三维模型非结构化网格生成
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 < handle
properties
% 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
end
properties (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
end
methods
function obj = Mesh3D(nodes, elements)
% 构造函数
if nargin >= 1
obj.nodes = nodes;
end
if nargin >= 2
obj.elements = elements;
end
end
function 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_elements
element_nodes = obj.nodes(obj.elements(i, :), :);
[quality, aspect] = obj.calculate_tetrahedron_quality(element_nodes);
obj.element_quality(i) = quality;
obj.aspect_ratio(i) = aspect;
end
end
function [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 > 0
quality = volume / ideal_volume;
else
quality = 0;
end
% 长宽比
aspect_ratio = max(edges) / min(edges);
end
function visualize(obj, show_quality)
% 可视化网格
if nargin < 2
show_quality = false;
end
figure('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();
end
end
function 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;
end
function 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;
end
function 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));
end
end
methods (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])];
end
end
function 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;
end
end
vertex_quality = vertex_quality ./ max(vertex_count, 1);
end
end
end
2. Delaunay三角剖分网格生成
classdef DelaunayMeshGenerator < handle
properties
points % 输入点集
constraints % 几何约束
boundary_faces % 边界面
mesh % 生成的网格
end
properties (Access = private)
tetrahedralizer % 四面体剖分器
quality_threshold = 0.1 % 质量阈值
end
methods
function obj = DelaunayMeshGenerator(points, boundary_faces)
% 构造函数
obj.points = points;
if nargin >= 2
obj.boundary_faces = boundary_faces;
end
end
function 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 < 2
options = struct();
end
% 设置默认参数
if ~isfield(options, 'refine')
options.refine = true;
end
if ~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.refine
tetrahedra = 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));
end
function 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
end
function 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_target
break;
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);
end
refined_tetrahedra = triangulation(elements, points);
end
function 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_elements
elem_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 > 0
quality(i) = volume / ideal_volume;
else
quality(i) = 0;
end
end
end
function [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
end
end
end
end
3. 前沿推进法网格生成
classdef AdvancingFrontMeshGenerator < handle
properties
boundary_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
end
properties (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
end
methods
function 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();
end
function 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 >= 2
obj.point_spacing = spacing_function;
else
obj.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);
end
iteration = iteration + 1;
if mod(iteration, 100) == 0
fprintf('迭代 %d: 前沿大小 = %d\n', iteration, length(obj.front));
end
end
% 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));
end
function 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');
end
function 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));
end
function 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, :) = [];
end
function 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;
end
function 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_spacing
valid = 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
end
function 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];
end
function 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
end
function 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');
end
function spacing = default_spacing(~, point)
% 默认间距函数
spacing = 1.0; % 常数间距
end
end
end
4. 八叉树网格生成
classdef OctreeMeshGenerator < handle
properties
geometry % 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
end
properties (Access = private)
size_function % 尺寸函数
balance_tree = true % 是否平衡八叉树
end
methods
function obj = OctreeMeshGenerator(geometry, size_function)
% 构造函数
obj.geometry = geometry;
if nargin >= 2
obj.size_function = size_function;
else
obj.size_function = @(x) obj.default_size_function(x);
end
end
function 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_tree
obj.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));
end
function 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);
end
function subdivide_node(obj, node)
% 递归细分八叉树节点
if node.level >= obj.max_level
return;
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 = 1:8
obj.subdivide_node(node.children(i));
end
end
end
function 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_size
need_subdivide = true;
end
% 基于几何特征的细分条件
if obj.intersects_geometry(node) && node.level < obj.max_level
need_subdivide = true;
end
end
function 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
end
function [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);
end
function leaf_nodes = collect_leaf_nodes(obj)
% 收集所有叶子节点
leaf_nodes = {};
obj.traverse_octree(obj.root_node, leaf_nodes);
end
function 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;
else
for i = 1:8
obj.traverse_octree(node.children(i), leaf_nodes);
end
end
end
function 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
end
function 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
end
function size = default_size_function(~, point)
% 默认尺寸函数
size = 0.1; % 常数尺寸
end
end
end
classdef OctreeNode < handle
properties
bbox % 包围盒 [xmin, xmax, ymin, ymax, zmin, zmax]
level % 节点级别
children % 子节点
parent % 父节点
end
methods
function obj = OctreeNode(bbox, level)
% 构造函数
obj.bbox = bbox;
obj.level = level;
obj.children = [];
end
function subdivide(obj)
% 细分八叉树节点
if ~isempty(obj.children)
return; % 已经细分过
end
xmin = 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 = 1:8
obj.children(i).parent = obj;
end
end
function 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
];
end
function size = get_size(obj)
% 获取节点尺寸
size = obj.bbox(2) - obj.bbox(1);
end
function [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 = [];
end
end
end
5. 网格优化和平滑
classdef MeshOptimizer < handle
properties
mesh % 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
end
methods
function obj = MeshOptimizer(mesh)
% 构造函数
obj.mesh = mesh;
end
function optimized_mesh = optimize(obj, method)
% 网格优化
if nargin >= 2
obj.optimization_method = method;
end
fprintf('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();
otherwise
error('不支持的优化方法: %s', obj.optimization_method);
end
fprintf('网格优化完成\n');
end
function optimized_mesh = laplacian_smoothing(obj)
% Laplacian平滑
nodes = obj.mesh.nodes;
elements = obj.mesh.elements;
for iter = 1:obj.max_iterations
new_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);
end
end
% 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;
else
break; % 质量不再改进，停止迭代
end
if mod(iter, 10) == 0
fprintf('迭代 %d: 平均质量 = %.3f\n', iter, mean(temp_mesh.element_quality));
end
end
optimized_mesh = Mesh3D(nodes, elements);
optimized_mesh.calculate_quality();
end
function 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)];
end
neighbor_indices = unique(neighbor_indices);
end
function 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();
end
function 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_iterations
improved = 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 success
improved = true;
end
end
end
end
iteration = iteration + 1;
fprintf('边翻转迭代 %d: 改进了 %d 条边\n', iteration, improved);
end
optimized_mesh = Mesh3D(nodes, elements);
optimized_mesh.calculate_quality();
end
function 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])];
end
edges = unique(sort(edges, 2), 'rows');
end
function [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 == 1
elem1 = i;
elseif count == 2
elem2 = i;
return;
end
end
end
end
end
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:resolution
for 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];
end
end
fprintf('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:resolution
i1 = 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:resolution
i1 = 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:resolution
i1 = 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];
end
fprintf('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
