What my plot looks like
What the plot should look like
The code is working like it should but im trying to get the labels to show up on each line from (1-8). Just like the picture above.
I have read a bunch of posts and tried to search Matlab but i havent been able to figure it out.
clc;clear;close all;
V_inf = 20; % freestream velocity
R = 1; % cylinder radius
n = 8; % number of panels
d_theta = 2*pi/n; % resolution of angles
alpha = 0; % angle of attack
theta = pi+pi/n:-d_theta:-pi+pi/n; % angles of boundary points of panels
X = R*cos(theta); % X coordinates of boundary points of panels
Y = R*sin(theta); % Y coordinates of boundary points of panels
Phi = zeros(n,1); % angle from Vinf to bottom of panel
beta = zeros(n,1); % angle from Vinf to outward normal of panel
conX = zeros(n,1); % X coordinates of control points
conY = zeros(n,1); % Y coordinates of control points
S = zeros(n,1); % panel length
for i = 1:n
Phi(i) = -alpha + atan2((Y(i+1)-Y(i)),(X(i+1)-X(i)));
beta(i) = Phi(i)+pi/2;
if beta(i)>2*pi, beta(i)=beta(i)-2*pi;
elseif beta(i)<0, beta(i)=beta(i)+2*pi; end
conX(i) = (X(i+1)+X(i))/2;
conY(i) = (Y(i+1)+Y(i))/2;
S(i) = sqrt((X(i+1)-X(i))^2 + (Y(i+1)-Y(i))^2);
end
close all
plot(R*cos(0:0.01:2*pi),R*sin(0:0.01:2*pi),'b', X,Y,'r',conX,conY,'g^');
axis equal; legend('Exact shape','Panel approximation','Control points')
xlabel('x, m'); ylabel('y, m'); title('Fig. 1 Panel layout (n = 8, R = 1m)');
Possibly plotting the labels along the points of a circle using the text() function may suffice. There's some shifting of points and flipping that needs to be done to get the order you wish but otherwise it's just 8 points taken along a circle that is smaller in diameter in comparison to the octagon. An alternative would be using the green triangles as reference instead but that involves more math. As long as your octagon is expected to be symmetrical vertically and horizontally this should work alright.
clc;clear;close all;
V_inf = 20; % freestream velocity
R = 1; % cylinder radius
n = 8; % number of panels
d_theta = 2*pi/n; % resolution of angles
alpha = 0; % angle of attack
theta = pi+pi/n:-d_theta:-pi+pi/n; % angles of boundary points of panels
X = R*cos(theta); % X coordinates of boundary points of panels
Y = R*sin(theta); % Y coordinates of boundary points of panels
Phi = zeros(n,1); % angle from Vinf to bottom of panel
beta = zeros(n,1); % angle from Vinf to outward normal of panel
conX = zeros(n,1); % X coordinates of control points
conY = zeros(n,1); % Y coordinates of control points
S = zeros(n,1); % panel length
for i = 1:n
Phi(i) = -alpha + atan2((Y(i+1)-Y(i)),(X(i+1)-X(i)));
beta(i) = Phi(i)+pi/2;
if beta(i)>2*pi, beta(i)=beta(i)-2*pi;
elseif beta(i)<0, beta(i)=beta(i)+2*pi; end
conX(i) = (X(i+1)+X(i))/2;
conY(i) = (Y(i+1)+Y(i))/2;
S(i) = sqrt((X(i+1)-X(i))^2 + (Y(i+1)-Y(i))^2);
end
close all
plot(R*cos(0:0.01:2*pi),R*sin(0:0.01:2*pi),'b', X,Y,'r',conX,conY,'g^');
axis equal; legend('Exact shape','Panel approximation','Control points')
xlabel('x, m'); ylabel('y, m'); title('Fig. 1 Panel layout (n = 8, R = 1m)');
%*************************************************************************%
%ADDING LABELS BY PLOTTING LABELS ALONG CIRCLE%
%*************************************************************************%
Radius = 0.8;
Number_Of_Data_Points = 9;
theta = linspace(0,2*pi,Number_Of_Data_Points);
X_Circle = Radius*cos(theta);
X_Circle = X_Circle(1:end-1);
Y_Circle = Radius*sin(theta);
Y_Circle = Y_Circle(1:end-1);
X_Circle = flip(circshift(X_Circle,3));
Y_Circle = flip(circshift(Y_Circle,3));
for Point_Index = 1: numel(conX)
X_Displacement = X_Circle(Point_Index);
Y_Displacement = Y_Circle(Point_Index);
text(X_Displacement,Y_Displacement,num2str(Point_Index),'HorizontalAlignment','center','fontsize',20);
end
To Plot on Control Points:
%*************************************************************************%
%ADDING LABELS BY PLOTTING LABELS ALONG CONTROL POINTS%
%*************************************************************************%
for Point_Index = 1: numel(conX)
text(conX(Point_Index),conY(Point_Index),num2str(Point_Index),'HorizontalAlignment','center','fontsize',20);
end
Related
The following code is used to plot a circular path:
% Head velocity
v = 1.5;
% Angular velocity
w = 1;
% Radius
R = v/w;
% Time
dt = 0.1;
t = 0:dt:(2*pi*R/v);
% Initial mobile robot position vector
x0 = 0; y0 = 0; th0 = 0;
P = [];
P(:,1) = [x0 y0 th0];
% Loop for all time steps
for k = 1 : length(t)
P(:,k+1) = P(:,k) + dt*[v*cos(P(3,k));v*sin(P(3,k));w];
plot(P(1,1:k+1),P(2,1:k+1))
pause(0.01)
axis square
axis([-2 2 -0.5 3.5])
end
, how can I manipulate the position vector to plot a right triangle path.
Thanks in advance.
I wish to generate a .gif file of a sphere that grows in size(radius) over time based on a specified function relating radius and time. I'm having some trouble with how to formulate the animation.
Here is what I have so far:
%% Parameters
dt = 0.05;
time = 0:dt:1;
radius = 1
%% generate sphere
[X, Y, Z] = sphere(25);
X=X*radius;
Y=Y*radius;
Z=Z*radius;
mySphere = surf(X,Y,Z, 'FaceLighting','gouraud');
axis equal
shading interp
mySphere.FaceAlpha = 0.3
view([61 15])
colormap bone
hold on
%% generate gif
filename = 'Sizechange.gif';
for n = 1:20
radius = 1 + time(n)
im = frame2im(getframe(1));
[imind,cm] = rgb2ind(im,256);
if n == 1;
imwrite(imind,cm,filename,'gif', 'Loopcount',inf,'DelayTime',dt);
else
imwrite(imind,cm,filename,'gif','WriteMode','append','DelayTime',dt);
end
end
Here I am trying to get it to go from radius 1 to radius 2 in steps of 0.05.
When I run this however, the gif stays still at 1 and there is no animation.
Any help would be greatly appreciated.
As #cris-luengo said, you should redraw your sphere for each iteration on the radius.
%% Parameters
dt = 0.05;
time = 0:dt:1;
radius = 1 ;
%% generate sphere
[X, Y, Z] = sphere(25);
X=X*radius;
Y=Y*radius;
Z=Z*radius;
%figure;
%mySphere = surf(X,Y,Z, 'FaceLighting','gouraud');
% axis equal
% shading interp
% mySphere.FaceAlpha = 0.3;
% view([61 15])
% colormap bone
% hold on
%% generate gif
filename = 'Sizechange.gif';
figure;
for n = 1:20
radius = 1+ time(n);
%====================================================
X=X*radius;
Y=Y*radius;
Z=Z*radius;
mySphere = surf(X,Y,Z, 'FaceLighting','gouraud');
axis equal
shading interp
mySphere.FaceAlpha = 0.3;
view([61 15])
colormap bone
%====================================================
im = frame2im(getframe(1));
[imind,cm] = rgb2ind(im,256);
if n == 1
imwrite(imind,cm,filename,'gif', 'Loopcount',inf,'DelayTime',dt);
else
imwrite(imind,cm,filename,'gif','WriteMode','append','DelayTime',dt);
end
end
I Have an issue to create some geometries inside a phantom with Filed II framework. I did create a circle, but now I have problem to create a square inside the phantom.
It is the following code to produce it in Matlab. The line of code that produce inside, is my issue. For the circle, I did calculate the distance of two points inside the circle and when it is less than the radius of the circle, they are inside the circle. But I have problem for triangle or square.
Phantom.x_size = 50/1000; % Width of phantom [mm]
Phantom.y_size = 10/1000; % Transverse width of phantom [mm]
Phantom.z_size = 60/1000; % Height of phantom [mm]
Phantom.z_start = 30/1000; % Start of phantom surface [mm];
N = Calculate_number_of_scatterers(Phantom);
N = 1000*ceil(N/1000);
% Create the general scatterers
x = (rand (N,1)-0.5)*Phantom.x_size;
y = (rand (N,1)-0.5)*Phantom.y_size;
z = rand (N,1)*Phantom.z_size + Phantom.z_start;
% Generate the amplitudes with a Gaussian distribution
amplitudes = randn(N,1);
%Make the cyst
r = 8/2/1000; %radius of cyst[mm]
xc = 10/1000; %place of the cyst
zc = 40/1000 + Phantom.z_start;
% [in,out] = inpolygon(xc,zc,x,z);
inside = ( ((x-xc).^2 + (z-zc).^2) < r^2); % scatteres inside the cyst
amplitudes = amplitudes .* (1-inside); % amplitude of the scatteres inside the cyst
Phantom.positions = [x y z];
Phantom.amplitudes = amplitudes;
figure;
plot3(Phantom.positions(:,1), Phantom.positions(:,3),Phantom.amplitudes,'.')
I have an axisymmetric flow with m x n grid points in r and z direction and I want to plot the temperature that is stored in a matrix with size mxn in a 3D cylindrical plot as visualized in the link below (My reputation is not high enough to include it as a picture).
I have managed to plot it in 2D (r,z plane) using contour but I would like to add the theta plane for visualization. How can I do this?
You can roll your own with multiple calls to surface().
Key idea is: for each surface: (1) theta=theta1, (2) theta=theta2, (3) z=zmax, (4) z=0, (5) r=rmax, generate a 3D mesh (xx,yy,zz) and the temperature map on that mesh. So you have to think about how to construct each surface mesh.
Edit: completed code is now provided. All magic number and fake data are put at (almost) the top of the code so it's easy to convert it into a general purpose Matlab function. Good luck!
% I have adjusted the range values to show the curved cylinder wall
% display a variable temperature
r = 0:0.1:2.6; % you can also try r = 0:0.1:3.0
z = 0:0.1:10; % you can also try z = 0:0.1:15;
[rr, zz] = meshgrid(r,z);
% fake temperature data
temp = 100 + (10* (3-rr).^0.6) .* (1-((zz - 7.5)/7.5).^6) ;
% visualize in 2D
figure(1);
clf;
imagesc(r,z,temp);
colorbar;
% set cut planes angles
theta1 = 0;
theta2 = pi*135/180;
nt = 40; % angle resolution
figure(2);
clf;
xx1 = rr * cos(theta1);
yy1 = rr * sin(theta1);
h1 = surface(xx1,yy1,zz,temp,'EdgeColor', 'none');
xx2 = rr * cos(theta2);
yy2 = rr * sin(theta2);
h2 = surface(xx2,yy2,zz,temp,'EdgeColor', 'none');
% polar meshgrid for the top end-cap
t3 = linspace(theta1, (theta2 - 2*pi), nt);
[rr3, tt3] = meshgrid(r,t3);
xx3 = rr3 .* cos(tt3);
yy3 = rr3 .* sin(tt3);
zz3 = ones(size(rr3)) * max(z);
temp3 = zeros(size(rr3));
for k = 1:length(r)
temp3(:,k) = temp(end,k);
end
h3 = surface(xx3,yy3,zz3,temp3,'EdgeColor', 'none');
% polar meshgrid for the bottom end-cap
zz4 = ones(size(rr3)) * min(z);
temp4 = zeros(size(rr3));
for k = 1:length(r)
temp4(:,k) = temp(1,k);
end
h4 = surface(xx3,yy3,zz4,temp4,'EdgeColor', 'none');
% generate a curved meshgrid
[tt5, zz5] = meshgrid(t3,z);
xx5 = r(end) * cos(tt5);
yy5 = r(end) * sin(tt5);
temp5 = zeros(size(xx5));
for k = 1:length(z)
temp5(k,:) = temp(k,end);
end
h5 = surface(xx5, yy5, zz5,temp5,'EdgeColor', 'none');
axis equal
colorbar
view(125,25); % viewing angles
I'm pretty new to different plots in Matlab and I'm trying to write a code that will show the flow field around a cylinder in Matlab. I'm at the very start and first of all I want to just make the circle in a rectangular domain (cylinder should not be right in the middle of the field).
So far, I have this set up but I want to know if it's possible to make the cylinder look more circular and less like an oval, especially because the domain is a rectangle and not a square. The points on the circle are correct but I want it to look better. Any tips on this? The code I have at the moment is:
U_i = 20; % Ambient velocity
a = 4; % cylinder radius
c = -a*5; % starting coordinate (x)
b = a*10; % ending coordinate (x)
d = -60; % starting coordinate (y)
e = 60; % ending coordinate (y)
n = a*50; % number of intervals (step size in grid)
[x,y] = meshgrid([c:(b-c)/n:b],[d:(e-d)/n:e]');
for i = 1:length(x)
for k = 1:length(x);
f = sqrt(x(i,k).^2 + y(i,k).^2);
if f < a
x(i,k) = 0;
y(i,k) = 0;
end
end
end
% Definition of polar variables
r = sqrt(x.^2+y.^2);
theta = atan2(y,x);
%% Creation of Streamline function
z = U_i.*r.*(1-a^2./r.^2).*sin(theta);%- G*log(r)/(2*pi);
%% Creation of Figure
m = 100;
s = ones(1,m+1)*a;
t = [0:2*pi/m:2*pi];
%% Streamline plot
contour(x,y,z,50);
hold on
polar(t,s,'-k');
% axis square
title('Stream Lines');
grid off