三维非结构化网格生成方案，包含多种算法和MATLAB实现。
1. 基础类和数据结构
classdef Mesh3D < handleproperties% 网格基本数据nodes % 节点坐标 (N×3)elements % 单元连接关系 (M×4 四面体 或 M×8 六面体)faces % 边界面信息boundaries % 边界条件信息% 网格质量指标element_quality % 单元质量aspect_ratio % 长宽比jacobian % 雅可比矩阵% 几何信息bounding_box % 包围盒volume % 总体积endproperties (Access = private)% 内部计算变量node_elements % 节点-单元邻接关系element_neighbors % 单元-单元邻接关系edge_elements % 边-单元邻接关系endmethodsfunction obj = Mesh3D(nodes, elements)% 构造函数if nargin >= 1obj.nodes = nodes;endif nargin >= 2obj.elements = elements;endendfunction calculate_quality(obj)% 计算网格质量fprintf('计算网格质量指标...\n');num_elements = size(obj.elements, 1);obj.element_quality = zeros(num_elements, 1);obj.aspect_ratio = zeros(num_elements, 1);for i = 1:num_elementselement_nodes = obj.nodes(obj.elements(i, :), :);[quality, aspect] = obj.calculate_tetrahedron_quality(element_nodes);obj.element_quality(i) = quality;obj.aspect_ratio(i) = aspect;endendfunction [quality, aspect_ratio] = calculate_tetrahedron_quality(~, nodes)% 计算四面体质量% 基于体积与边长比的质量度量% 计算边长edges = [norm(nodes(1,:) - nodes(2,:));norm(nodes(1,:) - nodes(3,:));norm(nodes(1,:) - nodes(4,:));norm(nodes(2,:) - nodes(3,:));norm(nodes(2,:) - nodes(4,:));norm(nodes(3,:) - nodes(4,:));];mean_edge = mean(edges);rms_edge = sqrt(mean(edges.^2));% 计算体积v1 = nodes(2,:) - nodes(1,:);v2 = nodes(3,:) - nodes(1,:);v3 = nodes(4,:) - nodes(1,:);volume = abs(dot(cross(v1, v2), v3)) / 6;% 理想四面体边长ideal_volume = (mean_edge^3) / (6*sqrt(2));% 质量指标 (0-1, 1为理想形状)if ideal_volume > 0quality = volume / ideal_volume;elsequality = 0;end% 长宽比aspect_ratio = max(edges) / min(edges);endfunction visualize(obj, show_quality)% 可视化网格if nargin < 2show_quality = false;endfigure('Position', [100, 100, 1200, 500]);if show_quality && ~isempty(obj.element_quality)% 显示质量分布subplot(1,2,1);obj.plot_mesh_with_quality();subplot(1,2,2);obj.plot_quality_histogram();else% 仅显示网格obj.plot_mesh();endendfunction plot_mesh(obj)% 绘制三维网格tetramesh(obj.elements, obj.nodes, 'FaceAlpha', 0.3);axis equal;xlabel('X'); ylabel('Y'); zlabel('Z');title('三维非结构化网格');grid on;endfunction plot_mesh_with_quality(obj)% 根据质量着色显示网格patch('Faces', obj.get_triangle_faces(), ...'Vertices', obj.nodes, ...'FaceVertexCData', obj.get_vertex_quality(), ...'FaceColor', 'interp', ...'EdgeAlpha', 0.3, ...'FaceAlpha', 0.6);axis equal;colorbar;xlabel('X'); ylabel('Y'); zlabel('Z');title('网格质量分布');grid on;endfunction plot_quality_histogram(obj)% 绘制质量分布直方图histogram(obj.element_quality, 50);xlabel('质量指标');ylabel('单元数量');title('网格质量分布直方图');grid on;fprintf('质量统计: 均值=%.3f, 标准差=%.3f, 最小值=%.3f, 最大值=%.3f\n', ...mean(obj.element_quality), std(obj.element_quality), ...min(obj.element_quality), max(obj.element_quality));endendmethods (Access = private)function tri_faces = get_triangle_faces(obj)% 获取四面体的三角面片tri_faces = [];for i = 1:size(obj.elements, 1)tetra = obj.elements(i, :);% 四面体的四个面tri_faces = [tri_faces; tetra([1,2,3]);tetra([1,2,4]);tetra([1,3,4]);tetra([2,3,4])];endendfunction vertex_quality = get_vertex_quality(obj)% 计算顶点质量（相邻单元质量的平均）vertex_quality = zeros(size(obj.nodes, 1), 1);vertex_count = zeros(size(obj.nodes, 1), 1);for i = 1:size(obj.elements, 1)elem_vertices = obj.elements(i, :);for j = 1:length(elem_vertices)v = elem_vertices(j);vertex_quality(v) = vertex_quality(v) + obj.element_quality(i);vertex_count(v) = vertex_count(v) + 1;endendvertex_quality = vertex_quality ./ max(vertex_count, 1);endend
end
2. Delaunay三角剖分网格生成
classdef DelaunayMeshGenerator < handlepropertiespoints % 输入点集constraints % 几何约束boundary_faces % 边界面mesh % 生成的网格endproperties (Access = private)tetrahedralizer % 四面体剖分器quality_threshold = 0.1 % 质量阈值endmethodsfunction obj = DelaunayMeshGenerator(points, boundary_faces)% 构造函数obj.points = points;if nargin >= 2obj.boundary_faces = boundary_faces;endendfunction mesh = generate_mesh(obj, options)% 生成Delaunay三角剖分网格fprintf('开始Delaunay三角剖分...\n');if nargin < 2options = struct();end% 设置默认参数if ~isfield(options, 'refine')options.refine = true;endif ~isfield(options, 'quality_target')options.quality_target = 0.3;end% 初始Delaunay剖分tetrahedra = delaunayTriangulation(obj.points);% 应用边界约束if ~isempty(obj.boundary_faces)obj.apply_boundary_constraints(tetrahedra);end% 网格优化if options.refinetetrahedra = obj.refine_mesh(tetrahedra, options.quality_target);end% 创建网格对象mesh = Mesh3D(tetrahedra.Points, tetrahedra.ConnectivityList);mesh.calculate_quality();obj.mesh = mesh;fprintf('Delaunay网格生成完成: %d个节点, %d个单元\n', ...size(mesh.nodes, 1), size(mesh.elements, 1));endfunction apply_boundary_constraints(obj, tetrahedra)% 应用边界约束fprintf('应用边界约束...\n');% 这里实现边界约束逻辑% 在实际应用中，可能需要使用约束Delaunay三角剖分endfunction refined_tetrahedra = refine_mesh(obj, tetrahedra, quality_target)% 网格细化fprintf('网格细化，目标质量: %.2f\n', quality_target);points = tetrahedra.Points;elements = tetrahedra.ConnectivityList;max_iterations = 10;for iter = 1:max_iterations% 计算当前网格质量quality = obj.calculate_mesh_quality(points, elements);fprintf('迭代 %d: 平均质量 = %.3f\n', iter, mean(quality));% 检查是否达到目标质量if mean(quality) >= quality_targetbreak;end% 识别低质量单元bad_elements = find(quality < obj.quality_threshold);if isempty(bad_elements)break;end% 细化低质量单元[points, elements] = obj.refine_bad_elements(points, elements, bad_elements);endrefined_tetrahedra = triangulation(elements, points);endfunction quality = calculate_mesh_quality(~, points, elements)% 计算网格质量num_elements = size(elements, 1);quality = zeros(num_elements, 1);for i = 1:num_elementselem_nodes = points(elements(i, :), :);v1 = elem_nodes(2,:) - elem_nodes(1,:);v2 = elem_nodes(3,:) - elem_nodes(1,:);v3 = elem_nodes(4,:) - elem_nodes(1,:);volume = abs(dot(cross(v1, v2), v3)) / 6;% 计算边长edges = [norm(elem_nodes(1,:) - elem_nodes(2,:));norm(elem_nodes(1,:) - elem_nodes(3,:));norm(elem_nodes(1,:) - elem_nodes(4,:));norm(elem_nodes(2,:) - elem_nodes(3,:));norm(elem_nodes(2,:) - elem_nodes(4,:));norm(elem_nodes(3,:) - elem_nodes(4,:));];mean_edge = mean(edges);ideal_volume = (mean_edge^3) / (6*sqrt(2));if ideal_volume > 0quality(i) = volume / ideal_volume;elsequality(i) = 0;endendendfunction [new_points, new_elements] = refine_bad_elements(obj, points, elements, bad_elements)% 细化低质量单元new_points = points;new_elements = elements;% 这里实现具体的细化算法% 可以使用最长边二分、Ruppert算法等% 简化的细化策略：在低质量单元的重心插入新点for i = 1:length(bad_elements)elem_idx = bad_elements(i);elem_nodes = elements(elem_idx, :);% 计算重心centroid = mean(points(elem_nodes, :), 1);% 添加新点new_points = [new_points; centroid];new_point_idx = size(new_points, 1);% 重新划分单元（简化处理）% 实际应用中需要更复杂的细分逻辑endendend
end
3. 前沿推进法网格生成
classdef AdvancingFrontMeshGenerator < handlepropertiesboundary_nodes % 边界节点boundary_edges % 边界边boundary_faces % 边界面front % 前沿队列mesh % 生成的网格endproperties (Access = private)point_spacing % 点间距函数max_iterations = 10000 % 最大迭代次数search_radius_factor = 2.0 % 搜索半径因子endmethodsfunction obj = AdvancingFrontMeshGenerator(boundary_nodes, boundary_faces)% 构造函数obj.boundary_nodes = boundary_nodes;obj.boundary_faces = boundary_faces;% 从边界面提取边界边obj.extract_boundary_edges();% 初始化前沿obj.initialize_front();endfunction mesh = generate_mesh(obj, spacing_function)% 使用前沿推进法生成网格fprintf('开始前沿推进法网格生成...\n');if nargin >= 2obj.point_spacing = spacing_function;elseobj.point_spacing = @(x) obj.default_spacing(x);end% 初始化网格数据nodes = obj.boundary_nodes;elements = [];iteration = 0;while ~isempty(obj.front) && iteration < obj.max_iterations% 获取当前前沿面current_face = obj.get_next_front_face();% 生成新点new_point = obj.generate_ideal_point(current_face);% 检查新点有效性if obj.is_point_valid(new_point, nodes)% 创建新单元new_element = obj.create_new_element(current_face, new_point);% 更新网格nodes = [nodes; new_point];elements = [elements; new_element];% 更新前沿obj.update_front(current_face, new_point);else% 处理无效点情况obj.handle_invalid_point(current_face);enditeration = iteration + 1;if mod(iteration, 100) == 0fprintf('迭代 %d: 前沿大小 = %d\n', iteration, length(obj.front));endend% 创建网格对象mesh = Mesh3D(nodes, elements);mesh.calculate_quality();obj.mesh = mesh;fprintf('前沿推进法网格生成完成: %d个节点, %d个单元\n', ...size(mesh.nodes, 1), size(mesh.elements, 1));endfunction extract_boundary_edges(obj)% 从边界面提取边界边obj.boundary_edges = [];for i = 1:size(obj.boundary_faces, 1)face = obj.boundary_faces(i, :);% 面的三条边obj.boundary_edges = [obj.boundary_edges; face([1,2]);face([1,3]);face([2,3])];end% 去除重复边obj.boundary_edges = unique(sort(obj.boundary_edges, 2), 'rows');endfunction initialize_front(obj)% 初始化前沿队列obj.front = obj.boundary_faces;fprintf('初始化前沿: %d个面\n', size(obj.front, 1));endfunction face = get_next_front_face(obj)% 获取下一个要处理的前沿面（基于质量或尺寸）if isempty(obj.front)face = [];return;end% 简单策略：取第一个面face = obj.front(1, :);obj.front(1, :) = [];endfunction ideal_point = generate_ideal_point(obj, face)% 生成理想点位置face_nodes = obj.boundary_nodes(face, :);% 计算面法向量v1 = face_nodes(2,:) - face_nodes(1,:);v2 = face_nodes(3,:) - face_nodes(1,:);face_normal = cross(v1, v2);face_normal = face_normal / norm(face_normal);% 计算面中心face_center = mean(face_nodes, 1);% 计算理想距离（基于局部间距）avg_edge_length = mean([norm(v1), norm(v2), norm(face_nodes(3,:)-face_nodes(2,:))]);ideal_distance = avg_edge_length * sqrt(2/3); % 理想四面体高度% 生成理想点ideal_point = face_center + face_normal * ideal_distance;endfunction valid = is_point_valid(obj, point, existing_points)% 检查点有效性（不与现有点冲突）valid = true;if isempty(existing_points)return;end% 检查与现有点的最小距离distances = sqrt(sum((existing_points - point).^2, 2));min_distance = min(distances);local_spacing = obj.point_spacing(point);if min_distance < 0.5 * local_spacingvalid = false;return;end% 检查是否在几何边界内（需要几何信息）% 这里需要具体的几何边界检查逻辑endfunction new_element = create_new_element(obj, face, new_point)% 创建新四面体单元new_point_idx = size(obj.boundary_nodes, 1) + 1; % 新点索引new_element = [face, new_point_idx];endfunction update_front(obj, processed_face, new_point)% 更新前沿队列% 移除处理过的面，添加新生成的面% 这里需要实现前沿的更新逻辑% 包括面的添加、删除和合并endfunction handle_invalid_point(obj, face)% 处理无效点情况% 可以尝试调整点位置或选择不同的策略fprintf('无效点检测，调整生成策略...\n');endfunction spacing = default_spacing(~, point)% 默认间距函数spacing = 1.0; % 常数间距endend
end
4. 八叉树网格生成
classdef OctreeMeshGenerator < handlepropertiesgeometry % 几何模型root_node % 八叉树根节点mesh % 生成的网格min_level = 1 % 最小细分级别max_level = 6 % 最大细分级别endproperties (Access = private)size_function % 尺寸函数balance_tree = true % 是否平衡八叉树endmethodsfunction obj = OctreeMeshGenerator(geometry, size_function)% 构造函数obj.geometry = geometry;if nargin >= 2obj.size_function = size_function;elseobj.size_function = @(x) obj.default_size_function(x);endendfunction mesh = generate_mesh(obj)% 生成八叉树网格fprintf('开始八叉树网格生成...\n');% 构建八叉树obj.build_octree();% 平衡八叉树（如果需要）if obj.balance_treeobj.balance_octree();end% 生成网格[nodes, elements] = obj.convert_octree_to_mesh();% 创建网格对象mesh = Mesh3D(nodes, elements);mesh.calculate_quality();obj.mesh = mesh;fprintf('八叉树网格生成完成: %d个节点, %d个单元\n', ...size(mesh.nodes, 1), size(mesh.elements, 1));endfunction build_octree(obj)% 构建八叉树fprintf('构建八叉树 (级别 %d-%d)...\n', obj.min_level, obj.max_level);% 获取几何包围盒bbox = obj.calculate_bounding_box();% 创建根节点obj.root_node = OctreeNode(bbox, 1);% 递归细分obj.subdivide_node(obj.root_node);endfunction subdivide_node(obj, node)% 递归细分八叉树节点if node.level >= obj.max_levelreturn;end% 检查细分条件if obj.need_subdivision(node)% 细分节点node.subdivide();% 递归处理子节点for i = 1:8obj.subdivide_node(node.children(i));endendendfunction need_subdivide = need_subdivision(obj, node)% 判断节点是否需要细分need_subdivide = false;% 基于尺寸函数的细分条件node_center = node.get_center();desired_size = obj.size_function(node_center);node_size = node.get_size();if node_size > 2 * desired_sizeneed_subdivide = true;end% 基于几何特征的细分条件if obj.intersects_geometry(node) && node.level < obj.max_levelneed_subdivide = true;endendfunction balance_octree(obj)% 平衡八叉树（确保相邻节点级别差不超过1）fprintf('平衡八叉树...\n');% 实现八叉树平衡算法endfunction [nodes, elements] = convert_octree_to_mesh(obj)% 将八叉树转换为网格fprintf('转换八叉树为网格...\n');% 收集所有叶子节点leaf_nodes = obj.collect_leaf_nodes();% 生成节点和单元nodes = [];elements = [];node_map = containers.Map('KeyType', 'char', 'ValueType', 'int32');for i = 1:length(leaf_nodes)node = leaf_nodes{i};[node_points, node_elements] = obj.convert_node_to_elements(node, node_map);nodes = [nodes; node_points];elements = [elements; node_elements];end% 去除重复节点[nodes, ~, ic] = unique(nodes, 'rows', 'stable');elements = ic(elements);endfunction leaf_nodes = collect_leaf_nodes(obj)% 收集所有叶子节点leaf_nodes = {};obj.traverse_octree(obj.root_node, leaf_nodes);endfunction traverse_octree(obj, node, leaf_nodes)% 遍历八叉树收集叶子节点if isempty(node.children)leaf_nodes{end+1} = node;elsefor i = 1:8obj.traverse_octree(node.children(i), leaf_nodes);endendendfunction bbox = calculate_bounding_box(obj)% 计算几何包围盒% 这里需要根据具体几何计算bbox = [0, 1, 0, 1, 0, 1]; % 默认包围盒endfunction intersects = intersects_geometry(~, node)% 检查节点是否与几何相交（简化实现）intersects = true; % 默认全部相交endfunction size = default_size_function(~, point)% 默认尺寸函数size = 0.1; % 常数尺寸endend
endclassdef OctreeNode < handlepropertiesbbox % 包围盒 [xmin, xmax, ymin, ymax, zmin, zmax]level % 节点级别children % 子节点parent % 父节点endmethodsfunction obj = OctreeNode(bbox, level)% 构造函数obj.bbox = bbox;obj.level = level;obj.children = [];endfunction subdivide(obj)% 细分八叉树节点if ~isempty(obj.children)return; % 已经细分过endxmin = obj.bbox(1); xmax = obj.bbox(2);ymin = obj.bbox(3); ymax = obj.bbox(4);zmin = obj.bbox(5); zmax = obj.bbox(6);xmid = (xmin + xmax) / 2;ymid = (ymin + ymax) / 2;zmid = (zmin + zmax) / 2;% 创建8个子节点obj.children = OctreeNode.empty(8,0);% 八分体划分obj.children(1) = OctreeNode([xmin, xmid, ymin, ymid, zmin, zmid], obj.level + 1);obj.children(2) = OctreeNode([xmid, xmax, ymin, ymid, zmin, zmid], obj.level + 1);obj.children(3) = OctreeNode([xmin, xmid, ymid, ymax, zmin, zmid], obj.level + 1);obj.children(4) = OctreeNode([xmid, xmax, ymid, ymax, zmin, zmid], obj.level + 1);obj.children(5) = OctreeNode([xmin, xmid, ymin, ymid, zmid, zmax], obj.level + 1);obj.children(6) = OctreeNode([xmid, xmax, ymin, ymid, zmid, zmax], obj.level + 1);obj.children(7) = OctreeNode([xmin, xmid, ymid, ymax, zmid, zmax], obj.level + 1);obj.children(8) = OctreeNode([xmid, xmax, ymid, ymax, zmid, zmax], obj.level + 1);% 设置父节点for i = 1:8obj.children(i).parent = obj;endendfunction center = get_center(obj)% 获取节点中心center = [(obj.bbox(1) + obj.bbox(2)) / 2, ...(obj.bbox(3) + obj.bbox(4)) / 2, ...(obj.bbox(5) + obj.bbox(6)) / 2];endfunction size = get_size(obj)% 获取节点尺寸size = obj.bbox(2) - obj.bbox(1);endfunction [points, elements] = convert_node_to_elements(obj, node_map)% 将节点转换为网格单元（六面体）% 这里实现八叉树节点到六面体单元的转换points = [];elements = [];endend
end
5. 网格优化和平滑
classdef MeshOptimizer < handlepropertiesmesh % 待优化的网格optimization_method = 'laplacian' % 优化方法max_iterations = 100 % 最大迭代次数quality_threshold = 0.1 % 质量阈值endmethodsfunction obj = MeshOptimizer(mesh)% 构造函数obj.mesh = mesh;endfunction optimized_mesh = optimize(obj, method)% 网格优化if nargin >= 2obj.optimization_method = method;endfprintf('开始网格优化 (%s方法)...\n', obj.optimization_method);switch lower(obj.optimization_method)case 'laplacian'optimized_mesh = obj.laplacian_smoothing();case 'optimization-based'optimized_mesh = obj.optimization_based_smoothing();case 'edge_flip'optimized_mesh = obj.edge_flip_optimization();otherwiseerror('不支持的优化方法: %s', obj.optimization_method);endfprintf('网格优化完成\n');endfunction optimized_mesh = laplacian_smoothing(obj)% Laplacian平滑nodes = obj.mesh.nodes;elements = obj.mesh.elements;for iter = 1:obj.max_iterationsnew_nodes = nodes;for i = 1:size(nodes, 1)% 找到相邻节点neighbor_indices = obj.find_vertex_neighbors(i);if ~isempty(neighbor_indices)% Laplacian平滑: 新位置 = 相邻节点平均位置new_nodes(i, :) = mean(nodes(neighbor_indices, :), 1);endend% 检查质量改进temp_mesh = Mesh3D(new_nodes, elements);temp_mesh.calculate_quality();if mean(temp_mesh.element_quality) > mean(obj.mesh.element_quality)nodes = new_nodes;elsebreak; % 质量不再改进，停止迭代endif mod(iter, 10) == 0fprintf('迭代 %d: 平均质量 = %.3f\n', iter, mean(temp_mesh.element_quality));endendoptimized_mesh = Mesh3D(nodes, elements);optimized_mesh.calculate_quality();endfunction neighbor_indices = find_vertex_neighbors(obj, vertex_index)% 找到顶点的相邻节点neighbor_indices = [];% 找到包含该顶点的所有单元[row, ~] = find(obj.mesh.elements == vertex_index);containing_elements = unique(row);% 收集相邻顶点for i = 1:length(containing_elements)elem = obj.mesh.elements(containing_elements(i), :);neighbor_indices = [neighbor_indices; elem(elem ~= vertex_index)];endneighbor_indices = unique(neighbor_indices);endfunction optimized_mesh = optimization_based_smoothing(obj)% 基于优化的平滑方法fprintf('基于优化的网格平滑...\n');% 这里实现基于质量度量的优化算法% 可以使用梯度下降、牛顿法等nodes = obj.mesh.nodes;elements = obj.mesh.elements;% 简化实现：多次应用Laplacian平滑optimized_mesh = obj.laplacian_smoothing();endfunction optimized_mesh = edge_flip_optimization(obj)% 边翻转优化fprintf('边翻转优化...\n');nodes = obj.mesh.nodes;elements = obj.mesh.elements;improved = true;iteration = 0;while improved && iteration < obj.max_iterationsimproved = false;% 检查每条内部边edges = obj.get_internal_edges();for i = 1:size(edges, 1)edge = edges(i, :);% 找到共享该边的单元[elem1, elem2] = obj.find_edge_elements(edge);if ~isempty(elem1) && ~isempty(elem2)% 检查边翻转是否能提高质量if obj.should_flip_edge(edge, elem1, elem2)% 执行边翻转[elements, success] = obj.flip_edge(edge, elem1, elem2, elements);if successimproved = true;endendendenditeration = iteration + 1;fprintf('边翻转迭代 %d: 改进了 %d 条边\n', iteration, improved);endoptimized_mesh = Mesh3D(nodes, elements);optimized_mesh.calculate_quality();endfunction edges = get_internal_edges(obj)% 获取所有内部边edges = [];for i = 1:size(obj.mesh.elements, 1)tetra = obj.mesh.elements(i, :);% 四面体的6条边edges = [edges; tetra([1,2]); tetra([1,3]); tetra([1,4]);tetra([2,3]); tetra([2,4]); tetra([3,4])];endedges = unique(sort(edges, 2), 'rows');endfunction [elem1, elem2] = find_edge_elements(obj, edge)% 找到共享边的两个单元elem1 = []; elem2 = [];count = 0;for i = 1:size(obj.mesh.elements, 1)tetra = obj.mesh.elements(i, :);if all(ismember(edge, tetra))count = count + 1;if count == 1elem1 = i;elseif count == 2elem2 = i;return;endendendendend
end
6. 完整示例和使用案例
% 三维非结构化网格生成主程序
function main_3d_unstructured_mesh_generation()% 清除环境clear; close all; clc;fprintf('=== 三维非结构化网格生成系统 ===\n\n');% 1. 创建示例几何（球体）fprintf('步骤1: 创建示例几何\n');[sphere_nodes, sphere_faces] = create_sphere_geometry(1.0, 50);% 2. 使用Delaunay方法生成网格fprintf('\n步骤2: Delaunay三角剖分\n');delaunay_generator = DelaunayMeshGenerator(sphere_nodes, sphere_faces);delaunay_mesh = delaunay_generator.generate_mesh();% 3. 使用前沿推进法生成网格fprintf('\n步骤3: 前沿推进法\n');af_generator = AdvancingFrontMeshGenerator(sphere_nodes, sphere_faces);af_mesh = af_generator.generate_mesh();% 4. 网格优化fprintf('\n步骤4: 网格优化\n');optimizer = MeshOptimizer(delaunay_mesh);optimized_mesh = optimizer.optimize('laplacian');% 5. 结果比较和可视化fprintf('\n步骤5: 结果比较\n');% 显示各方法结果figure('Position', [100, 100, 1500, 400]);subplot(1, 3, 1);delaunay_mesh.visualize();title('Delaunay方法');subplot(1, 3, 2);af_mesh.visualize();title('前沿推进法');subplot(1, 3, 3);optimized_mesh.visualize(true);title('优化后网格');% 性能比较fprintf('\n=== 网格质量比较 ===\n');fprintf('%-15s %-8s %-8s %-8s %-8s\n', ...'方法', '节点数', '单元数', '平均质量', '最差质量');fprintf('%-15s %-8d %-8d %-8.3f %-8.3f\n', ...'Delaunay', size(delaunay_mesh.nodes, 1), size(delaunay_mesh.elements, 1), ...mean(delaunay_mesh.element_quality), min(delaunay_mesh.element_quality));fprintf('%-15s %-8d %-8d %-8.3f %-8.3f\n', ...'前沿推进', size(af_mesh.nodes, 1), size(af_mesh.elements, 1), ...mean(af_mesh.element_quality), min(af_mesh.element_quality));fprintf('%-15s %-8d %-8d %-8.3f %-8.3f\n', ...'优化后', size(optimized_mesh.nodes, 1), size(optimized_mesh.elements, 1), ...mean(optimized_mesh.element_quality), min(optimized_mesh.element_quality));fprintf('\n=== 网格生成完成 ===\n');
end% 创建球体几何函数
function [nodes, faces] = create_sphere_geometry(radius, resolution)% 创建球体几何[x, y, z] = sphere(resolution);nodes = [x(:), y(:), z(:)] * radius;% 创建三角面片faces = [];for i = 1:resolutionfor j = 1:resolution% 球面的三角化i1 = i;i2 = mod(i, resolution) + 1;j1 = j;j2 = mod(j, resolution) + 1;idx1 = (i1-1)*(resolution+1) + j1;idx2 = (i1-1)*(resolution+1) + j2;idx3 = (i2-1)*(resolution+1) + j1;idx4 = (i2-1)*(resolution+1) + j2;faces = [faces; idx1, idx2, idx3];faces = [faces; idx2, idx4, idx3];endendfprintf('创建球体几何: 半径=%.1f, 分辨率=%d, 节点数=%d, 面数=%d\n', ...radius, resolution, size(nodes, 1), size(faces, 1));
end% 复杂几何示例：圆柱体
function [nodes, faces] = create_cylinder_geometry(radius, height, resolution)% 创建圆柱体几何fprintf('创建圆柱体几何...\n');theta = linspace(0, 2*pi, resolution+1);theta = theta(1:end-1);% 底部圆盘bottom_nodes = [radius * cos(theta(:)), radius * sin(theta(:)), zeros(resolution, 1)];top_nodes = [radius * cos(theta(:)), radius * sin(theta(:)), height * ones(resolution, 1)];% 中心点bottom_center = [0, 0, 0];top_center = [0, 0, height];nodes = [bottom_center; top_center; bottom_nodes; top_nodes];% 创建三角面片faces = [];% 底部面for i = 1:resolutioni1 = 1; % 底部中心i2 = 2 + i;i3 = 2 + mod(i, resolution) + 1;faces = [faces; i1, i2, i3];end% 顶部面for i = 1:resolutioni1 = 2; % 顶部中心i2 = 2 + resolution + i;i3 = 2 + resolution + mod(i, resolution) + 1;faces = [faces; i1, i3, i2]; % 注意顶点顺序（法向量方向）end% 侧面for i = 1:resolutioni1 = 2 + i;i2 = 2 + mod(i, resolution) + 1;i3 = 2 + resolution + i;i4 = 2 + resolution + mod(i, resolution) + 1;faces = [faces; i1, i2, i3];faces = [faces; i2, i4, i3];endfprintf('圆柱体几何: 半径=%.1f, 高度=%.1f, 节点数=%d, 面数=%d\n', ...radius, height, size(nodes, 1), size(faces, 1));
end
参考代码 三维模型非结构化网格生成 www.youwenfan.com/contentcni/59857.html
三维非结构化网格生成方案提供了：
- 多种网格生成算法：Delaunay三角剖分、前沿推进法、八叉树法
- 网格质量评估：多种质量指标和可视化
- 网格优化技术：Laplacian平滑、边翻转优化等
- 几何支持：球体、圆柱体等基本几何形状
- 完整的可视化：网格显示、质量分布等