Скачать или смотреть Creating a 3D Plot for a Function of Two Variables in MATLAB

Learn how to plot a complex function of two variables in MATLAB using `surf` and `meshgrid` techniques for effective visualization.
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This video is based on the question https://stackoverflow.com/q/68954845/ asked by the user 'Nick Bodden' ( https://stackoverflow.com/u/16763978/ ) and on the answer https://stackoverflow.com/a/68975013/ provided by the user 'Hadi' ( https://stackoverflow.com/u/3878321/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

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Mastering 3D Plots in MATLAB: Plotting a Function of Two Variables

When it comes to visualizing mathematical functions, the ability to create 3D plots can significantly enhance our understanding of complex relationships. In this guide, we will tackle the problem of plotting a specific function of two variables using MATLAB. We’ll guide you through the steps necessary to create a beautiful 3D representation of the function and address common challenges, such as pointwise minimization. Let’s get started!

The Challenge: Plotting a Function of Two Variables

The function we want to plot is defined as:

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Here, x and y are restricted to non-negative values and can range from 0 to a maximum of 10. Attempting to plot this function using the surf and meshgrid commands may initially seem straightforward. However, due to the pointwise minimization required to compute the value of f, a simple approach may not yield the desired results.

Step-by-Step Solution

Step 1: Creating a Meshgrid

To visualize the function in 3D, we first need to create a grid of values for x and y. In MATLAB, this can be efficiently achieved using the meshgrid function. We will set the ranges of both x and y from 0 to 10 with increments of 0.5.

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Step 2: Define the Function with Pointwise Minimization

Next, we need to compute the values of our function f. Since x and y are 2D matrices created by meshgrid, we will define a 3D matrix k that will help us handle the minimum operation across the two dimensions.

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Now, we can compute the function values z using the min function along the third dimension.

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Step 3: Plotting the 3D Surface

Finally, it’s time to visualize our function using the surf command, which will create a smooth surface plot.

[[See Video to Reveal this Text or Code Snippet]]

This will generate a 3D plot of the function, clearly showing how f varies with x and y.

Conclusion

By following these steps, you can effectively plot complex functions of two variables in MATLAB, accommodating features such as pointwise minimization. This technique allows you to visualize intricate relationships between variables in a clear and engaging way. Keep experimenting with different functions and parameters to further enhance your data analysis skills!

If you have any questions or need further assistance, feel free to leave a comment below. Happy plotting!