Boundary line for contour

Hello,

I want to draw a boundary line for my contour

you can see my contour (without bondary) and a contour with boundary (desired)

you can see my contour (without bondary)

here is my code:

clc,clear,close all;
% syms z y ;
B = 10;
H = 5;
C = 10;
L1 = 1;

Ri = B/2 + L1;
Rf = C + B/2 + L1;

y = linspace(-25,0,1000);
z = linspace(0,28,1000);
[Z,Y] = meshgrid(z,y);

r1 = sqrt((Y.^2)+(Z.^2));
r = abs(sqrt((Y.^2)+(Z.^2)) - Rf);
beta = asin( Z ./ sqrt((Y.^2)+(Z.^2)) );
beta(1000,1) = 0;
Rbeta = Ri + (2.*beta.*(Rf-Ri)./pi);
Rt0 = B/2+L1;
Rmaxtb = (Rt0.*Rbeta)./Ri;
Vmbeta = (2*(pi^2)*((B+(2*L1))^2)) ./ ((((2*L1*pi)+(pi*B)+(4.*beta.*C)).^2));

% Calculate the distance for condition
Rt00 = (B/2-L1);
Rmaxtbb = (Rt00.*Rbeta)./Ri;
% End

for i = 1:1:1000
    for j = 1:1:1000
        
if r(i,j)>Rbeta(i,j) | r1(i,j)>(Rf+Rmaxtbb(i,j))
    Vbeta(i,j)=0;
else
    Vbeta(i,j) = Vmbeta(i,j) * (1 - ((r(i,j)^2) / (Rmaxtb(i,j)^2)));
end

    end
end

ZZ = Z./B;
YY = Y./B;
contourf(ZZ,YY,Vbeta,100,'edgecolor','none')
colormap( flipud(gray(256)) )
colorbar
xlabel('z/D') 
ylabel('y/D')

any help is appreciated

Answer 1

[Star Strider]

Sometimes, a bit of absolute creativity (‘thinking outside the contour) is necessary.

I first did a meshc plot of your matrices to see what the ‘Vbeta’ matrix looked like in 3D. It has a sllight elevation with steep transitions at the edges. That led to experiments using the gradient function to calculate numerical derivatives of the ‘Vbeta’ matrix, and that led to this result (with code previous to this not copied here):

ZZ = Z./B;
YY = Y./B;
contourf(ZZ,YY,Vbeta,100,'edgecolor','none')
colormap( flipud(gray(256)) )
colorbar
xlabel('z/D') 
ylabel('y/D')

[~,dY] = gradient(Vbeta);
hold on
contour(ZZ.*(dY~=0),YY.*(dY~=0),ones(size(dY)).*(dY~=0), [0 1], '--k')
hold off

producing this plot:

I have no idea how robust this approach would be to similar plots, however it appears to work here. It uses a second contour call and logical indexing (of a sort) to ptroduce the necessary contours.

[Pooyan Jafari]

Thank you

it is working great!!

would you please help me with this one too!?

clc,clear,close all;
B = 10;
H = 20;
C = 10;
L1 = 5;

Ri = B/2 + L1;
Rf = C + B/2 + L1;

y = linspace(-25,0,1000);
z = linspace(0,25,1000);
[Z,Y] = meshgrid(z,y);

r1 = sqrt((Y.^2)+(Z.^2));
r = abs(sqrt((Y.^2)+(Z.^2)) - Rf);
beta = asin( Z ./ sqrt((Y.^2)+(Z.^2)) );
beta(1000,1) = 0;
Rbeta = Ri + (2.*beta.*(Rf-Ri)./pi);
Rt0 = B/2+L1;
Rmaxtb = (Rt0.*Rbeta)./Ri;

% Calculate the distance for condition
Rt00 = (B/2-L1);
Rmaxtbb = (Rt00.*Rbeta)./Ri;
% End

for i = 1:1:1000
    for j = 1:1:1000
        
cond(i,j) = Rf-Rbeta(i,j);
if (r1(i,j)<=cond(i,j)) | (r1(i,j)>(Rf+Rmaxtbb(i,j)))
    Vr(i,j)=0;
else


if r1(i,j)<Rf
        Vr(i,j) = -(399200400000000000*r(i,j)*pi^2*(2000*beta(i,j) + 999*pi - 100*pi*r(i,j))*(2000*beta(i,j) + 999*pi + 100*pi*r(i,j)))/((100*r(i,j) - 1999)*(2000*beta(i,j) + 999*pi)^5*(250000*cot(8359544324750471/18014398509481984) + 998001*tan(8359544324750471/18014398509481984) - 250000*cot(3541622469636805/2251799813685248) - tan(3541622469636805/2251799813685248)));
    else
        Vr(i,j) = -(399200400000000000*r(i,j)*pi^2*(2000*beta(i,j) + 999*pi - 99900*pi*r(i,j)*-1)*(2000*beta(i,j) + 999*pi + 99900*pi*r(i,j)*-1))/((100*r(i,j)*(-1) - 1999)*(2000*beta(i,j) + 999*pi)^5*(250000*cot(8359544324750471/18014398509481984) + 998001*tan(8359544324750471/18014398509481984) - 250000*cot(3541622469636805/2251799813685248) - tan(3541622469636805/2251799813685248)));
    end
end

    end
end
ZZ = Z./B;
YY = Y./B;
contourf(ZZ,YY,Vr,100,'edgecolor','none')
colormap( flipud(gray(256)) )
colorbar
xlabel('z/D') 
ylabel('y/D')

the difference is that here Vbeta is replaced by Vr.

I used your approach adn it didn't work for this one. Actually it draws the boundary for the contour, but the color of the contour is fading!! you can see the picture of the original contour and the contour with boundary with your approach

[Star Strider]

My pleasure!

Experiment with the caxis function to create the color axis range (herre the intensity of the gray colormap) that you want.

Example —

ZZ = Z./B;
YY = Y./B;
contourf(ZZ,YY,Vr,100,'edgecolor','none')
colormap( flipud(gray(256)) )
lim = caxis;
caxis(lim.*[1.50 0.50])                                     % Limits The Color Axis Range
colorbar
xlabel('z/D') 
ylabel('y/D')


[~,dY] = gradient(Vr);
hold on
contour(ZZ.*(dY~=0),YY.*(dY~=0),ones(size(dY)).*(dY~=0), [0 1], '--k')
hold off

Here, I multiplied the lower limit by 1.5 and the upper limit by 0.5 to decrease the range. Experiment with them to get the result you want.

EDIT — (1 Dec 2020 at 00:32)

Added new plot image —

.

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[Star Strider]

If my Answer helped you solve your problem, please Accept it!

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