3d Visualizations of optimization problems

[shammeer-s]

This PR extends the existing slice_plot functionality to support 2D and 3D visualizations of objective functions. The main enhancements include:

• Support for 3D surface plots and 2D contour plots using Plotly
• Pairwise visualization grid similar to seaborn.pairplot for higher-dimensional problems
• Separation of concerns: Function evaluations are decoupled from plotting logic
• Parallelized evaluations using batch evaluators for efficient performance
• Modular function evaluation handled in plot_data.py
• Unified interface: Users can choose between "slice", "3d", or "contour" via the projection argument in slice_plot

Future Improvements

• Clean up repeated code by moving common plot logic into helper functions.
• Simplify 3D subplot layout and camera setup to make the code easier to manage.
• Add interactive elements or show useful plots (like 1D slices) on the diagonal of pairwise plots.
• Move the 3D and contour plot logic into their own well-named functions for better structure.
• Rename some function parameters to make their purpose easier to understand.
• Use an enum to clearly define chart types and make the code safer and easier to follow.

[timmens]

Hey,

Thanks for the PR!

Before I start a thorough review of your changes, lets tackle some high-level issues:

1. Can you move the code from plot_data.py into the slice_plot.py module, unless it is also used in other plotting functions.
2. Can you re-order the functions such that the function that is exported by the module (slice_plot) is at the beginning, then the private slice plot functions, and lastly the plotting data code.
3. Can you create a small notebook where you showcase the usage of the new features (this does not need to pushed, you can just upload it in a comment here).

Thanks a lot! If you have any questions, let me know here or on Zulip!

[shammeer-s]

Hey @timmens,

Thanks for the feedback!

Sure, I’ll move the code from plot_data.py into slice_plot.py as suggested, since it’s not being used elsewhere. I’ll also re-order the functions so that the exported slice_plot function comes first.

I'll work on a small notebook to demonstrate the new features and share it here once it’s ready.

Also, I’ll take this opportunity to improve the modularity of the plotting logic a bit—cleaning it up should make the flow easier to understand.

Let me know if there's anything else I should add or keep in mind!