MATLAB Delaunay算法提取离散点边界的方法

function polygon = minimal_convex_polygon(points)
 % 进行 delaunay 三角剖分，将所有连接了的边保存在矩阵 lines 中
 triangles = sort(delaunay(points(1, :), points(2, :)), 2);
 lines = zeros(size(triangles, 1) * 3, 2);
 for i = 1:size(triangles, 1)
 lines(3 * i - 2,:) = [triangles(i, 1), triangles(i, 2)];
 lines(3 * i - 1,:) = [triangles(i, 1), triangles(i, 3)];
 lines(3 * i,:) = [triangles(i, 2), triangles(i, 3)];
 end
 % 去掉 lines 中出现次数超过一次的边
 [~, IA] = unique(lines, 'rows');
 lines = setdiff(lines(IA, :), lines(setdiff(1:size(lines, 1), IA), :), 'rows');
 % 跟踪 lines 中的数据点，将凸多边形的顶点编号保存在 seqs 中
 seqs = zeros(size(lines, 1) + 1,1);
 seqs(1:2) = lines(1, :);
 lines(1, :) = [];
 for i = 3:size(seqs)
 pos = find(lines == seqs(i - 1));
 row = rem(pos - 1, size(lines, 1)) + 1;
 col = ceil(pos / size(lines, 1));
 seqs(i) = lines(row, 3 - col);
 lines(row, :) = [];
 end
 % 根据 seqs ， 得到凸多边形顶点坐标
 polygon = points(:, seqs);
end

plot(Pp(1,:),Pp(2,:), '*r', 'LineWidth', 4);  % Pp第一行为x坐标，第二行为y坐标
polygon = minimal_convex_polygon(Pp);
hold on;
plot(polygon(1, :), polygon(2, :), 'LineWidth', 2);