Delaunay图的角度计算

Question

我用MATLAB绘制了一个Delaunay图，如下所示：-

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我想计算一下图中的所有角度。对于所有无序形式的点，我都有x和y值，我不知道如何对这些点进行排序，因为x和y值对于同一行中的那些点是接近的。

Answer 1

这样做的一个方法是：

x = randn(1,4)*10;
y = randn(1,4)*10;

%calculate the triangulation
tri = delaunay(x,y);

%Plot the graph
triplot(tri,x,y)
hold on

plot(x,y,'ro')
text(x,y,strsplit(num2str(1:length(x))))


% Determine each angle
for i = 1:size(tri,1)
    per = perms(tri(i,:));
    [~, ind] = unique(per(:,2)); %avoid to calculate two time the same angle.
    per = per(ind,:); %the 3 * 3 points that create the angle of each triangle
    for j = 1:3
       P_1 = per(j,1);
       P1 = [x(P_1),y(P_1)];
       P_2 = per(j,2);
       P2 = [x(P_2),y(P_2)];
       P_3 = per(j,3);
       P3 = [x(P_3),y(P_3)];
       ANG = rad2deg(atan2(abs(det([P3-P2;P1-P2])),dot(P3-P2,P1-P2))); %P2 is the point in the middle
       fprintf('Node %d %d %d angle %f\n',P_1, P_2, P_3, ANG)
    end
end