matlab - Matlab不规则形状冲浪样图

Question

我打算使用Matlab在其状态空间上绘制随机过程的概率分布。状态空间可以用一个 150x150 矩阵的下三角来表示。请看图（没有网格的冲浪图）在某个时间点的概率分布。

我们可以看到，图中有高度的对称性，但是因为它被绘制成一个方阵，所以看起来有点奇怪。如果我们可以变换矩形，绘图看起来会很完美。我的问题是，如何使用Matlab将下三角形部分绘制/转换为等边三角形？

Answer 1

此功能应该为您完成这项工作。如果没有，请告诉我。

function matrix_lower_tri_to_surf(A)
%Displays lower triangle portion of matrix as an equilateral triangle
%Martin Stålberg, Uppsala University, 2013-07-12
%mast4461 at gmail

siz = size(A);
N = siz(1);
if ~(ndims(A)==2) || ~(N == siz(2))
    error('Matrix must be square');
end

zeds = @(N) zeros(N*(N+1)/2,1); %for initializing coordinate vectors
x = zeds(N); %x coordinates
y = zeds(N); %y coordinates
z = zeds(N); %z coordinates, will remain zero
r = zeds(N); %row indices
c = zeds(N); %column indices

l = 0; %base index
xt = 1:N; %temporary x coordinates
yt = 1; %temporary y coordinates

for k = N:-1:1
    ind = (1:k)+l; %coordinate indices
    l = l+k; %update base index

    x(ind) = xt; %save temporary x coordinates

    %next temporary x coordinates are the k-1 middle pairwise averages
    %calculated by linear interpolation through convolution
    xt = conv(xt,[.5,.5]);
    xt = xt(2:end-1);

    y(ind) = yt; %save temporary y coordinates
    yt = yt+1; %update temporary y coordinates

    r(ind) = N-k+1; %save row indices
    c(ind) = 1:k; % save column indices
end

v = A(sub2ind(size(A),r,c)); %extract values from matrix A
tri = delaunay(x,y); %create triangular mesh

h = trisurf(tri,x,y,z,v,'edgecolor','none','facecolor','interp'); %plot surface
axis vis3d; view(2); %adjust axes projection and proportions
daspect([sqrt(3)*.5,1,1]); %adjust aspect ratio to display equilateral triangle

end %end of function