypot(*(np.subtract(c, a)))
lbc = np.hypot(*(np.subtract(c, b)))
score = cr / max(lab * lac, lab * lbc, lac * lbc, 1e-12)
if best_score is None or score > best_score:
best_k, best_score = k, score
if best_k is None:
# 兜底: 耳切失败(理论不应发生), 取最大正面积顶点
m = len(idx)
areas = [(cross3(P[idx[(k-1)%m]], P[idx[k]], P[idx[(k+1)%m]]), k)
for k in range(m)]
areas.sort(reverse=True)
best_k = areas[0][1]
log(" ! 耳切兜底触发")
i0, i1, i2 = (idx[(best_k - 1) % len(idx)], idx[best_k],
idx[(best_k + 1) % len(idx)])
tris.append((i0, i1, i2))
idx.pop(best_k)
tris.append((idx[0], idx[1], idx[2]))
return tris
T = np.asarray(ear_clip(B.tolist()), np.int64)
log(f" 耳切三角化: {len(T)} 三角形")
# 内部点: R 深处格子中心, 间隔 ~0.3
inner2 = R.copy()
for _ in range(2):
ne = inner2.copy()
ne[1:, :] &= inner2[:-1, :]; ne[:-1, :] &= inner2[1:, :]
ne[:, 1:] &= inner2[:, :-1]; ne[:, :-1] &= inner2[:, 1:]
inner2 = ne
step = max(1, int(round(0.3 / RES)))
cand = []
for j in range(0, H, step):
for i in range(0, W, step):
if inner2[j, i]:
cand.append((X0 + i * RES, Y0 + j * RES))
cand = np.asarray(cand)
log(f" 内部插入点候选 {len(cand)}")
# 逐点插入(拆分包含它的三角形 -> 拓扑恒不翻转)
xy = np.vstack([B, cand])
n_cand = len(cand)
extra = 0
Ta = [list(map(int, t)) for t in T]
for ci in range(n_cand):
p = xy[Nb + ci]
m = len(Ta)
TA = np.asarray(Ta)
a = xy[TA[:, 0]]; b = xy[TA[:, 1]]; c = xy[TA[:, 2]]
d = ((b[:, 1] - c[:, 1]) * (a[:, 0] - c[:, 0]) + (c[:, 0] - b[:, 0]) * (a[:, 1] - c[:, 1]))
with np.errstate(divide='ignore', invalid='ignore'):
l1 = ((b[:, 1] - c[:, 1]) * (p[0] - c[:, 0]) + (c[:, 0] - b[:, 0]) * (p[1] - c[:, 1])) / d
l2 = ((c[:, 1] - a[:, 1]) * (p[0] - c[:, 0]) + (a[:, 0] - c[:, 0]) * (p[1] - c[:, 1])) / d
l3 = 1 - l1 - l2
hit = np.where((l1 > 5e-3) & (l2 > 5e-3) & (l3 > 5e-3)
& (l1 < 1 - 5e-3) & (l2 < 1 - 5e-3) & (l3 < 1 - 5e-3))[0]
if len(hit) == 0:
continue
t = int(hit[0])
i0, i1, i2 = Ta[t]
vnew = Nb + ci
Ta[t] = [i0, i1, vnew]
Ta.append([i1, i2, vnew])
Ta.append([i2, i0, vnew])
extra += 1
T = np.asarray([t for t in Ta if t[0] != t[1] and t[1] != t[2] and t[0] != t[2]], np.int64)
xy = xy[:Nb + n_cand]
# 内部顶点 XY 轻度 Laplacian 平滑(边界固定), 消除细长三角形; 有翻转则回退
es = np.unique(np.sort(np.concatenate([T[:, [0, 1]], T[:, [1, 2]], T[:, [2, 0]]]), axis=1), axis=0)
src = np.concatenate([es[:, 0], es[:, 1]])
dst = np.concatenate([es[:, 1], es[:, 0]])
deg = np.bincount(src, minlength=len(xy)).astype(float)
def tri_areas(xy, T):
cr = xy[T[:, 1]] - xy[T[:, 0]]
cs = xy[T[:, 2]] - xy[T[:, 0]]
return cr[:, 0] * cs[:, 1] - cr[:, 1] * cs[:, 0]
xy_best = xy.copy()
for _ in range(8):
sx = np.bincount(src, weights=xy[dst, 0], minlength=len(xy))
sy = np.bincount(src, weights=xy[dst, 1], minlength=len(xy))
new = np.stack([sx, sy], 1) / np.maximum(deg, 1)[:, None]
xy2 = xy.copy()
xy2[Nb:] = 0.5 * xy[Nb:] + 0.5 * new[Nb:]
if tri_areas(xy2, T).min() > 1e-6:
xy = xy2
xy_best = xy2.copy()
else:
break
xy = xy_best
# 边翻转优化(Lawson): 公共边换成严格更短的对角线(总边长严格递减 -> 必收敛),
# 不新增顶点即可消除耳切弦两侧的细长退化三角形(表面粗糙的根源)
def flip_pass(Tl, XY):
em = {}
for fi, t in enumerate(Tl):
a, b, c = t
for u, v in ((a, b), (b, c), (c, a)):
em.setdefault((min(u, v), max(u, v)), []).append(fi)
eset = set(em)
n = 0
for (u, v), fs in em.items():
if len(fs) != 2:
continue
f1, f2 = fs
if not (u in Tl[f1] and v in Tl[f1] and u in Tl[f2] and v in Tl[f2]):
continue # 本趟已被改动的面, 下趟再处理
w1 = next(x for x in Tl[f1] if x != u and x != v)
w2 = next(x for x in Tl[f2] if x != u and x != v)
if w1 == w2 or (min(w1, w2), max(w1, w2)) in eset:
continue
pu, pv = XY[u], XY[v]
s1 = (pv[0]-pu[0])*(XY[w1][1]-pu[1]) - (pv[1]-pu[1])*(XY[w1][0]-pu[0])
s2 = (pv[0]-pu[0])*(XY[w2][1]-pu[1]) - (pv[1]-pu[1])*(XY[w2][0]-pu[0])
if s1 * s2 >= 0:
continue # w1,w2 须在 uv 两侧(凸四边形)
q1, q2 = XY[w1], XY[w2]
s3 = (q2[0]-q1[0])*(pu[1]-q1[1]) - (q2[1]-q1[1])*(pu[0]-q1[0])
s4 = (q2[0]-q1[0])*(pv[1]-q1[1]) - (q2[1]-q1[1])*(pv[0]-q1[0])
if s3 * s4 >= 0:
continue
if np.hypot(*(XY[w2] - XY[w1])) >= np.hypot(*(XY[v] - XY[u])):
continue # 新对角线须更短
# 凸四边形 u->a->v->b (a 在 u->v 右侧, b 在左侧) 沿对角线 a-b 拆分
if s1 > 0: # w1 左, w2 右
Tl[f1] = [u, w2, w1]
Tl[f2] = [v, w1, w2]
else: # w1 右, w2 左
Tl[f1] = [u, w1, w2]
Tl[f2] = [v, w2, w1]
eset.add((min(w1, w2), max(w1, w2)))
n += 1
return n
Tlist = [list(map(int, t)) for t in T]
nflips = 0
for _p in range(200):
k = flip_pass(Tlist, xy)
nflips += k
if k == 0:
break
log(f" 边翻转优化: {nflips} 次, 收敛于 {_p+1} 趟")
# 残余长边轻度细分(翻转后仅少量, 不会级联)
MAXEDGE = 0.5
nsplit = 0
for _p in range(6):
emap = {}
for fi, (a, b, c) in enumerate(Tlist):
for u, v in ((a, b), (b, c), (c, a)):
emap.setdefault((min(u, v), max(u, v)), []).append(fi)
longe = [(u, v) for (u, v) in emap if np.hypot(*(xy[v] - xy[u])) > MAXEDGE]
if not longe:
break
mid = {}
newpts = []
for u, v in longe:
mid[(u, v)] = len(xy) + len(newpts)
newpts.append((xy[u] + xy[v]) / 2.0)
xy = np.vstack([xy, np.asarray(newpts)])
nsplit += len(newpts)
newT = []
for (a, b, c) in Tlist:
mab = mid.get((min(a, b), max(a, b)))
mbc = mid.get((min(b, c), max(b, c)))
mca = mid.get((min(c, a), max(c, a)))
if mab is None and mbc is None and mca is None:
newT.append([a, b, c])
elif mbc is None and mca is None:
newT += [[a, mab, c], [mab, b, c]]
elif mab is None and mca is None:
newT += [[a, b, mbc], [a, mbc, c]]
elif mab is None and mbc is None:
newT += [[a, b, mca], [mca, b, c]]
elif mca is None:
newT += [[a, mab, mbc], [mab, b, mbc], [a, mbc, c]]
elif mab is None:
newT += [[a, b, mbc], [a, mbc, mca], [mbc, c, mca]]
elif mbc is None:
newT += [[a, mab, mca], [mab, b, c], [mab, c, mca]]
else:
newT += [[a, mab, mca], [mab, b, mbc], [mca, mbc, c], [mab, mbc, mca]]
Tlist = newT
T = np.asarray(Tlist, np.int64)
log(f" 残余长边细分(>{MAXEDGE}): 新增 {nsplit} 中点, 总三角形 {len(T)}")
cr = xy[T[:, 1]] - xy[T[:, 0]]
cs = xy[T[:, 2]] - xy[T[:, 0]]
area = cr[:, 0] * cs[:, 1] - cr[:, 1] * cs[:, 0]
if area.min() <= 0:
raise SystemExit(f"三角形定向异常 (min area {area.min():.2e})")
log(f" 实际插入 {extra} 点, 总三角形 {len(T)}, 最小有向面积 {area.min():.5f} (>0 = 无翻转)")
nV = len(xy)
# ----------------------- 组装实体 -----------------------
log("== 7. 组装填充实体 ==")
def bilinear(Grd, pts):
fx = (pts[:, 0] - X0) / RES
fy = (pts[:, 1] - Y0) / RES
i = np.clip(np.floor(fx).astype(int), 0, W - 2)
j = np.clip(np.floor(fy).astype(int), 0, H - 2)
tx = np.clip(fx - i, 0, 1); ty = np.clip(fy - j, 0, 1)
v = (Grd[j, i] * (1 - tx) * (1 - ty) + Grd[j, i + 1] * tx * (1 - ty) +
Grd[j + 1, i] * (1 - tx) * ty + Grd[j + 1, i + 1] * tx * ty)
return v
zf = bilinear(hf, xy)
zb = bilinear(hb, xy)
zb = np.minimum(zb, zf - 0.15)
zb = np.maximum(zb, zf - 50)
Pf = np.column_stack([xy, zf])
Pb = np.column_stack([xy, zb])
faces = []
for a, b, c in T:
faces.append((a, b, c)) # 前表面(法向 +z, 向外)
for a, b, c in T:
faces.append((a + nV, c + nV, b + nV)) # 后表面(翻转, 法向 -z, 向外)
# 侧墙: 用细分后的三角化边界环(1-面有向边链成 CCW 环, 与盘边界严格一致)
dired = {}
unded = {}
for a, b, c in T:
for u, v in ((a, b), (b, c), (c, a)):
dired[(u, v)] = dired.get((u, v), 0) + 1
for (u, v) in dired:
unded[(min(u, v), max(u, v))] = unded.get((min(u, v), max(u, v)), 0) + 1
bnext = {}
for (u, v) in dired:
if unded[(min(u, v), max(u, v))] == 1:
bnext[u] = v
ring = [next(iter(bnext))]
while bnext[ring[-1]] != ring[0]:
ring.append(bnext[ring[-1]])
Nr = len(ring)
for i in range(Nr):
u, v = ring[i], ring[(i + 1) % Nr]
faces.append((u, v + nV, v)) # (F_i, B_{i+1}, F_{i+1})
faces.append((u, u + nV, v + nV)) # (F_i, B_i, B_{i+1})
Ff = np.asarray(faces, np.int64)
Pall = np.vstack([Pf, Pb])
# 定向: 与原模型一致
def signed_vol(P, Tt):
a = P[Tt[:, 0]]; b = P[Tt[:, 1]]; c = P[Tt[:, 2]]
return float(np.sum(np.einsum('ij,ij->i', a, np.cross(b, c))) / 6.0)
vfill = signed_vol(Pall, Ff)
vorig = signed_vol(V, F)
if vfill * vorig < 0:
Ff = Ff[:, [0, 2, 1]]
vfill = -vfill
# 期望体积 = 三角形 2D 面积 x 平均厚度 (验证定向正确性)
exp_vol = float(np.sum(0.5 * np.abs(area) * ((zf[T[:, 0]] + zf[T[:, 1]] + zf[T[:, 2]]
- zb[T[:, 0]] - zb[T[:, 1]] - zb[T[:, 2]]) / 3.0)))
log(f" 填充实体体积 {vfill:.2f} (期望 {exp_vol:.2f}), 原模型 {vorig:.0f}, 定向一致")
if abs(vfill - exp_vol) > 0.02 * abs(exp_vol) + 1e-6:
raise SystemExit("体积校验失败: 面片定向不一致")
# 水密性: 无向边计数 + 有向边方向一致性
e2 = np.sort(np.concatenate([Ff[:, [0, 1]], Ff[:, [1, 2]], Ff[:, [2, 0]]]), axis=1)
ue, cnt = np.unique(e2, axis=0, return_counts=True)
de = np.concatenate([Ff[:, [0, 1]], Ff[:, [1, 2]], Ff[:, [2, 0]]])
ude, udcnt = np.unique(de, axis=0, return_counts=True)
log(f" 水密性: 非流形边(计数!=2) {int((cnt != 2).sum())} / {len(ue)}, "
f"方向冲突边 {int((udcnt != 1).sum())} (两者都应为 0)")
# 镜片光滑度: 前表面相邻面二面角(打印外观指标)
nv = np.cross(Pall[Ff[:, 1]] - Pall[Ff[:, 0]], Pall[Ff[:, 2]] - Pall[Ff[:, 0]])
nv = nv / np.linalg.norm(nv, axis=1, keepdims=True)
fcen = Pall[Ff].mean(1)
emap2 = {}
for fi, (a, b, c) in enumerate(Ff):
for u, v in ((a, b), (b, c), (c, a)):
emap2.setdefault((min(u, v), max(u, v)), []).append(fi)
lang, lloc = [], []
for (u, v), fs in emap2.items():
if len(fs) == 2 and nv[fs[0], 2] > 0.5 and nv[fs[1], 2] > 0.5:
m = fcen[fs[0]]
if 2.2 < abs(m[0]) < 6.3 and 12.5 < m[1] < 16.2: # 左右镜片开口
lang.append(np.degrees(np.arccos(np.clip(nv[fs[0]] @ nv[fs[1]], -1, 1))))
lloc.append(m)
lang = np.asarray(lang)
if len(lang):
k = np.argmax(lang)
log(f" 镜片光滑度(相邻面二面角): 中位 {np.median(lang):.2f}°, p90 {np.percentile(lang, 90):.2f}°, "
f"max {lang[k]:.2f}° @ ({lloc[k][0]:.1f},{lloc[k][1]:.1f}) (中位应<2°)")
# 嵌入校验
gmargin = (gz1f - hf)[R & frame_band & wall_zone]
log(f" 前表面低于本地框面(墙区): 最小余量 {np.nanmin(gmargin):.3f} (应>0)")
gmargin2 = (gz1f - hf)[R & frame_band]
log(f" 前表面低于本地框面(内部允许贴齐): 最小余量 {np.nanmin(gmargin2):.3f} (应>-0.10)")
bmargin = (hb - bzs)[R & have_b]
log(f" 后表面高于最后表面: 最小余量 {np.nanmin(bmargin):.3f} (应>0)")
embed = (fz - hb)[R & real_f]
log(f" 底面嵌入真实脸面: 最小 {np.nanmin(embed):.3f} (应>-0.05, 负=缝隙), "
f"中位 {np.nanmedian(embed):.2f}")
inR = inside_mask(xy, R)
log(f" 圆盘顶点落在 R 内比例 {inR.mean()*100:.1f}%")
# ----------------------- 输出 -----------------------
log("== 8. 输出 ==")
with open(OUT_FILL, "w") as f:
f.write("# fill mesh between glasses and face\n")
f.write(f"o fill\n")
for p in Pall:
f.write(f"v {p[0]:.5f} {p[1]:.5f} {p[2]:.5f}\n")
for a, b, c in Ff:
f.write(f"f {a+1} {b+1} {c+1}\n")
log(f" {OUT_FILL}: {len(Pall)} 顶点, {len(Ff)} 面")
with open(IN_OBJ) as f:
orig = f.read()
with open(OUT_MERGED, "w") as f:
f.write(orig.rstrip("\n") + "\n")
f.write("o fill\n")
off = len(V)
for p in Pall:
f.write(f"v {p[0]:.5f} {p[1]:.5f} {p[2]:.5f}\n")
for a, b, c in Ff:
f.write(f"f {a+1+off} {b+1+off} {c+1+off}\n")
log(f" {OUT_MERGED}: 原模型 + 填充 (顶点偏移 {off})")
# ----------------------- 预览 -----------------------
front = np.where(g1f, gz1, np.nan)
mix = np.where(R & np.isfinite(hf), np.where(np.isfinite(front), np.maximum(front, hf), hf), front)
front = mix
panels = []
span = (4, 12)
def to_img(Grd, span):
G = np.where(np.isfinite(Grd), Grd, span[0])
t = np.clip((G - span[0]) / (span[1] - span[0]), 0, 1)
return (t * 255).astype(np.uint8)
for name, Grd in (("front-depth", front), ("fill-front", np.where(R, hf, np.nan)),
("thickness", np.where(R, hf - hb, np.nan))):
im = Image.fromarray(to_img(np.flipud(Grd), span if "thick" not in name else (0, 4)))
im = im.resize((W * 4, H * 4), Image.NEAREST)
d = ImageDraw.Draw(im)
pts = [((b[0] - X0) / RES * 4, (Y1 - b[1]) / RES * 4) for b in B]
d.line(pts + pts[:1], fill=255, width=2)
panels.append((name, im))
cw = sum(p.width for _, p in panels) + 20
ch = max(p.height for _, p in panels)
combo = Image.new("L", (cw, ch), 60)
xoff = 0
for name, p in panels:
combo.paste(p, (xoff, 0)); xoff += p.width + 10
combo.save(OUT_PREVIEW)
log(f" {OUT_PREVIEW}: 3 面板(前深度/填充前表面/厚度), 红线=平滑边界")
log("\n== 完成 ==")
with open("fill_report.txt", "w") as f:
f.write("\n".join(report) + "\n")
print("报告已写入 fill_report.txt")
Reference in new issue View Git Blame Copy Permalink