Need help in plotting the 3 variable function's contour
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clc
clear all
close all
% format long
step = 10;
z = linspace(0,1.2e-6,step);
x = linspace(-0.1e-6,0.1e-6,step);
y=linspace(-0.1e-6,0.1e-6,step);
%r=sqrt(x.^2+y.^2);
z1 = 1e-6;
L = 9.995498999999999e-07;
a1 = 8.999974099901931e-10;
s = linspace(-L,L,1e5);
F0 = 3.15e7;
Mat_V = zeros(length(z),length(x),length(y));
for i = 1 : length(z)
i
for j = 1 : length(x)
for k= 1:length(y)
if abs(sqrt(x(j).^2+y(k).^2)) > sqrt((a1*z1)*(1-(z(i)*z(i)/z1/z1)))
F_f = s ./((sqrt(x(j).^2+y(k).^2) + (z(i)-s).^2).^0.5);
V_f = @(z,F_f) F0 * z1 / (z1 * log((L+z1)/(-L+z1)) - 2 * L) * (trapz(s,F_f)) - F0 * z;
Mat_V(i,j,k) = V_f(z(i),F_f);
else
Mat_V(i,j,k) = 0;
end
end
end
end
[X,Y,Z] = ndgrid(x,y,z) ;
F =Mat_V(Z,X,Y) ;
figure
hold on
for i = 1:100
surf(X(:,:,i),Y(:,:,i),Z(:,:,i),F(:,:,i)) ;
end
axis([-3 3 -3 3]);grid minor
view(3);
shading interp
%set(gca,'FontSize',25,'fontweight','bold')
%size = 35;
%xlabel('X ({\mu}m)','FontSize',size,'fontweight','bold')
%ylabel('Z ({\mu}m)','FontSize',size,'fontweight','bold')
%axis equal
2 个评论
Walter Roberson
2022-7-22
Mat_V(i,j,k) = V_f(z(i),F_f);
That is an array assignment with integer indices.
F =Mat_V(Z,X,Y) ;
That is an attempt to index the array with non-integer indices. Perhaps you want to use permute()?
Yasir Iqbal
2022-7-22
采纳的回答
format long g
step = 10;
z = linspace(0,1.2e-6,step);
x = linspace(-0.1e-6,0.1e-6,step);
y=linspace(-0.1e-6,0.1e-6,step);
%r=sqrt(x.^2+y.^2);
z1 = 1e-6;
L = 9.995498999999999e-07;
a1 = 8.999974099901931e-10;
s = linspace(-L,L,1e5);
F0 = 3.15e7;
Mat_V = zeros(length(z),length(x),length(y));
for i = 1 : length(z)
i
for j = 1 : length(x)
for k= 1:length(y)
if abs(sqrt(x(j).^2+y(k).^2)) > sqrt((a1*z1)*(1-(z(i)*z(i)/z1/z1)))
F_f = s ./((sqrt(x(j).^2+y(k).^2) + (z(i)-s).^2).^0.5);
V_f = @(z,F_f) F0 * z1 / (z1 * log((L+z1)/(-L+z1)) - 2 * L) * (trapz(s,F_f)) - F0 * z;
Mat_V(i,j,k) = V_f(z(i),F_f);
else
Mat_V(i,j,k) = 0;
end
end
end
end
[X,Y,Z] = ndgrid(x,y,z) ;
F = permute(Mat_V, [2 3 1]); %created as z x y
figure
hold on
for i = 1:size(F,3)
surf(X(:,:,i),Y(:,:,i),Z(:,:,i),F(:,:,i)) ;
end
xlim auto; ylim auto; grid minor
view(3);
shading interp
5 个评论
Yasir Iqbal
2022-7-23
Walter Roberson
2022-7-23
hold off
at the bottom of the code
Note that your original axis limit was -3 to 3 but the range of your variables is much smaller.
Have you considered not using surf for this purpose, and instead use several isosurface() calls with different levels, and making sure to set the Alpha (transparency) level below 1 so that the inner shells can be seen?
Do you have a sample plot that you are trying to be similar to?
Yasir Iqbal
2022-7-23
I modified the code to be slightly more efficient.
You will notice that the outputs are essentially flat. If you look at the term that I write into the temporary variable "temp" and save overall into the array Temp, you will find that that term is at most 6E-14 and so the subtraction of F0*z(i) that you were doing is contributing all of the significant value to the Mat_V result -- to withing round-off error for plotting purposes, your calculations just produce flat sheets at different z levels.
format long g
step = 10;
z = linspace(0,1.2e-6,step);
x = linspace(-0.1e-6,0.1e-6,step);
y=linspace(-0.1e-6,0.1e-6,step);
z1 = 1e-6;
L = 9.995498999999999e-07;
a1 = 8.999974099901931e-10;
s = linspace(-L,L,1e5);
F0 = 3.15e7;
Mat_V = zeros(length(z),length(x),length(y));
Temp = Mat_V;
for i = 1 : length(z)
zi = z(i);
for j = 1 : length(x)
xj = x(j);
for k= 1:length(y)
yk = y(k);
if abs(sqrt(xj.^2+yk.^2)) > sqrt((a1*z1)*(1-(zi*zi/z1/z1)))
F_f = s ./((sqrt(xj.^2+yk.^2) + (zi-s).^2).^0.5);
temp = z1 / (z1 * log((L+z1)/(-L+z1)) - 2 * L) * (trapz(s,F_f));
V_f = F0 * (temp - zi);
Mat_V(i,j,k) = V_f;
Temp(i,j,k) = temp;
else
Mat_V(i,j,k) = nan;
end
end
end
end
[X,Y,Z] = meshgrid(x,y,z) ;
F = permute(Mat_V, [2 3 1]); %created as z x y
fig = figure();
[Fmin, Fmax] = bounds(F, 'all');
Fvec = linspace(Fmin, Fmax, 6);
for K = 1 : length(Fvec)
isosurface(X, Y, Z, F, Fvec(K));
end
set(findobj(fig, 'type', 'patch'), 'FaceAlpha', 0.5)
[Tmin, Tmax] = bounds(Temp, 'all')
format long g
step = 10;
z = linspace(0,1.2e-6,step);
x = linspace(-0.1e-6,0.1e-6,step);
y=linspace(-0.1e-6,0.1e-6,step);
z1 = 1e-6;
L = 9.995498999999999e-07;
a1 = 8.999974099901931e-10;
s = linspace(-L,L,1e5);
F0 = 3.15e7;
Mat_V = zeros(length(z),length(x),length(y));
Temp = Mat_V;
for i = 1 : length(z)
zi = z(i);
for j = 1 : length(x)
xj = x(j);
for k= 1:length(y)
yk = y(k);
if abs(sqrt(xj.^2+yk.^2)) > sqrt((a1*z1)*(1-(zi*zi/z1/z1)))
F_f = s ./((sqrt(xj.^2+yk.^2) + (zi-s).^2).^0.5);
temp = z1 / (z1 * log((L+z1)/(-L+z1)) - 2 * L) * (trapz(s,F_f));
V_f = F0 * (temp - zi);
Mat_V(i,j,k) = V_f;
Temp(i,j,k) = temp;
else
Mat_V(i,j,k) = nan;
end
end
end
end
[X,Y,Z] = meshgrid(x,y,z) ;
F = permute(Mat_V, [2 3 1]); %created as z x y
fig = figure();
[Fmin, Fmax] = bounds(F, 'all');
Fvec = linspace(Fmin, Fmax, 6);
for K = 1 : length(Fvec)
isosurface(X, Y, Z, F, Fvec(K));
end
set(findobj(fig, 'type', 'patch'), 'FaceAlpha', 0.5)
title('colored by MAT_V')
fig2 = figure()
[Tmin, Tmax] = bounds(Temp, 'all');
Tvec = linspace(Tmin, Tmax, 5);
for K = 1 : length(Tvec)
isosurface(X, Y, Z, Temp, Tvec(K));
end
set(findobj(fig2, 'type', 'patch'), 'FaceAlpha', 0.5)
title('colored by MAT_V without -F0*z term')
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