matlab - 将矩阵旋转一定角度

Question

一个下午浪费在了以下问题上:

我在某个空间域中有一个深度值矩阵。我在域中定义了一条线，然后删除了这条线下方的值。

代码使用 findnearest函数查找最接近特定值的数组元素的索引。

clear all
close all

dx = 5;
dz = 1;

%angle between line and ground
a=atan(0.05);

%%%define domain
xi = 0:dx:20e3;
zi = 0:dz:1000;
m=length(zi);
n=length(xi);

%create grid
[x,z] = meshgrid(xi,zi);

%z where line starts
zs = 700;
%set line
 for i = 1:findnearest(xi,zi(zs)*1/a)
  xind(i) = i;
  zind(i) = findnearest(zi, fix(-xi(i)*a +zi(zs))); 
 end


depth = repmat(zi',1,n); %simply the coordinate zi repeated for all xi

 %calculate distance from the line
 for ii=1:n %for every x

    zslope = -a*xi(ii)+zi(zs);%equation of the line

    zz(ii)=zslope;
   if zslope>=0 %if the line is still in the domain (z>0)
     for jj=1:m %for every z

       if zi(jj)>=zslope %above the line

         Zs(jj,ii) = zi(jj)-zslope; %height above the line

        elseif zi(jj)<zslope %below the line (ground)
%            
          Zs(jj,ii)=NaN; 

       end
     end%for on z

   elseif zslope<0 %the line is no longer in the domain

       for jj=1:m %for every z

          Zs(jj,ii) = zi(jj)-zslope; %height above the line

       end
   end
end%for on x 

figure
imagesc(Zs)
colorbar
title('distance from the line')

%zone above the line
maskINT=zeros(m,n);
inds = find(Zs>=0); %erase values under the line
maskINT(inds)=1;


figure
imagesc(depth);colorbar
title('depth')

figure
imagesc(depth.*maskINT);colorbar
title('depth  above the line')

figure
contour(depth.*maskINT);colorbar
set(gca,'YDir','Reverse')
title('depth')

生成的深度矩阵如下:

用contour表示的是这样的:

我想将深度矩阵旋转一个角度 (-pi/2-a?) 或对其应用一些变换，这样深度等高线就会垂直于平行于第一行:

我简单地使用了各种旋转矩阵，但没有很好的结果......

Answer 1

我没有完整的答案，但我确实通过一些调整找到了解决这个问题的方法。

我做了什么:

当你有分界线时，这就是重要的值(value)观。对于旋转区域内的点，我找到了 x 方向的值并从原始深度矩阵复制它。为了简单起见，我让 x 数据上的值与 y 具有相同的距离。

在这些改编之后我得到了这个: 请注意，我也为我所做的做了标记。

但是，在您的代码中，X/Y 比率并不相同。如果我只是将我的代码部分复制到你的代码中，我会得到垂直线，因为你的角度是 ~0，尽管在图像中接近 45 度。要进行适当的调整，您实际上需要按值而不是索引进行比较，就像我所做的那样。

这里是改编后的代码(为了比较，查找 %ADDED 注释):

clear all
close all

dx = 1; %ADDED
dz = 1;

%angle between line and ground
angle=pi/3;  %ADDED
a=atan(angle);

%%%define domain
xi = 0:dx:1000;%ADDED
zi = 0:dz:1000;%ADDED
m=length(zi);
n=length(xi);



%%%ADDED %prealocating
Zs=zeros(m,n);
Zs2=zeros(m,n);
depth2=zeros(m,n);
zz=zeros(1,n);



%create grid
[x,z] = meshgrid(xi,zi);

%z where line starts
zs = 700;
%set line
for i = 1:findnearest(xi,zi(zs)*1/a)
    xind(i) = i;
    zind(i) = findnearest(zi, fix(-xi(i)*a +zi(zs)));
end


depth = repmat(zi',1,n); %simply the coordinate zi repeated for all xi

%calculate distance from the line
for ii=1:n %for every x

    zslope = -a*xi(ii)+zi(zs);%equation of the line

    zz(ii)=zslope;
    if zslope>=0 %if the line is still in the domain (z>0)
        for jj=1:m %for every z

            if zi(jj)>=zslope %above the line

                Zs(jj,ii) = zi(jj)-zslope; %height above the line

            elseif zi(jj)<zslope %below the line (ground)
                %
                Zs(jj,ii)=NaN;

                %ADDED
                Zs2(jj,ii)=abs(zi(jj)-zslope);%height above the line
                depth2(jj,ii)= depth(jj+round(Zs2(jj,ii)*cos(angle)),ii);

            end
        end%for on z

    elseif zslope<0 %the line is no longer in the domain

        for jj=1:m %for every z

            Zs(jj,ii) = zi(jj)-zslope; %height above the line

        end
    end
end%for on x

figure
imagesc(Zs)
colorbar
title('distance from the line')


%ADDED
figure
imagesc(depth2)
colorbar
title('depth2')


%zone above the line
maskINT=zeros(m,n);
inds = find(Zs>=0); %erase values under the line
maskINT(inds)=1;

%ADDED
figure
imagesc(depth2+depth.*maskINT)
colorbar
title('depth summed')


figure
imagesc(depth);colorbar
title('depth')

figure
imagesc(depth.*maskINT);colorbar
title('depth  above the line')

figure
contour(depth.*maskINT);colorbar
set(gca,'YDir','Reverse')
title('depth')