Matlab - GRAFICOS EN 3D

function h = ezimplot3(varargin)

% EZIMPLOT3    Easy to use 3D implicit plotter.

%   EZIMPLOT3(FUN) plots the function FUN(X,Y,Z) = 0 (vectorized or not) 

%   over the default domain:

%   -2*PI < X < 2*PI, -2*PI < Y < 2*PI, -2*PI < Z < 2*PI.

%   FUN can be a string, an anonymous function handle, a .M-file handle, an

%   inline function or a symbolic function (see examples below)

%

%   EZIMPLOT3(FUN,DOMAIN)plots FUN over the specified DOMAIN instead of the

%   default domain. DOMAIN can be vector [XMIN,XMAX,YMIN,YMAX,ZMIN,ZMAX] or

%   vector [A,B] (to plot over A < X < B, A < Y < B, A < Z < B).

%

%   EZIMPLOT3(..,N) plots FUN using an N-by-N grid. The default value for

%   N is 60.

%   EZIMPLOT3(..,'color') plots FUN with color 'color'. The default value

%   for 'color' is 'red'. 'color' must be a valid Matlab color identifier.

%

%   EZIMPLOT3(axes_handle,..) plots into the axes with handle axes_handle

%   instead of into current axes (gca).

%

%   H = EZIMPLOT3(...) returns the handle to the patch object this function

%   creates.

%

% Example: 

% Plot x^3+exp(y)-cosh(z)=4, between -5 and 5 for x,y and z

%

%   via a string:

% f = 'x^3+exp(y)-cosh(z)-4'

% ezimplot3(f,[-5 5])

%

%   via a anonymous function handle:

% f = @(x,y,z) x^3+exp(y)-cosh(z)-4

% ezimplot3(f,[-5 5])

%

%   via a function .m file:

%------------------------------%

% function out = myfun(x,y,z)

% out = x^3+exp(y)-cosh(z)-4;

%------------------------------%

% ezimplot3(@myfun,[-5 5])   or  ezimplot('myfun',[-5 5])

%

%   via a inline function:

% f = inline('x^3+exp(y)-cosh(z)-4')

% ezimplot3(f,[-5 5])

%

%   via a symbolic expression:

% syms x y z

% f = x^3+exp(y)-cosh(z)-4

% ezimplot3(f,[-5 5]) 

%

% Note: this function do not use the "ezgraph3" standard, like ezsurf,

% ezmesh, etc, does. Because of this, ezimplot3 only tries to imitate that

% interface. A future work must be to modify "ezgraph3" to include a

% routine for implicit surfaces based on this file

%

%   Inspired by works of:   Artur Jutan   UWO 02-02-98 ajutan@julian.uwo.ca

%   Made by:            Gustavo Morales   UC  04-12-09 gmorales@uc.edu.ve

%

%%% Checking & Parsing input arguments:

if ishandle(varargin{1})

   cax = varargin{1}; % User selected axes handle for graphics

   axes(cax);

   args{:} = varargin{2:end}; %ensuring args be a cell array

else

   args = varargin;

end

[fun domain n color] = argcheck(args{:});

%%% Generating the volumetric domain data:

xm = linspace(domain(1),domain(2),n);

ym = linspace(domain(3),domain(4),n);

zm = linspace(domain(5),domain(6),n);

[x,y,z] = meshgrid(xm,ym,zm);

%%% Formatting "fun"

[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

%%% Evaluating "f_handle" in domain:

try

  fvalues = f_handle(x,y,z);        % fvalues: volume data

catch ME

  error('Ezimplot3:Functions', 'FUN must have no more than 3 arguments');

end

%%% Making the 3D graph of the 0-level surface of the 4D function "fun":

h = patch(isosurface(x,y,z,fvalues,0)); % "patch" handles the structure...

                                        % sent by "isosurface"

isonormals(x,y,z,fvalues,h)% Recalculating the isosurface normals based...

                           % on the volume data

set(h,'FaceColor',color,'EdgeColor','none');

%%% Aditional graphic details:

xlabel('x');ylabel('y');zlabel('z');% naming the axis

alpha(0.7) % adjusting for some transparency

grid on; view([1,1,1]); axis equal; camlight; lighting gouraud

%%% Showing title:

title([f_text,' = 0']);

%

%--------------------------------------------Sub-functions HERE---

function [f dom n color] = argcheck(varargin)

%ARGCHECK(arg) parses "args" to the variables "f"(function),"dom"(domain)

%,"n"(grid size) and "c"(color)and TRIES to check its validity

switch nargin

       case 0

            error('Ezimplot3:Arguments',...

            'At least "fun" argument must be given');

       case 1

            f = varargin{1};

            dom = [-2*pi, 2*pi]; % default domain: -2*pi < xi < 2*pi

            n = 60;              % default grid size

            color = 'red';       % default graph color

       case 2

            f = varargin{1};

            if isa(varargin{2},'double') && length(varargin{2})>1

               dom = varargin{2};

               n = 60;

               color = 'red';

            elseif isa(varargin{2},'double') && length(varargin{2})==1

               n = varargin{2};

               dom = [-2*pi, 2*pi];

               color = 'red';

            elseif isa(varargin{2},'char')

               dom = [-2*pi, 2*pi];

               n = 60;

               color = varargin{2};

            end

       case 3                  % If more than 2 arguments are given, it's

            f = varargin{1};   % assumed they are in the correct order

            dom = varargin{2};

            n = varargin{3};

            color = 'red';     % default color

       case 4                  % If more than 2 arguments are given, it's

            f = varargin{1};   % assumed they are in the correct order

            dom = varargin{2};

            n = varargin{3};

            color = varargin{4};

       otherwise

            warning('Ezimplot3:Arguments', ...

            'Attempt will be made only with the 4 first arguments');

            f = varargin{1};

            dom = varargin{2};

            n = varargin{3};

            color = varargin{4};

end

if  length(dom) == 2

    dom = repmat(dom,1,3);        %domain repeated in all variables

elseif length(dom) ~= 6

    error('Ezimplot3:Arguments',...

    'Input argument "domain" must be a row vector of size 2 or size 6');

end

%

%--------------------------------------------

function [f_hand f_text] = fix_fun(fun)

% FIX_FUN(fun) Converts "fun" into an anonymous function of 3 variables (x,y,z)

% with handle "f_hand" and a string "f_text" to use it as title

types = {'char','sym','function_handle','inline'}; % cell array of 'types'

type = ''; %Identifing FUN object class

for i=1:size(types,2)

    if isa(fun,types{i})

       type = types{i};

       break;

    end

end

switch type

       case 'char' % Formatting FUN if it is char type. There's 2 possibilities:

       % A string with the name of the .m file   

            if exist([fun,'.m'],'file')

               syms x y z;

               if nargin(str2func(fun)) == 3

                  f_sym = eval([fun,'(x,y,z)']); % evaluating FUN at the sym point (x,y,z)

               else

                  error('Ezimplot3:Arguments',...

                  '%s must be a function of 3 arguments or unknown function',fun);

               end

               f_text = strrep(char(f_sym),' ',''); % converting to char and eliminating spaces

               f_hand = eval(['@(x,y,z)',vectorize(f_text),';']); % converting string to anonymous f_handle

            else

       % A string with the function's expression

               f_hand = eval(['@(x,y,z)',vectorize(fun),';']); % converting string to anonymous f_handle

               f_text = strrep(fun,'.',''); f_text = strrep(f_text,' ',''); % removing vectorization & spaces

            end

       case 'sym' % Formatting FUN if it is a symbolic object

            f_hand = eval(['@(x,y,z)',vectorize(fun),';']); % converting string to anonymous f_handle

            f_text = strrep(char(fun),' ',''); % removing spaces 

       case {'function_handle', 'inline'} % Formatting FUN if it is a function_handle or an inline object

            syms x y z;

            if nargin(fun) == 3 && numel(symvar(char(fun))) == 3 % Determining if # variables == 3

               f_sym = fun(x,y,z);   % evaluating FUN at the sym point (x,y,z)

            else

               error('Ezimplot3:Arguments',...

               '%s must be function of 3 arguments or unknown function',char(fun));

            end

            f_text = strrep(char(f_sym),' ','');  % converting into string to removing spaces

            f_hand = eval(['@(x,y,z)',vectorize(f_text),';']); % converting string to anonymous f_handle

    otherwise

            error('First argument "fun" must be of type character, simbolic, function handle or inline');

end

>> f = 'x^3+exp(y)-cosh(z)-4';  ezimplot3(f,[-5 5]);