smooth the surf or pcolor graph

I having a trouble in making my graph more clear and smooth in other words, make the locations with high value of Z be much more clear or distributed among the adjacent points soth that it can be obvious that at certain location we have high Z. a sample of my data is attached and the below is the code I'm using. the attached figure is what I'm really looking for to have. Thanks in advance

num = readtable("01)90.xlsx") ; 
 
% Take all the data under each variable name
x=num{1:1:end, contains(num.Properties.VariableNames, 'x')};
y=num{1:1:end, contains(num.Properties.VariableNames, 'y')};
z=num{1:1:end, contains(num.Properties.VariableNames, 'v')};

% Convert the matrix to 1 column only (scalar)
x=x(:);
y=y(:);
z=z(:);

% Delete rows that contain NaNs with reference to the variable z
i=1; [m,n]=size(x); 
    while i<=m
        
        if isnan(z(i,1))
        x(i,:)=[];
        y(i,:)=[];
        z(i,:)=[];
        i=i-1;      
        end
        i=i+1; [m,n]=size(x);  
        
    end

x0 = min(x) ; x1 = max(x) ; 
y0 = min(y) ; y1 = max(y) ; 
xi = linspace(x0,x1,100) ; 
yi = linspace(y0,y1,100) ; 
[X,Y] = meshgrid(xi,yi) ;

Z = griddata(x,y,z,X,Y) ;

% Get boundary coordinates 

idx = boundary(x,y) ; 
xb = x(idx) ; yb = y(idx) ; 

% Get points lying inside the boundary 
idx = inpolygon(X,Y,xb,yb) ;
Z(~idx) = NaN ;

f=pcolor(X,Y,Z);

colorbar
shading interp 
axis([-800 800 -800 800]);

Answer 1

[Mathieu NOE]

hello

looking first at your data distribution (histogram(Z)) I noticed 90% of the data is between 15 and 300 , very few samples are present above 300 so a linear colorbar was in my mind not the optimal choice

so the next idea was to plot the data with a log scaled colorbar . This is how the result looks now :

code is below :

clc
close all
clear all

num = readtable("01)90.xlsx") ; 
 
% Take all the data under each variable name
x=num{1:1:end, contains(num.Properties.VariableNames, 'x')};
y=num{1:1:end, contains(num.Properties.VariableNames, 'y')};
z=num{1:1:end, contains(num.Properties.VariableNames, 'v')};
% Convert the matrix to 1 column only (scalar)
x=x(:);
y=y(:);
z=z(:);
% Delete rows that contain NaNs with reference to the variable z
i=1; [m,n]=size(x); 
    while i<=m
        
        if isnan(z(i,1))
        x(i,:)=[];
        y(i,:)=[];
        z(i,:)=[];
        i=i-1;      
        end
        i=i+1; [m,n]=size(x);  
        
    end
x0 = min(x) ; x1 = max(x) ; 
y0 = min(y) ; y1 = max(y) ; 
xi = linspace(x0,x1,100) ; 
yi = linspace(y0,y1,100) ; 
[X,Y] = meshgrid(xi,yi) ;
Z = griddata(x,y,z,X,Y) ;
% Get boundary coordinates 
idx = boundary(x,y) ; 
xb = x(idx) ; yb = y(idx) ; 
% Get points lying inside the boundary 
idx = inpolygon(X,Y,xb,yb) ;
Z(~idx) = NaN ;

f=pcolor(X,Y,log10(Z));
 N = 32; % colorbar discrete values
 cmap = colormap(jet(N)) ; %Create Colormap
 cbh = colorbar ; %Create Colorbar
 cbh.Ticks = linspace(min(log10(Z),[],'all'), max(log10(Z),[],'all'), N) ; %Create N ticks from min to max of Z array
 tmp = round(logspace(log10(min(Z,[],'all')), log10(max(Z,[],'all')), N));
 cbh.TickLabels = num2cell(tmp) ;    %Replace the labels of these N ticks with the numbers defined in "tmp"
 
shading interp 
axis([-800 800 -800 800]);

[Abdulkarim Almukdad]

Thank you very much for your response. However, the figure you have provided is still not exactly what I'm looking for. I agree with you regarding the data and I already tried to delete all the data above 300 and 400. I also don't know if the problem is in my data or I'm not following the correct codes.

I'm curious if I take the average of Z at each repeated x and y coordinates expecially if I take the average not only about the repeated coordinates but rather the average of Z that surrounds each x and y coordinates like a small circle. would you please help me with that? I believe this can make the high Z values be distributed somehow on the adjacent points.

Many thanks in advance

[Mathieu NOE]

hello

regarding averaging - don't you think this will simply "distort" the representation of your data ? the "hot" areas will look larger but does it reflect the "real" thing ?

[Abdulkarim Almukdad]

it will be used only as a representation that at this location we have hot area, also averaging doesn't change in the results it only reduces the fluctuations which exactly what I need.

Do you know how can I do this?

you help is highly appreciated.

[Mathieu NOE]

this is the code with 2D smoothing

num = readtable("01)90.xlsx") ; 
 
% Take all the data under each variable name
x=num{1:1:end, contains(num.Properties.VariableNames, 'x')};
y=num{1:1:end, contains(num.Properties.VariableNames, 'y')};
z=num{1:1:end, contains(num.Properties.VariableNames, 'v')};
% Convert the matrix to 1 column only (scalar)
x=x(:);
y=y(:);
z=z(:);
% Delete rows that contain NaNs with reference to the variable z
i=1; [m,n]=size(x); 
    while i<=m
        
        if isnan(z(i,1))
        x(i,:)=[];
        y(i,:)=[];
        z(i,:)=[];
        i=i-1;      
        end
        i=i+1; [m,n]=size(x);  
        
    end
x0 = min(x) ; x1 = max(x) ; 
y0 = min(y) ; y1 = max(y) ; 
xi = linspace(x0,x1,100) ; 
yi = linspace(y0,y1,100) ; 
[X,Y] = meshgrid(xi,yi) ;
Z = griddata(x,y,z,X,Y) ;

% Get boundary coordinates 
idx = boundary(x,y) ; 
xb = x(idx) ; yb = y(idx) ; 
% Get points lying inside the boundary 
idx = inpolygon(X,Y,xb,yb) ;
Z(~idx) = NaN ;

% 2D smoothing 
Nr = 5;
Nc = 5;
Z = smooth2a(Z,Nr,Nc);% This function smooths the data using a mean filter over a 
% rectangle of size (2*Nr+1)-by-(2*Nc+1).

f=pcolor(X,Y,log10(Z));
 N = 16; % colorbar discrete values
 cmap = colormap(jet(N)) ; %Create Colormap
 cbh = colorbar ; %Create Colorbar
 cbh.Ticks = linspace(min(log10(Z),[],'all'), max(log10(Z),[],'all'), N) ; %Create N ticks from min to max of Z array
 tmp = round(logspace(log10(min(Z,[],'all')), log10(max(Z,[],'all')), N));
 cbh.TickLabels = num2cell(tmp) ;    %Replace the labels of these N ticks with the numbers defined in "tmp" 
shading interp 
axis([-800 800 -800 800]);

it uses the function smotth2a (from :smooth2a - File Exchange - MATLAB Central (mathworks.com) ) ( (a ttached)

smoothing will have an impact on the min / max amplitude, the more you smooth (average) , the more you reduce the amplitude , so a very hot local point will be transformed into a larger area but with significantly lower values

without smoothing : range goes from 15 to 850

with smoothing : range goes from 50 to 200

[Abdulkarim Almukdad]

That was very helpful thanks a lot. I just have one question to further understand the codes.

Can you please explain to me what does the log scale affect on the representation?

[Mathieu NOE]

the decision to plot in linear or log scale is either dictated by the physical laws (like for sound, the ear has a non linear response to sound amplitude so we use log scale to say that each increase of X dB (log amplitude) correspond to a similar perceived increase of sound intensity) or it can be simply because we want to have a colormap whith more steps in the low amplitude range , and less steps in the high amplitue range. The choice of a log is arbitrary, as you could choose another non linear function (power / polynamial function could also be used). So this is your decision if you stick to linear or non linear z scale mapping; also when your data has a very large factor between the min and max , a log scale is more appropriate to show the small amplitude values that would otherwise be unnoticed if displayed with a linear scale.

[Mathieu NOE]

Just for fun, I get back to linear Z scale plotting but kept the smoothing;

the result looks fine too :

code :

num = readtable("01)90.xlsx") ; 
 
% Take all the data under each variable name
x=num{1:1:end, contains(num.Properties.VariableNames, 'x')};
y=num{1:1:end, contains(num.Properties.VariableNames, 'y')};
z=num{1:1:end, contains(num.Properties.VariableNames, 'v')};
% Convert the matrix to 1 column only (scalar)
x=x(:);
y=y(:);
z=z(:);
% Delete rows that contain NaNs with reference to the variable z
i=1; [m,n]=size(x); 
    while i<=m
        
        if isnan(z(i,1))
        x(i,:)=[];
        y(i,:)=[];
        z(i,:)=[];
        i=i-1;      
        end
        i=i+1; [m,n]=size(x);  
        
    end
x0 = min(x) ; x1 = max(x) ; 
y0 = min(y) ; y1 = max(y) ; 
xi = linspace(x0,x1,100) ; 
yi = linspace(y0,y1,100) ; 
[X,Y] = meshgrid(xi,yi) ;
Z = griddata(x,y,z,X,Y) ;

% Get boundary coordinates 
idx = boundary(x,y) ; 
xb = x(idx) ; yb = y(idx) ; 
% Get points lying inside the boundary 
idx = inpolygon(X,Y,xb,yb) ;
Z(~idx) = NaN ;

% 2D smoothing 
Nr = 5;
Nc = 5;
Z = smooth2a(Z,Nr,Nc);% This function smooths the data using a mean filter over a 
% rectangle of size (2*Nr+1)-by-(2*Nc+1).

f=pcolor(X,Y,Z);
 N = 16; % colorbar discrete values
 cmap = colormap(jet(N)) ; %Create Colormap
 colorbar
shading interp 
axis([-800 800 -800 800]);

[Abdulkarim Almukdad]

Thank you very much I highly really appreciate your responses.

[Mathieu NOE]

You're welcome !