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### Highlights from Ezimplot3: implicit 3D functions plotter

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# Ezimplot3: implicit 3D functions plotter

### Gustavo Morales (view profile)

10 Apr 2009 (Updated )

Plots a 3D surface defined implicitly

File Information
Description

At last Matlab do it!!!
Useful tool to plot a 3D implicit surface defined in cartesian coordinates. You can give f(x,y,z) = 0 as a string or as a function handle. Type <help ezimplot3> for usage. Remember to leave your comments and ratings...Thanks!

;)

Acknowledgements

Implot.M inspired this file.

This file inspired Tan Plane: Tangent Plane Expression & Display.

Required Products Symbolic Math Toolbox
MATLAB release MATLAB 7.6 (R2008a)
06 Jul 2015 Daniel Blixt

### Daniel Blixt (view profile)

Nice function. I have an spectrum problem which yields the following equation
0=sin(kx/2)*sin(ky/2)*sin(k*(1-x-y)/2)*(sin(k/2)-sin(kx/2)*sin(ky/2)*sin(k*(1-x-y)/2))
It have multiple solutions and I want to display the figure so that you can distinguish between the different levels (surfaces) of solutions.
I also have restrictions that cannot be satisfied by your function. I have x+y+z(x,y)=1. x≤y≤z.
Can you help me solve these two problem

In other words x and y takes values on the triangle limited by

x=0, 0≤y≤1/2

0≤y=x≤1/3

1/3≤y=1/2-x/2≤1/2

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03 Sep 2013 Matt J

### Matt J (view profile)

Very nice. I think it would be a great favor to the community, though, if you would generalize it so that when you already have a function handle, it doesn't require the Symbolic Toolbox. This is very easy to do by circumventing fix_fun as follows

if ~isempty(which('syms'))
[f_handle f_text] = fix_fun(fun); % f_handle is the anonymous f-handle for "fun"
% f_text is "fun" ready to be a title
elseif isa(fun,'function_handle')
f_handle=fun; f_text='';
else
error 'Cannot process input function'
end

Other minor remarks:

1. The syntax ezimplot3(fun,domain, color) does not parse correctly

2. You have a missing % in your help text, making about half of it disappear when doing help/doc ezimplot3

13 Feb 2013 Andrey Zhigachev

### Andrey Zhigachev (view profile)

Nice function! Thank you, I was looking for such as one for a long time.

02 Jun 2012 Gkcn

### Gkcn (view profile)

Dear Gustavo,thank you for your useful function.I tried to use it for plotting my own equation but it gives many surfaces together although i need only one surface around first root of my equation.Please can you help me how can i find it?
my equation is:

tan(sqrt(y)*(1-1/x)*z)-sqrt(y)*(x-z^2)/(x+y)*z=0

1<=x<=10 , 0.1<=y<=10 , 0<=z<=1

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22 Jun 2011 Shahab

### Shahab (view profile)

Nice Job Gustavo
I just needed an implicit plot in the middle of my code somewhere to show an obstacle...
You saved me a few days of work.
Thx man

26 Jan 2011 Daniel Lopes

### Daniel Lopes (view profile)

Nice code! Well done!
You should try to combine it with the implicitplot3d(.)[go this website http://www-users.math.umd.edu/~jmr/241/surfaces.html].
It realy gives an excelent visual result as an alternative to the cranky mesh from isosurface(.) :S.

%% ____________________________________
figure,
syms x y z;
h=x^2+y^2+z^2;
implicitplot3d(h, 1, -3, 3, -3, 3, -3, 3, 40); axis equal
hold on
ezimplot3(h-1,[-5 5])

07 Oct 2010 Gustavo Morales

### Gustavo Morales (view profile)

Sorry for not being a good software documenter. I'm just a Electrical Engineer .... all the "symbol part" of the code, you can replace it...

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06 Oct 2010 Jonathan

### Jonathan (view profile)

This seems like a good function. However, I could not discover it since my time has been fruitlessly spent. This function requires the symbolic toolbox, yet no mention of this was explicitly included on this page or in the function help.

23 Jul 2010 Michelle Gledhill

### Michelle Gledhill (view profile)

Hello Gustavo,
Is there a way to add a contour plot on the x-y-plane in a similar way that the function "surfc" does?

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21 May 2010 Gustavo Morales

### Gustavo Morales (view profile)

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12 May 2010 Camilla Colombo

### Camilla Colombo (view profile)

Hi Gustavo,

I sent you an email to gmorales@uc.edu.ve

Thanks
Camilla

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02 May 2010 Gustavo Morales

### Gustavo Morales (view profile)

Hi Camilla!
Your funcion has others arguments than x,y,z?
Can you send me the code of your function?... Send it by email...

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16 Apr 2010 Camilla Colombo

### Camilla Colombo (view profile)

Dear Gustavo,

thank you for your function. I am trying to plot an implicit function coded into an m. file. However i get an error and i think this is due to the fact that my function contains some "if condition". So I get the error at line 168 of ezimplot3:
f_sym = eval([fun,'(x,y,z)']); % evaluating FUN at the sym point (x,y,z)

do you know a way to avoid this problem?

Camilla

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01 Mar 2010 Gustavo Morales

### Gustavo Morales (view profile)

Hi Hisham.. ok! send me the code of M1 by email...

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24 Feb 2010 Hisham Moideen

### Hisham Moideen (view profile)

hi Gustavo,
I tried plotting the way you suggested.

h1=ezimplot3(M1,[0.02 5 0 4 0 0.35]);

where M1 is the determinant of a matrix involving the three variables alpha,gamma,R.

I got the following error:
"??? Error using ==> ezimplot3 at 82
FUN must have no more than 3 arguments"

To make sure i dont have more than 3 unknowns, i substituted specific values for each and got a single value for my Function M1.

Is is possible that i could send you my code of generating M1 and maybe you could help me.

Problem is my function M1 is not a simple function. Its a determinant of a matrix of order 8. Some of the terms in my matrix is polynomial fit of alpha and R. So the determinant is one crazy looking expression. Matlab cant output my entire determinant value (out of line limit error).

Appreciate any help in this regard!!!

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24 Feb 2010 Gustavo Morales

### Gustavo Morales (view profile)

Hi...
*fun can be a string, an anonymous function handle, a .M-file handle, an inline function or a symbolic function. Any other variable present at the function (aside from alpha, gamma and R), must have a known value, that is, your function must depend only of alpha, gamma and R.
*>> domain = [min-alpha max-alpha min-gamma max-gamma min-R max-R];
ezimplot3(fun,domain);

test with the examples of help: >> help ezimplot3

regards from Venezuela!

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23 Feb 2010 Hisham Moideen

### Hisham Moideen (view profile)

hi Gustavo,

I have an implicit function, but the variables are alpha, gamma and R.
Can i use ezimplot3() to output my function?

Also is it possible to input different range for my variables like
ezimplot3(M1,[0.2 6 0 5 0 0.34]), will that work?

Appreciate the help and code.

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22 Oct 2009 Gustavo Morales

### Gustavo Morales (view profile)

Hi!
> h = ezimplot3() outputs a handle for the patch object. So you can do the folowing:
> set(h,'FaceColor','none','EdgeColor','k')

"I prefer being useful than being important"

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22 Oct 2009 Brian Bak

### Brian Bak (view profile)

Hi Gustavo Morales

Just as you wrote the boundaries was not large enough for the surfaces to be plottet.

Do you have any suggestions to how you kan change the surface to be a grid instead of a color?

Very nice program btw!

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22 Oct 2009 Gustavo Morales

### Gustavo Morales (view profile)

I didn't understand you... so... have you already discovered the mistake? I was trying to do something about it, and that's what I've found:
> f = '(x/(4 - 3*y))^2 + (z/(4 - 3 *y))^2 -1';
> ezimplot3(f,[-3000 3000 -10000 10000 -3000 3000]);

It produces a nice graph... maybe the function that you provided is too small...
Regards!

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22 Oct 2009 Gustavo Morales

### Gustavo Morales (view profile)

the numeric answer you get is a handle for the patch object

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22 Oct 2009 Brian Bak

### Brian Bak (view profile)

My mistake it was just the boundaries that where wrong.

22 Oct 2009 Brian Bak

### Brian Bak (view profile)

Hi

Does anyone no why I can't plot the following:

f = '(x/(400^2 - 0.3*y))^2 + (z/(400^2 - 0.3 *y))^2 -1';
ezimplot3(f,[-3000 3000 -10000 10000 -3000 3000])

It just shows an empty plot from 0 to 1 on all axes. And gives the output: ans = 0.0037

31 Aug 2009 Gustavo Morales

### Gustavo Morales (view profile)

Dave, as you should know, you only can see plots for explicit R2 to R functions, so the index "i" must be at most 2. Your function is also known as "Parabola", and has this other explicit (not implicit) form:
f(x,y) = x^2 + y^2 ... a paraboloid
I suggest that use instead the following command:

>> plotobjective(@dejong1fcn,[-5.12 5.12;-5.12 5.12]);

;-)

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25 Aug 2009 Dave Yap

### Dave Yap (view profile)

Dear Gustavo, really nice and neat program.
I would like to plot a DeJong1 test function as below,
f1(x)=sum(x(i)^2), i=1:n, -5.12<=x(i)<=5.12

I'm unable to plot the Dejong1 test function.
Could you pls help me on this?
my email is dyfw@hotmail.com. Thanks in advance.

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01 Aug 2009 Gustavo Morales

### Gustavo Morales (view profile)

I'd like to study ezgraph3 throughly to make -ezimplot3- a "real command", and maybe some day, Mathworks could take it ;)
And...There's a way.... try writing:
>>help ezimplot3
for usage

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29 Jul 2009 Tamara Kolda

### Tamara Kolda (view profile)

This is fantastic! Just what I was looking for and what ezplot3 should do!

One questions/suggestion: Is there a way to also choose the color of the surface that's plotted? I was able to do it manually using the get/set commands, but I was hoping to be able to do it using the function directly.

Thanks for sharing this with the community.

12 Apr 2009 1.1

Now you can give it the name of your "function.m" file
A lot of input errors catched (I said "a lot", not "all") ;)

18 Apr 2009 1.2

*Now supports symbolic and inline classes as input
*Now you can pass it a 'color' argument
*Code was rearranged, so it would be more readable. One day ezimplot3 could connect with Matlab's "ezgraph3"

03 May 2009 1.3

-Cleaned some bugs up
-Now you can give an axis handle to make the plot
-Simplified code

07 Oct 2010 1.4