Fill area between two curves

Hello,

I am tring to fill the area between the two ellipses. I am importing the values from Excel to plot the figure. After that I would like to fill the two ellipses with two different colors. How do I do that?.

CODE:

clc
clear all

load Phase12.mat
x = Phase1.x;
y = Phase1.z;
plot(x,y);
fill(x,y,'g');
hold on

a = Phase1.a;
b = Phase1.b;
plot(a,b);
% fill(a,b,'q')

x,y,a and b are the names of the four columns that I have imported from excel. x,y represents the bigger ellipse. I tried using some of the patch codes, but it did not work out. Can someone please help me with this?

[Adam Danz]

Just FYI so you don't have to wait for your answers in the future, this topic has been addressed many times in the forum and there is a clear example in the patch documentation.

Answer 1

[Star Strider]

Try something like this:

t = linspace(0, 2*pi);
x = ([1;2]*cos(t)).';                                                               % Produces (Nx2) Matrix
y = ([1;2]*sin(t)).';                                                               % Produces (Nx2) Matrix

figure
patch([x(:,2); flipud(x(:,1))], [y(:,2); flipud(y(:,1))], 'g', 'EdgeColor','none')  % Create ‘patch’ Object
hold on
plot(x(:,1), y(:,1), '-r')                                                          % Circle Outlines
plot(x(:,2), y(:,2), '-r')                                                          % Circle Outlines
hold off
axis('equal')

If your data are row vectors, do this:

patch([x fliplr(a)], [y fliplr(b)], 'g')

If they are column vectors:

patch([x; flipud(a)], [y; flipud(b)], 'g')

That should work.

[Shri Harsha Bharadwaj]

Hello,

Thanks for the quick reply. I am a beginner in MATLAB. So, in the code that you have written above where does my data come into play. It does not right?. What you have in the top is just a similar example where you have used two equations to generate the circles. How do I generate something similar using my data?

Also adding

patch([x; flipud(a)], [y; flipud(b)], 'g')

to the code I have above, gives me the image attached.

while

patch([x fliplr(a)], [y fliplr(b)], 'g')

does not change anything.

Do you think there is some issue while exporting my data from EXCEL?. Its just 4 columns of data ( x,y,a and b respectively).

[Star Strider]

My code should work.

Attach your data so I can see what the problem is with it.

[Shri Harsha Bharadwaj]

Hello,

Thanks again for the quick response. Attached is the excel sheet that I import to create the plots.

[Star Strider]

My pleasure!

There are NaN values in some of your data. That was the problem.

This works:

T1 = readtable('3Phase1.csv', 'VariableNamingRule','preserve');

xz = [T1.x T1.z];                                                                       % Concatenate Vectors
xz = xz(~any(isnan(xz),2),:);                                                           % Remove ‘NaN’ Rows
ab = [T1.a T1.b];                                                                       % Concatenate Vectors
ab = ab(~any(isnan(ab),2),:);                                                           % Remove ‘NaN’ Rows

figure
patch([xz(:,1); flipud(ab(:,1))], [xz(:,2); flipud(ab(:,2))], 'g', 'EdgeColor','none')  % Create ‘patch’ Object
hold on
plot(xz(:,1), xz(:,2), '-b')                                                            % Curve Outlines
plot(ab(:,1), ab(:,2), '-b')                                                            % Curve Outlines
hold off
axis('equal')

producing:

It is easier to concatenate the vectors into their respective matrices in order to remove the NaN values.

Other than removing the NaN values and adapting my code to your variables, my original code is essentially unchanged.

[Shri Harsha Bharadwaj]

Thank you Sir. I really appreciate the help.

I just had one more question. If I wanted to color the smaller ellipse in the center, would I have to do something similar to this?

Again, I cannot tell you how helpful this has been. I will look some of these commands up in detail to understand what actually is happening in the code.

[Star Strider]

My pleasure!

(I slightly edited my earlier Comment to make the code more robust.)

‘If I wanted to color the smaller ellipse in the center, would I have to do something similar to this?’

Yes, however it would be easier. To fill the inner curve, simply add this patch call:

patch(ab(:,1), ab(:,2), 'r')                                                            % Fill Inner Curve

so the slightly revised, complete code is now:

T1 = readtable('3Phase1.csv', 'VariableNamingRule','preserve');

xz = [T1.x T1.z];                                                                       % Concatenate Vectors
xz = xz(~any(isnan(xz),2),:);                                                           % Remove ‘NaN’ Rows
ab = [T1.a T1.b];                                                                       % Concatenate Vectors
ab = ab(~any(isnan(ab),2),:);                                                           % Remove ‘NaN’ Rows

figure
patch([xz(:,1); flipud(ab(:,1))], [xz(:,2); flipud(ab(:,2))], 'g', 'EdgeColor','none')  % Create ‘patch’ Object
hold on
plot(xz(:,1), xz(:,2), '-b')                                                            % Curve Outlines
plot(ab(:,1), ab(:,2), '-b')                                                            % Curve Outlines
patch(ab(:,1), ab(:,2), 'r')                                                            % Fill Inner Curve
hold off
axis('equal')

producing:

Of course, choose whatever line colours and inner-curve fill colour you want.

[Shri Harsha Bharadwaj]

Hello Sir,

Thanks a lot for all the help you have provided me with this. I really appreciate it. It works perfectly. I will make some modifications with respect to the colours.

Is it okay if I keep the question open, so that I can ask you if I have any more questions?

Thanks a ton again.

[Star Strider]

My pleasure!

It will be open as long as you want it to be. I will continue to respond as best I can.

Meanwhile, it appears that I did solve the problem as originally posted. If my Answer helped you solve your problem, please Accept it!

.

[Shri Harsha Bharadwaj]

Thanks a lot. I will do the same.

[Star Strider]

As always, my pleasure!

Thank you!

[Shri Harsha Bharadwaj]

Hello @Star Strider,

Hope you are doing well. I have been trying to remove the empty cells when plotting, but I have been having some issues.

When I plot the graph in Excel, I get the image attached below.

But when I import the same thing and try to plot it in MATLAB, I see a line.

I have been using your code from before. Can you please help me out with this?

clc
clear all

T1 = readtable('0.1399s.xlsx', 'VariableNamingRule','preserve');
YZ = [T1.Y T1.Z];
YZ = YZ(~any(isnan(YZ),2),:);
figure
plot(YZ(:,1),YZ(:,2),'b')
patch(YZ(:,1),YZ(:,2),'b')

[Star Strider]

The problem is that the ‘x’ coordinate ‘crosses over’ at that point, and nothing I can come up with (sort, sortrows, unique) fixes it.

This fixes the plot:

k = boundary(YZ(:,1), YZ(:,2), 0.95);

with:

patch(YZ(k,1),YZ(k,2),'b')

however I have no idea how to fix the underlying data. The boundary function was introduced in R2014b.

[Shri Harsha Bharadwaj]

Hello @Star Strider,

Thanks for the quick reply sir. I am not too worried about the data. I have the images now properly. Thank you.

[Star Strider]

As always, my pleasure!

[Shri Harsha Bharadwaj]

Hello @Star Strider,

Sir, if I wanted to compute the area of the irregular shape seen above, how would I do it?

Most of what I found have something to do with image processing, which I believe is not required for me, as my shape is already on the axes.

polyarea() gives me area for a polygon. I could not find anything for my case. Can you please help me out with this?

It tried using area(), but that does not seem to work either.

[Star Strider]

Both trapz and polyarea work here, with reapect to the boundary call result. The area function would not work here because it produces an area plot.

The area given by trapz:

Area = trapz(YZ(k,1),YZ(k,2))

Area =
    -9.872788536391784e-07

and by polyarea:

AreaP = polyarea(YZ(k,1),YZ(k,2))

AreaP =
     9.872788536391784e-07

differ only in the sign of the result. The magnitudes are the same.

(I would not use the original data because of the sign-reversal in ‘YZ(:,1)’ that caused problems for the patch call.)

Choose whichever result works best in your application.

[Shri Harsha Bharadwaj]

Thanks for the help sir. I apologize for the late reply.

[Star Strider]

As always, my pleasure!

[Shri Harsha Bharadwaj]

@Star Strider Hello sir,

I am trying to compute the perimeter of these irregular shapes. I came across a reference code to do that.

% Contour coordinates
A=xlsread('justplastic0.5.xlsx','A1:B100');
% Compute perimeter
N=size(A,1);
D=A(:,2:N)-A(:,1:(N-1));
D=sqrt(sum(D.^2,2)); % edge lenghts
P=sum(D); % perimeter

But I get wrong numbers with the code above.

Essentially, I am trying to figure out the Circularity of these blobs. Hence, I am trying to compute the area and perimeter.

I apologize that I keep coming back with more questions. I can create seperate questions from now on, if that is better. Is there a way I can club the code above with the one that you wrote, so that I can get everything with a single code.

[Star Strider]

I do not understand what that code is supposed to do.

Also, what are the data in ‘planeat11mm.xlsx’? There are 4 columns, ‘x’, ‘z’, ‘a’, and ‘b’. What should be done with them?

[Shri Harsha Bharadwaj]

Hello @Star Strider,

justplastic0.5.xlsx, has just one set of data. So, I would like to compute the perimeter of just one blob.

But in the case of planeat11mm.xlsx, there are two sets of data. I would like to compute the perimeter of both the inner shape and the outer shape.

[Shri Harsha Bharadwaj]

Also @Star Strider, I came across something called alpha value, maybe I should be using that. Any suggestions are welcome. Thanks.

[Star Strider]

It turns out that I made a stupid mistake in my code, and multiplied instead of addied.

That is now corrected, and this works, giving reasonable results:

T1 = readtable('justplastic0.5.xlsx');
T2 = readtable('planeat11mm.xlsx');

pwr10 = @(x) [x/10^fix(log10(x)-1) fix(log10(x)-1)];

x1 = T1.z;
y1 = T1.x;
dx1 = gradient(x1);
dy1 = gradient(y1);
C1 = trapz(sqrt(dx1.^2 + dy1.^2));

figure
plot(x1, y1)
grid
axis('equal')
text(mean(T1.z), mean(T1.x), sprintf('$C = %.3f\\times 10^{%d}$', pwr10(C1)), 'Horiz','center','Vert','middle',  'Interpreter','latex')

x2 = T2.z(~isnan(T2.z));
y2 = T2.x(~isnan(T2.x));
dx2 = gradient(x2);
dy2 = gradient(y2);
C2 = trapz(sqrt(dx2.^2 + dy2.^2));

figure
plot(T2.z,T2.x)
grid
axis('equal')
text(mean(x2), mean(y2), sprintf('$C = %.3f\\times 10^{%d}$', pwr10(C2)), 'Horiz','center','Vert','middle',  'Interpreter','latex')

x3 = T2.a;
y3 = T2.b;
dx3 = gradient(x3);
dy3 = gradient(y3);
C3 = trapz(sqrt(dx3.^2 + dy3.^2));

figure
plot(x3, y3)
grid
axis('equal')
text(mean(T2.a), mean(T2.b), sprintf('$C = %.3f\\times 10^{%d}$', pwr10(C3)), 'Horiz','center','Vert','middle',  'Interpreter','latex')

The circumference prints out in the centre of each figure in the plot. (The ‘pwr10’ function just creates an interesting string for the plots. It may not be robust, and is not required for the code.)

Since the first data set is a roughly circular plot, I checked that calculation with:

x11 = T1.z;
y11 = T1.x;
x11 = x11 - mean(x11);
y11 = y11 - mean(y11);
f = @(r) ((x11).^2 + (y11).^2 - r^2);
r = fsolve(f, 1E-4);
C11 = 2*pi*r;

That gives essentially the same result as ‘C1’.

I almost cannot imagine that I spent several hours on this and in all that time completely failed to notice that I multiplied instead of added in the trapz calls. With that correction , it works!

[Shri Harsha Bharadwaj]

@Star Strider Thanks for the help and clarification sir. I really appreciate it. Please let me know either way.

[Star Strider]

As always, my pleasure!

My corrected, working code is in my previous Comment.

[Shri Harsha Bharadwaj]

@Star Strider This is perfect. Works like a charm. Thanks for spending much time of your day to help me out. Have a great day sir.

[Star Strider]

As always, my pleasure!

The time I spent was my fault! It actually should only have required a few minutes.

[Shri Harsha Bharadwaj]

Hello @Star Strider,

Hope you are doing well sir. I had one last question that I wanted to run by you.

Given an irregular figure, it is possible to calculate the centerline distance from the leading end to the trailing end.

The red line illustrates the centerline length that I want to compute. I made the centerline in word. Is there a way we can generate a centerline like this automatically in MATLAB and calculate the length of the centerline?. Even an approximation would be good, especially in the curvature part.

I have also attached the excel file for your reference.

Thanks for the help.

[Star Strider]

I worked on that for a couple hours. I have absolutely no idea how to draw that centrelline, and I cannot find any functions that would do it.

Sorry.

[Shri Harsha Bharadwaj]

@Star Strider No problem sir. Thanks for the help. Have a great day.

[Shri Harsha Bharadwaj]

Hello @Star Strider ,

Hope you are doing well. This might be a very simple question for you.

I am trying to 3D plot something like this.

Given I have the data, how would I plot this?. Most of the codes that I looked up for 3D plotting uses some sort of an equation in one of the variables.

https://www.mathworks.com/help/matlab/visualize/creating-3-d-plots.html - Should I be using the surf function?

EDIT:

I looked into your older answers - https://www.mathworks.com/matlabcentral/answers/829218-3d-plot-from-excel#answer_699128?s_tid=prof_contriblnk

https://www.mathworks.com/matlabcentral/answers/810390-3d-plot-from-excel-data?s_tid=answers_rc1-2_p2_MLT

But not the same.

[Star Strider]

I wish it was simple! I have no idea how to plot them because I have no idea what the variables are.

The plot3 function would appear to be appropriate. Experriment with it to get the result you want.

My best effort —

C1 = readcell('https://www.mathworks.com/matlabcentral/answers/uploaded_files/617108/test1.csv');
T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/617108/test1.csv', 'VariableNamingRule','preserve');
First10Rows = T1(1:10,:)

First10Rows = 10×7 table
    Chart Count    Velocity [ m s^-1 ]      Z      Var4    Chart Count_1    Velocity [ m s^-1 ]_1     Z_1 
    ___________    ___________________    _____    ____    _____________    _____________________    _____

         0                     0          0.008    NaN           0                0.000377           0.006
         1               0.00156          0.008    NaN           1                0.000678           0.006
         2               0.00313          0.008    NaN           2                0.000979           0.006
         3               0.00469          0.008    NaN           3                 0.00128           0.006
         4               0.00626          0.008    NaN           4                 0.00158           0.006
         5               0.00782          0.008    NaN           5                 0.00188           0.006
         6               0.00939          0.008    NaN           6                 0.00218           0.006
         7                 0.011          0.008    NaN           7                 0.00248           0.006
         8                0.0125          0.008    NaN           8                 0.00279           0.006
         9                0.0141          0.008    NaN           9                 0.00309           0.006

figure
plot3(T1{:,3},T1{:,5},T1{:,2})
hold on
plot3(T1{:,3},T1{:,5},T1{:,6})
hold off
grid on

The arguments to the plot3 call refer to the columns of ‘T1’, so ‘T1{:,1}’ is the first column, and so for the others.

I added the readcell call because readtable read in one of the variables as NaN and I wanted to see what that was. It turns out to apparently be a vector of empty cells.

[Shri Harsha Bharadwaj]

@Star Strider Thanks for the help sir. I just had one question. The Z axis values are different. Could ou please tell as as to why they are being plotted at the same location?

EDIT:

Also ,when I have varying Y as well, all the Y points seem to originate from the same location. When I plot the graph in excel, I have something like this.

But when I do the same in MATLAB. both the Y and Z values do not vary. I am not sure if how I said this makes much sense. The bounds on the blue line is between [-1,1]* 10^-3, whereas the bounds of the orange line is different. But when plotted in MATLAB, they both have the same bounds of [-1,1]*10^-3.

[Star Strider]

As always, my pleasure!

They are plotted in the same location because I have no idea what the variables are, or how you would like them plotted. The ‘Velocity’ variables are obviously the dependent variables, however I have no idea what the independent variables should be. (The plot3 function requires two independent variables and one dependent variable.)

Perhaps —

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/617108/test1.csv', 'VariableNamingRule','preserve');
First10Rows = T1(1:10,:)

First10Rows = 10×7 table
    Chart Count    Velocity [ m s^-1 ]      Z      Var4    Chart Count_1    Velocity [ m s^-1 ]_1     Z_1 
    ___________    ___________________    _____    ____    _____________    _____________________    _____

         0                     0          0.008    NaN           0                0.000377           0.006
         1               0.00156          0.008    NaN           1                0.000678           0.006
         2               0.00313          0.008    NaN           2                0.000979           0.006
         3               0.00469          0.008    NaN           3                 0.00128           0.006
         4               0.00626          0.008    NaN           4                 0.00158           0.006
         5               0.00782          0.008    NaN           5                 0.00188           0.006
         6               0.00939          0.008    NaN           6                 0.00218           0.006
         7                 0.011          0.008    NaN           7                 0.00248           0.006
         8                0.0125          0.008    NaN           8                 0.00279           0.006
         9                0.0141          0.008    NaN           9                 0.00309           0.006

figure
plot3(T1{:,1},T1{:,3},T1{:,2})
hold on
plot3(T1{:,5},T1{:,7},T1{:,6})
hold off
grid on

would work instead.

[Shri Harsha Bharadwaj]

Thanks for the help sir. I was testing it out. Thanks a ton again.

[Star Strider]

As always, my pleasure!

Apparently the data file changed (I have been away doing other things), since it is not the same one I initially plotted.