Plot the area of the surface

Question

Atom 2023-8-16

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2009142-plot-the-area-of-the-surface

评论： Atom 2023-8-19

采纳的回答： Ruchika

Plot area of the surface

that lies inside

The equation

can be written in polar coordinate as $r^2=a^2 \sin(2\theta)$ which is a loop.

Please help me to plot the surface. Please highlight the portion of the surface by a color.

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Answer 1

Ruchika 2023-8-16

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https://ww2.mathworks.cn/matlabcentral/answers/2009142-plot-the-area-of-the-surface#answer_1288292

编辑：Ruchika 2023-8-16

在 MATLAB Online 中打开

Hi, you can use the 'surf' function to plot the surface in MATLAB and highlight the portion that lies inside the given equation. Following is the MATLAB code that accomplishes this:

% Define the range of theta

theta = linspace(0, 2*pi, 100);

% Define the value of a

a = 1; % Replace with the desired value

% Calculate the maximum value of r based on the given equation

r_max = a * sqrt(abs(sin(2*theta)));

% Create a meshgrid for theta and r

[Theta, R] = meshgrid(theta, linspace(0, max(r_max), 100));

% Convert polar coordinates to Cartesian coordinates

X = R.*cos(Theta);

Y = R.*sin(Theta);

Z = X.*Y;

% Create a figure and plot the surface

figure;

surf(X, Y, Z, 'EdgeColor', 'none');

% Set the color for the portion inside the given equation

inside_color = [0.8, 0.2, 0.2]; % Reddish color

% Highlight the portion inside the equation by setting color

Z_highlighted = Z;

Z_highlighted((X.^2 + Y.^2).^2 > 2*a^2*X.*Y) = NaN;

% Plot the highlighted portion

hold on;

surf(X, Y, Z_highlighted, 'FaceColor', inside_color, 'EdgeColor', 'none');

% Set the view and labels

view(3);

xlabel('X');

ylabel('Y');

zlabel('Z');

% Add a color bar to indicate the highlighted portion

colormap(gca, [inside_color; get(gca, 'color')]);

c = colorbar;

c.Label.String = 'Highlighted Portion';

% Adjust the plot settings

axis equal;

title('Surface Plot of az = xy');

Kindly replace 'a' with the desired value for the equation.

Please refer to the following documentation to know more about the 'surf' function :

Surface plot - MATLAB surf (mathworks.com)

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Ruchika 2023-8-16

Hi, the portion of the surface az = xy that lies inside the region defined by r^2 = a^2 * sin(2θ) is represented by the red surface in the plot.

In polar coordinates, the equation r^2 = a^2 * sin(2θ) represents a loop-shaped curve. The portion of the surface az = xy that lies inside this loop is highlighted in red in the plot.

Atom 2023-8-19

In this plot the cylindrical shape of (X.^2 + Y.^2).^2 = 2*a^2*X.*Y is missing. Would you modify the code so that one can visualize a transparent cylindrical shape. Your code visualizes the area of the given surface inside the cylinder.

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Answer 2

Constantino Reyes-Aldasoro 2023-8-16

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2009142-plot-the-area-of-the-surface#answer_1288282

This forum does not work like this. You have to try to do the coding first and when you run into problems, then you ask for help adding the coding that you have already done.

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Atom 2023-8-16

True, but I am unable to understand how to start.. In polar coordinate r^2=a^2 \sin(2\theta) will look like two loops... How to plot, I dont know really

John D'Errico 2023-8-16

编辑：John D'Errico 2023-8-16

This is why, had I seen the question long ago, it would have been closed immediately. As now, the student thinks it is ok to post questions about homework, with no attempt made.

Not understanding how to do homework just means that a question should have been directed to the teacher. Or the students in the class could have discussed the problem amongst themselves. (That is how I survived one difficult class long ago.) And not being able to do a homework problem does not cost much.

Finally, I would point out that @Atom has posted and gotten away with 48 separate questions. Many of which seem to be like this. So I will now be forced to watch more carefully.

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