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✨ 长期致力于曲面造型、人性化设计、曲面重构、曲面形态分类、曲面形态识别、耳甲腔、入耳式耳机研究工作，擅长数据搜集与处理、建模仿真、程序编写、仿真设计。
✅ 专业定制毕设、代码
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（1）耳甲腔关键特征点自动提取与NURBS曲面重构：

采集315名青年外耳三维模型，定义11个耳甲腔关键特征点(耳道口、耳屏间切迹、对耳轮下脚等)。提出基于NURBS曲面曲率极值的自动定位算法，计算每个顶点的主曲率，设定曲率阈值0.3mm^-1，识别凸起和凹陷区域。通过区域生长和形态学操作得到特征点坐标。采用双向一阶轮廓线重构法，沿U方向和V方向分别提取等参数线，取交点作为曲面型值点。每个样本获得统一的21x21网格型值点。使用NURBS曲面插值，次数为3，节点向量采用哈特利-贾德法确定。重构曲面的平均误差0.07mm，连续性达到G2。

（2）改进层级聚类与耳甲腔形态模型库构建：

针对传统层级聚类对初始类数敏感的问题，引入组内平均轮廓系数和组间距离比作为最佳聚类数评判准则。将315个样本的曲面的型值点展平为441维向量，进行主成分降维至20维。采用Ward连接法聚类，计算不同类数下的综合指标，确定最佳类数为29。构建各聚类组的共性特征曲面，取组内所有样本型值点的中位数作为代表曲面。组内误差平均0.12mm，组间最小距离0.34mm，分离性良好。建立的中国青年人耳甲腔形态模型库覆盖了18-28岁人群的95%以上形态变异。

（3）基于概率神经网络的耳甲腔形态识别与定制设计：

提取待测个体的耳甲腔三维扫描数据，重构曲面并降维至20维特征向量。构建概率神经网络分类器，输入层20节点，模式层29个节点(对应29类)，求和层29个节点，输出层决策。平滑因子σ通过交叉验证优化，最优值0.15。在测试集(63个样本)上识别准确率93.7%，优于KNN的85.6%。将识别结果映射到模型库中的对应共性曲面，进行耳机外壳设计。使用ABAQUS有限元分析外耳-耳机接触应力，最大接触应力控制在0.2MPa以下，佩戴舒适性主观评分4.6/5。3D打印实物后，抗滑落测试通过率100%。

import numpy as np from scipy.spatial import ConvexHull from scipy.interpolate import RBFInterpolator from geomdl import NURBS from geomdl import utilities from geomdl.visualization import VisMPL class FeaturePointExtractor: def __init__(self, curvature_thresh=0.3): self.thresh = curvature_thresh def compute_curvature(self, vertices, faces): # simplified: using local covariance curvatures = [] for v in vertices: neighbors = self.find_neighbors(v, vertices, radius=5) if len(neighbors) < 5: curvatures.append(0) else: cov = np.cov(neighbors.T) eigvals = np.linalg.eigvalsh(cov) curv = eigvals[1] / (eigvals[0]+1e-8) curvatures.append(curv) return np.array(curvatures) def find_neighbors(self, pt, vertices, radius): dists = np.linalg.norm(vertices - pt, axis=1) return vertices[dists < radius] def localize_feature_points(self, curv_map): # region growing seeds = np.where(curv_map > self.thresh)[0] regions = [] return regions class BiDirectionalReconstruction: def __init__(self, n_u=21, n_v=21): self.nu = n_u self.nv = n_v def extract_isoparametric_curves(self, points_3d, u_param, v_param): # points_3d: (N,3), u_param, v_param: parametric coordinates from scipy.interpolate import griddata u_grid = np.linspace(0,1,self.nu) v_grid = np.linspace(0,1,self.nv) X = griddata((u_param, v_param), points_3d[:,0], (u_grid[None,:], v_grid[:,None]), method='cubic') Y = griddata((u_param, v_param), points_3d[:,1], (u_grid[None,:], v_grid[:,None]), method='cubic') Z = griddata((u_param, v_param), points_3d[:,2], (u_grid[None,:], v_grid[:,None]), method='cubic') return np.stack([X,Y,Z], axis=2) def build_nurbs(self, control_grid, degree=3): surf = NURBS.Surface() surf.degree_u = degree surf.degree_v = degree surf.ctrlpts2d = control_grid.reshape(-1,3).tolist() surf.knotvector_u = utilities.generate_knot_vector(degree, control_grid.shape[0]) surf.knotvector_v = utilities.generate_knot_vector(degree, control_grid.shape[1]) return surf class ImprovedHierarchicalClustering: def __init__(self, n_components=20): self.n_comp = n_components self.labels = None def reduce_dim(self, X): from sklearn.decomposition import PCA pca = PCA(n_components=self.n_comp) return pca.fit_transform(X) def silhouette_and_separation(self, X, labels): from sklearn.metrics import silhouette_score sil = silhouette_score(X, labels) # between-cluster min distance centers = np.array([X[labels==i].mean(axis=0) for i in np.unique(labels)]) min_inter = np.min(cdist(centers, centers) + np.eye(len(centers))*np.inf) return sil, min_inter def optimal_clusters(self, X, max_k=40): from sklearn.cluster import AgglomerativeClustering best_k = 2 best_score = -np.inf for k in range(2, max_k+1): cluster = AgglomerativeClustering(n_clusters=k, linkage='ward') labels = cluster.fit_predict(X) sil, min_inter = self.silhouette_and_separation(X, labels) score = sil * (1 - np.exp(-min_inter/0.5)) if score > best_score: best_score = score best_k = k return best_k def fit(self, X): X_red = self.reduce_dim(X) k_opt = self.optimal_clusters(X_red) cluster = AgglomerativeClustering(n_clusters=k_opt, linkage='ward') self.labels = cluster.fit_predict(X_red) return self.labels class ProbabilisticNNRecognizer: def __init__(self, sigma=0.15): self.sigma = sigma self.pnn = None def fit(self, X, y): from sklearn.neighbors import KernelDensity self.classes = np.unique(y) self.kdes = {} for c in self.classes: Xc = X[y==c] kde = KernelDensity(bandwidth=self.sigma, kernel='gaussian') kde.fit(Xc) self.kdes[c] = kde def predict(self, X): log_probs = np.zeros((len(X), len(self.classes))) for i, c in enumerate(self.classes): log_probs[:, i] = self.kdes[c].score_samples(X) return self.classes[np.argmax(log_probs, axis=1)] def predict_proba(self, X): probs = np.zeros((len(X), len(self.classes))) for i, c in enumerate(self.classes): probs[:, i] = np.exp(self.kdes[c].score_samples(X)) return probs / probs.sum(axis=1, keepdims=True) class CustomDesignWorkflow: def __init__(self, model_library): self.library = model_library # dict mapping class_id -> mean_surface self.recognizer = ProbabilisticNNRecognizer() def train_recognizer(self, features, labels): self.recognizer.fit(features, labels) def design_earphone(self, ear_scan, output_stl='custom_earphone.stl'): # extract features from ear_scan using FeaturePointExtractor and reconstruction # simplified: compute 20-dim feature vector features = self.extract_features(ear_scan) pred_class = self.recognizer.predict(features.reshape(1,-1))[0] template_surf = self.library[pred_class] # modify outer shape for earphone housing offset_surf = self.offset_surface(template_surf, offset=2.0) self.export_stl(offset_surf, output_stl) return pred_class def offset_surface(self, surf, offset): # simple offset along normal return surf def export_stl(self, surf, filename): pass def extract_features(self, mesh): # use PCA coefficients from the same projection as training return np.random.randn(20) # placeholder