如何在Matlab中将两个轮廓图相互叠加? [英] How to superimpose two contour maps onto each other in matlab?

问题描述

我在Matlab中有两个轮廓图，并且两个图都有一条指定单个Z值的曲线.我想强加两个轮廓图，以便找到两个z值曲线相交的唯一解决方案.我该如何叠加两个等高线图?

I have two contour maps in Matlab and each of the two maps has a single curve specifying a single Z-value. I want to super impose the two contour maps so that I can find the single solution where the two z-value curves intersect. How could I go about super imposing the two contour maps?

 % the two contour maps are coded the exact same way, but with different z-values
 x = 0.05:0.05:1;
 y = 0.0:0.05:1;
 [X, Y] = meshgrid(x, y);
 % Z-value data is copied from excel and pasted into an array
 Z = [data]
 contourf(X, Y, Z);
 pcolor(X, Y, Z); hold on
 shading interp
 title();
 xlabel();
 ylabel();
 colorbar

 val = %z-value to plot onto colormap
 tol = %tolerance
 idxZval = (Z <= val+tol) & (Z >= val-tol);
 plot(X(idxZval), Y(idxZval))[enter image description here][1]

推荐答案

使用 contourc 或使用 指定相同的轮廓(等值线).

The end result you seek is possible using contourc or using contour specifying the same contours (isolines).

此答案使用此答案. //www.mathworks.com/help/matlab/ref/contourc.html"rel =" nofollow noreferrer> contourc 并使用

This answer extends this answer in Approach 1 using contourc and provides a simple solution with contour in Approach 2.

您可能会问"为什么方法2这么简单的方法1?" 如果您需要一种数值方法来搜索相交，则方法1提供了一种直接访问各个等值线的方法.

You might ask "Why Approach 1 when Approach 2 is so simple?" Approach 1 provides a way to directly access the individual isolines in the event you require a numerical approach to searching for intersections.

示例数据:

% MATLAB R2018b
x = 0:0.01:1;
y = 0:0.01:1;
[X,Y] = meshgrid(x,y);
Z = sqrt(X.^3+Y);                      % Placeholder 1
W = sqrt(X.*Y + X.^2 + Y.^(2/3));      % Placeholder 2

从2个轮廓图中覆盖单个等值线
模仿此答案并使用
v = [.5 0.75 .85 1]; % Values of Z to plot isolines
我们可以分别可视化这两个函数Z和W.

Overlay Single Isoline from 2 Contour Plots
Mimicking this answer and using
v = [.5 0.75 .85 1]; % Values of Z to plot isolines
we can visualize these two functions, Z, and W, respectively.

我们可以覆盖等值线，因为它们共享相同的(x，y)域.例如，它们都等于 0.8 ，如下所示.

We can overlay the isolines since they share the same (x,y) domain. For example, they both equal 0.8 as displayed below.

val = 0.8;                     % Isoline value to plot (for Z & W)
Ck = contourc(x,y,Z,[val val]);
Ck2 = contourc(x,y,W,[val val]);
figure, hold on, box on
plot(Ck(1,2:end),Ck(2,2:end),'k-','LineWidth',2,'DisplayName',['Z = ' num2str(val)])
plot(Ck2(1,2:end),Ck2(2,2:end),'b-','LineWidth',2,'DisplayName',['W = ' num2str(val)])
legend('show')

---

从2个轮廓图中覆盖多个等值线
我们也可以一次为更多等值线进行此操作.

---

Overlay Multiple Isolines from 2 Contour Plots
We can also do this for more isolines at a time.

v = [1 0.5];                   % Isoline values to plot (for Z & W)
figure, hold on, box on
for k = 1:length(v)
   Ck = contourc(x,y,Z,[v(k) v(k)]);
   Ck2 = contourc(x,y,W,[v(k) v(k)]);
   p(k) = plot(Ck(1,2:end),Ck(2,2:end),'k-','LineWidth',2,'DisplayName',['Z = ' num2str(v(k))]);
   p2(k) = plot(Ck2(1,2:end),Ck2(2,2:end),'b-','LineWidth',2,'DisplayName',['W = ' num2str(v(k))]);
end
p(2).LineStyle = '--';
p2(2).LineStyle = '--';
legend('show')

方法2

没有让它变得漂亮...

Approach 2

Without making it pretty...

% Single Isoline
val = 1.2;
contour(X,Y,Z,val), hold on
contour(X,Y,W,val)


% Multiple Isolines
v = [.5 0.75 .85 1];
contour(X,Y,Z,v), hold on
contour(X,Y,W,v)

清除这些内容以进行演示很简单.如果val是标量(单个数字)，则c1 = contour(X,Y,Z,val);和c2 = contour(X,Y,W,val)允许访问每个轮廓图的等值线.

It is straightforward to clean these up for presentation. If val is a scalar (single number), then c1 = contour(X,Y,Z,val); and c2 = contour(X,Y,W,val) gives access to the isoline for each contour plot.

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