Interpolation of a scatter plot

Hello ;I would be most grateful if someone could give me a helping hand. i have a scatter plot where the the third variable is velocity color coded for each pair of (x,y)I woud like to interpolate this plot to have more points.below is a figure of what i have and my code as well . thanks in advance.

the interpolated points are the red piont of the second figure is having just 9 pionts. i would like to apply that to the first figure which is what i have .

plotTypes  = {'mean_velocity','std_velocity','mean_pd',  'std_pd'};
for i = 1: length(plotTypes)
    figure
    plotType = plotTypes{i};
    %subplot(1,length(plotTypes), i);
     hold all ;
    legendLabels = cell(1,length(plotData));
    for j = 1:length(plotData)
        xPlot= plotData{j}.data(:, idx.x);
        yPlot= plotData{j}.data(:, idx.(plotTypes{i}));
        plot(xPlot,yPlot, '-o','color',k(j,:));
        legendLabels{j} = ['Y = ', num2str(plotData{j}.y)];
    end
    legend(legendLabels);
    title(plotTypes{i}, 'Interpreter', 'none');
    xlabel('x position')
    ylabel(plotTypes{i},  'Interpreter', 'none')
end
%% Generating the 3D color plot
% figure
for i = 1: length(plotTypes)
    figure
    legendLabels = cell(1,length(plotData));
    %     subplot(1,length(plotTypes), i);
    hold all
    for N=1:size(plotData,2)
       pz =150;
       plotData{1,N}.data();
       x=plotData{1,N}.data(:,1);
        y= plotData{1,N}.data(:,2);
        %if i ==3
        %  z= plotData{1,N}.data(:,(i+2));
        %end%         Z(:,N) =plotData{1,N}.data(:,(i+2));
        scatter(x,y,pz,plotData{1,N}.data(:,(i+2)),'filled')
        legendLabels{N} = ['Y = ', num2str(plotData{N}.y)];
      end
      %%Interpolation into a gridded data
      %F =scatteredInterpolant(x,y,Z);
      %[xq,yq]=meshgrid(linspace(20,230,100));
      %cq =F(xq,yq);
      %h=pcolor(xq,yq,cq)
      %legendLabels{N} = ['Y = ', num2str(plotData{N}.y)];
      legend(legendLabels);
      title(['3D plot of position against ',plotTypes{i}], 'Interpreter', 'none')
      xlabel('X(mm)')
      ylabel('Y(mm)')
      H = colorbar;
      ylabel(H, plotTypes{i});
end

[Akira Agata]

Seems that interp2 function would be one possible solution.

Answer 1

[Akira Agata]

Seems that scatteredInterpolant function would be better. Here is an example.

% Read data file
T = readtable('data.xlsx');

% Make interpolation function F = f(x,y)
F = scatteredInterpolant(T.xcoordinate,T.ycoordinate,T.mean_velocity);

% Make a grid points (20-by-20, for example)
[xmin,xmax] = bounds(T.xcoordinate);
[ymin,ymax] = bounds(T.ycoordinate);
[xGrid,yGrid] = meshgrid(linspace(xmin,xmax,20),linspace(ymin,ymax,20));

% Calculate interpolated value for each grid point
zGrid = F(xGrid,yGrid);

% Visualize the result
figure
scatter(xGrid(:),yGrid(:),[],zGrid(:),'filled')
colorbar

[Yannick Tabot Njami]

Thank you very much Mr Agata, you solve my problem .i appreciate you !

Answer 2

[KSSV]

Read about interp2, griddata. If not working attach your data.

[Yannick Tabot Njami]

% 

Bellow is my entire code And attached you would fine my data as well .plotData{1,4}. has 7 rows due to error that why at the centere of the color plot there is a missing point there . The rest are all 8 rows. just a hint.

%%This Script selects file of of specific format(.txt) and
%% mport  them each for data analysis.
%% the Analyzed data are  then plotted  as per requirement


clear all ;cla;

%% processing the  parent folder
myfolder ='C:\Users\TABOT\Desktop\Windkanal_Data\Yannick\Yannick_2019_01_03';
%% checking to snsure that folder actually exist
if~isdir(myfolder)
    Error_message =sprintf('Error,Folder not found:\n %s',myfolder);
end
%%  getting list of all files with File pattern .txt
filepattern =fullfile(myfolder,'*.txt');
txtfiles=dir(filepattern);
%% sorting out the zero measurement and calculating  Time sequence ,samples and mean voltage

zerofile =fullfile(myfolder,'20190301_00_20_20.txt');
offsetdata =importdata(zerofile);
zerovoltage =offsetdata.data(:,2);
mean_Uo =mean(zerovoltage);
%% ignoring the off set file after being used
txtfiles(1)=[];

%% preallocating memeory
mean_pd = zeros(length(txtfiles),1);
mean_velocity =zeros(length(txtfiles),1);
std_pd=zeros(length(txtfiles),1);
std_velocity =zeros(length(txtfiles),1);
velocity =zeros(length(txtfiles),1);
mean_voltage =zeros(length(txtfiles),1);
pd =zeros(length(zerovoltage),1);
Non_Avg_table = zeros(length(zerovoltage),5);
velocities =zeros(length(zerovoltage),1);
all_nonaveragetable(1,64) =struct('table',[],'x_position',[],'y_position',[]);



%% looping over each file in the directory txtfiles
for k =1 : length(txtfiles)
    % getting the name of each file base on its  x and y coordinates
    % and  importing the content of the file current file
    fn_parts =split(txtfiles(k).name,{'_','.'});
    
    coor_x =str2double(fn_parts{3});
    coor_y =str2double(fn_parts{4});
    filecontents =importdata(fullfile(txtfiles(k).folder,txtfiles(k).name));
    
    %% referring to voltage and samples of each file consisting of a struture and sample value
   
    voltage =filecontents.data(:,2);
    samples =filecontents.data(:,1);
    time_sequence =samples/1000;
    
    for ii=1: length(voltage)
        
        %% Looping over the voltage and calculating pd and velocities respectively
        
        pd(ii)=abs( 474.6*(voltage(ii)-mean_Uo));
        velocities(ii)=sqrt(2*pd(ii)/1.2);
        
    end
    %% calculating the various  mean and standard deviation of the respective parameters
    
    mean_pd(k) = mean(pd);
    velocity(k) = sqrt(2*mean_pd(k)/1.2);
    mean_voltage(k) = mean(voltage);
    mean_velocity(k) = mean(velocities);
    std_velocity(k) =std(velocities);
    std_pd(k)=std(pd);
    %%  Generating table of non-average values and forming a structure of 1x 64
    %%  of 3 fields
    Non_Avg_table= table(samples,time_sequence,voltage ,velocities,pd);
    all_nonaveragetable(k).table= Non_Avg_table;
    %%getting the coordinate of each point
    all_nonaveragetable(k).x_position=coor_x;
    all_nonaveragetable(k).y_position=coor_y;
    
    
end
%% Extracting the x and y Coordinate and  transposing
xcoordinate =(extractfield(all_nonaveragetable,'x_position'))';
ycoordinate =(extractfield(all_nonaveragetable,'y_position'))';

%% Generating the table  of average values
Average_Table = table(xcoordinate,ycoordinate,mean_velocity,std_velocity, mean_pd ,std_pd);

[data,txt] =xlsread('data.xlsx');
idx = struct('x',1, 'y',2, 'mean_velocity', 3, 'std_velocity', 4, 'mean_pd', 5, 'std_pd', 6);

%% Gathering and sorting data

plotTypes  = {'mean_velocity','std_velocity','mean_pd',  'std_pd'};

% stepval = 30;
yValues = [20 50 80 110 140 170 200 230]; 
indextoFind =cell(1,length(yValues));

plotData = cell(1,length(yValues));
for i= 1:length(yValues)
    foundIndex  =  find(data(:, idx.y) == yValues(i));
    tempData = sortrows(data(foundIndex,:)); %% Get all data and sort row-wise for each yValues
    plotData{i} = struct('y', yValues(i), 'data',tempData) ;%% here store data to be  plotted
end

%% Plot Data
k =[1 ,0 ,0 ;0, 1, 0 ;0 ,1 ,.5;.5 .5 .5 ;.1 ,.1, .25; 1 ,1, 0; 0, 0,1;0 ,0.5 ,1];
% figure
for i = 1: length(plotTypes)
    figure
     plotType = plotTypes{i};
%      subplot(1,length(plotTypes), i);
      hold all ;
    legendLabels = cell(1,length(plotData));
    for j = 1:length(plotData)
        xPlot= plotData{j}.data(:, idx.x);
        yPlot= plotData{j}.data(:, idx.(plotTypes{i}));
        plot(xPlot,yPlot, '-o','color',k(j,:));
        
       
        legendLabels{j} = ['Y = ', num2str(plotData{j}.y)];
    end
    legend(legendLabels);
    title(plotTypes{i}, 'Interpreter', 'none');
    xlabel('x position')
    ylabel(plotTypes{i},  'Interpreter', 'none')
    
   
end
 
%% Generating the 3D color plot
% figure

for i = 1: length(plotTypes)
    figure
    legendLabels = cell(1,length(plotData));
   
   

%     subplot(1,length(plotTypes), i);
      hold all

  
    for N=1:size(plotData,2)
      
         pz =150;
        plotData{1,N}.data();
        x=plotData{1,N}.data(:,1);
        y= plotData{1,N}.data(:,2);
%         if i ==3
%           z= plotData{1,N}.data(:,(i+2));
%          
%         end%         Z(:,N) =plotData{1,N}.data(:,(i+2));
% %        

      scatter(x,y,pz,plotData{1,N}.data(:,(i+2)),'filled')
       legendLabels{N} = ['Y = ', num2str(plotData{N}.y)];

        
    end
     
    %%Interpolation into a gridded data
%      F =scatteredInterpolant(x,y,Z);
%     
%        [xq,yq]=meshgrid(linspace(20,230,100));
%        cq =F(xq,yq);
% %        h=pcolor(xq,yq,cq)
%        
       
    
                   
%         legendLabels{N} = ['Y = ', num2str(plotData{N}.y)];
         
    legend(legendLabels);
    title(['3D plot of position against ',plotTypes{i}], 'Interpreter', 'none')
    xlabel('X(mm)')
    ylabel('Y(mm)')
    H = colorbar;
    ylabel(H, plotTypes{i});

 end