Common part of 2D and 3D plot

Question

M 2022-6-5

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1734070-common-part-of-2d-and-3d-plot

评论： Star Strider 2022-6-7

Hi, I have a 3D plot that are plotted based on data (the data attached and shown with blue in the figure below), and a 2d curve on the yz plane. I want to know which part of 2d curve is on the 3d plot. here is the information for the figure:

For 2D plot on the yz: f=0.07.*z.^2./(0.09+z.^2) and g=0.003+0.01.*(42./(42+(y-z).^4)) and I want to plot g-f=0 in yz plane.

and 3D curve has data attached here. for example in this figure that is 3d I want to know where is the 2D curve on the yz plane that I showed. I would appreciate any help

A = importdata(curve3dfinal)

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Answer 1

Star Strider 2022-6-5

1
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1734070-common-part-of-2d-and-3d-plot#answer_979420

在 MATLAB Online 中打开

I am not certain what result you want.

It is straightforward to rotate the 3D plot to give a 2D view from the Z-axis —

Uz = unzip('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1022280/curve3dfinal.zip');

% type(Uz{1})

C3DF = readmatrix(Uz{1})

C3DF = 30001×3

0.0033 1.2649 0.4327 0.0033 1.2645 0.4327 0.0032 1.2640 0.4326 0.0032 1.2636 0.4326 0.0032 1.2632 0.4325 0.0032 1.2627 0.4325 0.0032 1.2623 0.4324 0.0032 1.2619 0.4323 0.0032 1.2614 0.4322 0.0032 1.2610 0.4321

x = C3DF(:,1);

y = C3DF(:,2);

z = C3DF(:,3);

figure

plot3(x, y, z)

grid on

view(20,30)

xlabel('X')

ylabel('Y')

zlabel('Z')

title('3D View')

figure

plot3(x, y, z)

grid on

view(0,90)

xlabel('X')

ylabel('Y')

zlabel('Z')

title('View From Z-Axis')

.

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Star Strider 2022-6-5

在 MATLAB Online 中打开

I am completely lost.

Importing my code fron your other post, I get this result —

Uz = unzip('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1022280/curve3dfinal.zip');

% type(Uz{1})

C3DF = readmatrix(Uz{1})

C3DF = 30001×3

0.0033 1.2649 0.4327 0.0033 1.2645 0.4327 0.0032 1.2640 0.4326 0.0032 1.2636 0.4326 0.0032 1.2632 0.4325 0.0032 1.2627 0.4325 0.0032 1.2623 0.4324 0.0032 1.2619 0.4323 0.0032 1.2614 0.4322 0.0032 1.2610 0.4321

x = C3DF(:,1);

y = C3DF(:,2);

z = C3DF(:,3);

% figure

% plot3(x, y, z)

% grid on

% view(90,0)

% xlabel('X')

% ylabel('Y')

% zlabel('Z')

% title('View From X-Axis')

f = @(z) 0.07.*z.^2./(0.09+z.^2);

g = @(y,z) 0.003+0.01.*(42./(42+(y-z).^4));

N = 25;

yv = linspace(0, 0.25, N); % Use 'Curve' Limits

zv = linspace(0, 1.5, N); % Use 'Curve' Limits

[Y,Z] = ndgrid(yv,zv);

% figure

% surf(Y,Z,f(Z))

% colormap(turbo)

%

% figure

% surf(Y,Z,g(Y,Z))

% colormap(turbo)

figure

% surf(g(Y,Z)-f(Z),Y,Z)

hold on

plot3(x, y, z, '-g', 'LineWidth',2)

contour3(Y,Z,g(Y,Z)-f(Z), [0 0], '-r', 'LineWidth',2) % Plot Contour At 0

hold off

xlabel('X')

ylabel('Y')

zlabel('Z')

grid on

colormap(turbo)

legend('Curve Data','Contour3', 'Location','best')

% view(90,0)

view(30,30)

.

Star Strider 2022-6-6

在 MATLAB Online 中打开

I am having a very difficult time conceptualizing this. If the contour needs to be in th (Y,Z) plane, that means it has to be defined as the ‘X’ matrix in the contour3 call, and that yields nothing in the plot because it does not go to 0 in Z’ and that is required for contour3 as written earlier.at least with respect to the limits defined in the curve in the .zip file.

Uz = unzip('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1022280/curve3dfinal.zip');

% type(Uz{1})

C3DF = readmatrix(Uz{1})

C3DF = 30001×3

0.0033 1.2649 0.4327 0.0033 1.2645 0.4327 0.0032 1.2640 0.4326 0.0032 1.2636 0.4326 0.0032 1.2632 0.4325 0.0032 1.2627 0.4325 0.0032 1.2623 0.4324 0.0032 1.2619 0.4323 0.0032 1.2614 0.4322 0.0032 1.2610 0.4321

x = C3DF(:,1);

y = C3DF(:,2);

z = C3DF(:,3);

% figure

% plot3(x, y, z)

% grid on

% view(90,0)

% xlabel('X')

% ylabel('Y')

% zlabel('Z')

% title('View From X-Axis')

f = @(z) 0.07.*z.^2./(0.09+z.^2);

g = @(y,z) 0.003+0.01.*(42./(42+(y-z).^4));

N = 25;

yv = linspace(0, 0.25, N); % Use 'Curve' Limits

zv = linspace(0, 1.5, N); % Use 'Curve' Limits

[Y,Z] = ndgrid(yv,zv);

% figure

% surf(Y,Z,f(Z))

% colormap(turbo)

%

% figure

% surf(Y,Z,g(Y,Z))

% colormap(turbo)

figure

surf(g(Y,Z)-f(Z),Y,Z)

hold on

plot3(x, y, z, '-g', 'LineWidth',2)

contour3(g(Y,Z)-f(Z),Y,Z, [0 0], '-r', 'LineWidth',2) % Plot Contour At 0

hold off

xlabel('X')

ylabel('Y')

zlabel('Z')

grid on

colormap(turbo)

% legend('Curve Data','Contour3', 'Location','best')

% view(90,0)

view(30,30)

I honestly have no idea how this is supposed to work, or what the desired result is. The surface (as it now appears to be defined as the ‘X’ matrix variable in the surf plot) seems to have nothing in common with the curve in thd .zip file.

Unless I can understand how this is suposed to work, I will delete my answer in the next day or two and you can see if someone else has a solution.

.

Star Strider 2022-6-6

在 MATLAB Online 中打开

This is the best I can do —

Uz = unzip('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1022280/curve3dfinal.zip');

% type(Uz{1})

C3DF = readmatrix(Uz{1})

C3DF = 30001×3

0.0033 1.2649 0.4327 0.0033 1.2645 0.4327 0.0032 1.2640 0.4326 0.0032 1.2636 0.4326 0.0032 1.2632 0.4325 0.0032 1.2627 0.4325 0.0032 1.2623 0.4324 0.0032 1.2619 0.4323 0.0032 1.2614 0.4322 0.0032 1.2610 0.4321

x = C3DF(:,1);

y = C3DF(:,2);

z = C3DF(:,3);

% figure

% plot3(x, y, z)

% grid on

% view(90,0)

% xlabel('X')

% ylabel('Y')

% zlabel('Z')

% title('View From X-Axis')

f = @(z) 0.07.*z.^2./(0.09+z.^2);

g = @(y,z) 0.003+0.01.*(42./(42+(y-z).^4));

N = 25;

yv = linspace(0, 0.25, N); % Use 'Curve' Limits

zv = linspace(0, 1.5, N); % Use 'Curve' Limits

[Y,Z] = ndgrid(yv,zv);

% figure

% surf(Y,Z,f(Z))

% colormap(turbo)

%

% figure

% surf(Y,Z,g(Y,Z))

% colormap(turbo)

figure

% surf(g(Y,Z)-f(Z),Y,Z)

hold on

plot3(x, y, z, '-g', 'LineWidth',2)

h = fimplicit(@(Z,Y)g(Y,Z)-f(Z), '-r','LineWidth',2);

% contour3(Y, Z, g(Y,Z)-f(Z),Z,[0 0], '-r', 'LineWidth',2) % Plot Contour At 0

hold off

xlabel('X')

ylabel('Y')

zlabel('Z')

grid on

colormap(turbo)

legend('Curve Data','Contour', 'Location','best')

% view(90,0)

view(30,30)

This is the best I can do.

Stopping here.

Experiment to get the result you want.

.

Star Strider 2022-6-6

在 MATLAB Online 中打开

Giving it one last try —

Uz = unzip('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1022280/curve3dfinal.zip');

% type(Uz{1})

C3DF = readmatrix(Uz{1})

C3DF = 30001×3

0.0033 1.2649 0.4327 0.0033 1.2645 0.4327 0.0032 1.2640 0.4326 0.0032 1.2636 0.4326 0.0032 1.2632 0.4325 0.0032 1.2627 0.4325 0.0032 1.2623 0.4324 0.0032 1.2619 0.4323 0.0032 1.2614 0.4322 0.0032 1.2610 0.4321

x = C3DF(:,1);

y = C3DF(:,2);

z = C3DF(:,3);

% figure

% plot3(x, y, z)

% grid on

% view(90,0)

% xlabel('X')

% ylabel('Y')

% zlabel('Z')

% title('View From X-Axis')

f = @(z) 0.07.*z.^2./(0.09+z.^2);

g = @(y,z) 0.003+0.01.*(42./(42+(y-z).^4));

N = 25;

yv = linspace(min(y), max(y), N); % Use 'Curve' Limits

zv = linspace(min(z), max(z), N); % Use 'Curve' Limits

[Y,Z] = meshgrid(yv,zv);

% figure

% surf(Y,Z,f(Z))

% colormap(turbo)

%

% figure

% surf(Y,Z,g(Y,Z))

% colormap(turbo)

figure

% surf(g(Y,Z)-f(Z),Y,Z)

hold on

hp31 = plot3(x, y, z, '-g', 'LineWidth',2);

h = fimplicit(@(Z,Y)g(Y,Z)-f(Z), 'LineWidth',0.1, 'Color',[1 1 1 0]);

% get(h)

hp32 = plot3(h.ZData, h.YData, h.XData, '-r', 'LineWidth',2);

% contour3(Y, Z, g(Y,Z)-f(Z),Z,[0 0], '-r', 'LineWidth',2) % Plot Contour At 0

hold off

xlabel('X')

ylabel('Y')

zlabel('Z')

grid on

colormap(turbo)

axis([0 max(x) 0 max(y) 0 1.1]) % Set Axis limits

legend([hp31,hp32],'Curve Data','Contour', 'Location','best')

% view(90,0)

view(30,30)

This does not show the complete contour, only the part that it has in common with the green loop curve. (To see all of it, comment the axis call.) Change the argument order in the ‘hp32’ plot3 call to get different results.

.

M 2022-6-7

Fantastic. Very appreciate...

I removed my comments that are not necessary

Star Strider 2022-6-7

As always, my pleasure!

I finally figured it out!

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Answer 2

Sam Chak 2022-6-6

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1734070-common-part-of-2d-and-3d-plot#answer_979615

编辑：Sam Chak 2022-6-6

在 MATLAB Online 中打开

HI @M

If the points of the desired function h are projected to the y–z plane, then the curve should look like this:

f = @(z) 0.07*z.^2./(0.09 + z.^2);
g = @(z, y) 0.003 + 0.01*(42./(42 + (y - z).^4));
fcn = @(z, y) g(z, y) - f(z);
fyz = fimplicit(fcn, [-0.15 0.15 -5 5]);
z = fyz.XData;
y = fyz.YData;
plot(y, z, 'linewidth', 1.5)

On 3D, I think the function

looks like this:

h = 0.003 + 0.01*(42./(42 + (y - z).^4)) - (0.07*z.^2./(0.09 + z.^2));
plot3(y, z, h, 'linewidth', 1.0)

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Common part of 2D and 3D plot

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Common part of 2D and 3D plot

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