Unwanted contour lines generated by contour()

Hi,

I can't seem to figure out why contour() is plotting the additional contours on the outer edge of the shape produced by pcolor().

The following function was used to calculate the values for the matrix M used to create the pcolor plot;

function val = TBM(theta,beta,M_upstream,g)
    % Description: TBM function solves Theta-Beta-Mach Relation for required values
    
    % Specifying option to turn off fsolve dialogue in the command window
    option = optimset('Display','off');

    % Solving for theta
    % Identifying required variable
    if theta == 0
        % Creating function handle of TBM equation in terms of required
        % variable
        TBM_eq = @(theta) 2*cotd(beta)*((M_upstream^2*(sind(beta))^2-1)/(M_upstream^2*(g+cosd(2*beta))+2)) - tand(theta);
        
        % Solving equation for required variable
        val = fsolve(TBM_eq,0.1,option);
    
    % Solving for beta
    elseif beta == 0
        TBM_eq = @(beta) 2*cotd(beta)*((M_upstream^2*(sind(beta))^2-1)/(M_upstream^2*(g+cosd(2*beta))+2)) - tand(theta);
        val = fsolve(TBM_eq,0.1,option);

    % Solving for upstream Mach number
    elseif M_upstream == 0
        TBM_eq = @(M_upstream) 2*cotd(beta)*((M_upstream^2*(sind(beta))^2-1)/(M_upstream^2*(g+cosd(2*beta))+2)) - tand(theta);
        val = fsolve(TBM_eq,0.1,option);
    end
end

The following code produces the plot;

clear all; close all; clc

% Values
g = 1.4; % Ratio of specific heats for given gas

% Define the range of theta and beta values
theta = 0.5:0.5:50; % Range of theta from 0 to 50 degrees
beta = linspace(90,0.5,length(theta)); % Range of beta from 0 to 90 degrees

% Calculate Mach numbers for every theta beta combination
Mach = zeros(length(theta),length(beta));
for i = 1:1:length(theta)
    for j = 1:1:length(beta)
        M = TBM(theta(i),beta(j),0,g); % Mach number calculated using a function
        if M <= 10
            Mach(j,i) = M;
        end
    end
end

%%
% Create the heatmap for specified Mach numbers
figure("Name","Theta-Beta-Mach Relation Plot");
h = pcolor(theta,beta,Mach); % Pseudocolor plot used instead of heatmap
colormap turbo
c = colorbar;
c.Label.String = "M";
h.EdgeColor = "None";
hold on

% Add contours to heatmap
M_cont = [1.1:0.1:2 2.1:0.2:4 4.25:0.25:5 6 7 8 10];
[c,h] = contour(theta,beta,Mach,M_cont,"EdgeColor","w");
clabel(c,h,"FontSize",8,"Color","w")
xlabel("Theta (degrees)");
ylabel("Beta (degrees)");
title("Theta-Beta-Mach Relation");

As shown above, the additional contours produce the thick white outline.

Any help is greatly appreciated. Thanks!

Answer 1

[Chunru]

Yo5ur function curve has very abrupt change near the ege (see one vertical slice of data). Therefore you will see many contour lines near the edge (to the dark color). Check out if the generated data is what you expect.

clear all; close all; clc
% Values
g = 1.4; % Ratio of specific heats for given gas
% Define the range of theta and beta values
theta = 0.5:0.5:50; % Range of theta from 0 to 50 degrees
beta = linspace(90,0.5,length(theta)); % Range of beta from 0 to 90 degrees
% Calculate Mach numbers for every theta beta combination
% Mach = zeros(length(theta),length(beta));
Mach = nan(length(theta),length(beta));
for i = 1:1:length(theta)
    for j = 1:1:length(beta)
        M = TBM(theta(i),beta(j),0,g); % Mach number calculated using a function
        if M <= 10
            Mach(j,i) = M;
        end
    end
end
%%
% Create the heatmap for specified Mach numbers
figure("Name","Theta-Beta-Mach Relation Plot");
h = pcolor(theta,beta,Mach); % Pseudocolor plot used instead of heatmap
colormap turbo
c = colorbar;
c.Label.String = "M";
h.EdgeColor = "None";
hold on
% Add contours to heatmap
M_cont = [1.1:0.1:2 2.1:0.2:4 4.25:0.25:5 6 7 8 10];
%M_cont = [1.1:0.1:2 2.1:0.3:2.7  ];
% M_cont = [2.7 2.7]
[c,h] = contour(theta,beta,Mach,M_cont,"EdgeColor","w");
clabel(c,h,"FontSize",8,"Color","w")
xlabel("Theta (degrees)");
ylabel("Beta (degrees)");
title("Theta-Beta-Mach Relation");

whos

  Name          Size              Bytes  Class                                      Attributes

  M             1x1                   8  double                                               
  M_cont        1x28                224  double                                               
  Mach        100x100             80000  double                                               
  beta          1x100               800  double                                               
  c             2x4823            77168  double                                               
  g             1x1                   8  double                                               
  h             1x1                   8  matlab.graphics.chart.primitive.Contour              
  i             1x1                   8  double                                               
  j             1x1                   8  double                                               
  theta         1x100               800  double                                               

figure
plot(Mach(:, 50))  % a verticle slice of data

function val = TBM(theta,beta,M_upstream,g)
    % Description: TBM function solves Theta-Beta-Mach Relation for required values
    
    % Specifying option to turn off fsolve dialogue in the command window
    option = optimset('Display','off');
    % Solving for theta
    % Identifying required variable
    if theta == 0
        % Creating function handle of TBM equation in terms of required
        % variable
        TBM_eq = @(theta) 2*cotd(beta)*((M_upstream^2*(sind(beta))^2-1)/(M_upstream^2*(g+cosd(2*beta))+2)) - tand(theta);
        
        % Solving equation for required variable
        val = fsolve(TBM_eq,0.1,option);
    
    % Solving for beta
    elseif beta == 0
        TBM_eq = @(beta) 2*cotd(beta)*((M_upstream^2*(sind(beta))^2-1)/(M_upstream^2*(g+cosd(2*beta))+2)) - tand(theta);
        val = fsolve(TBM_eq,0.1,option);
    % Solving for upstream Mach number
    elseif M_upstream == 0
        TBM_eq = @(M_upstream) 2*cotd(beta)*((M_upstream^2*(sind(beta))^2-1)/(M_upstream^2*(g+cosd(2*beta))+2)) - tand(theta);
        val = fsolve(TBM_eq,0.1,option);
    end
end

[Walter Roberson]

Right. And in particular you clabel() in white and your contour edges are in white, and with there being a lot of contour edges in a small area there (because of the big change in value), there are a lot of white contour edges and white labels packed into a small area, giving the impression of a white edge.

[Dominic Babula]

Thanks for bringing that to my attention. Considering this, the generated data is expected. I essentially terminated the pcolor plot at M-values >= 10 by setting them to zero, which caused these spikes in value. This was done as the display of larger M-values was not required.

I do not want to display these contours, how would you go about this? Is there a simple way to do it?

Thanks!

[Chunru]

Use nan instead of 0 as updated above