Converting MATLAB figures into `matplotlib` figures?

[foreverallama]

With some more observation, I've observed that MATLAB figures can be saved as a variable into MAT-files, which is saved as an object of class matlab.ui.Figure, which can be read using matio.load_from_mat. This leads to an interesting project idea, where one may be able to directly translate MATLAB figures (along with all of the figures' properties) into a matplotlib figure.

I'm not sure if this has any real use case. If you really wanted such interoperability, you would be saving the data instead of the plot, and it really doesn't take much time to redraw a figure from scratch. Nonetheless, this is an interesting project theoretically, and could be looked into.

Additional Context

I've only looked at very simple plots so far, and this will need to be more carefully studied using different types of figures. But so far this is what I've observed with the class matlab.ui.Figure:

Properties

This class has a whole bunch of properties, listed below:

Property Name	Description
StoragePosition	Object of class matlab.ui.internal.UnitPos
StorageOuterPosition	Object of class matlab.ui.internal.UnitPos
PaperPositionStorage	Object of class matlab.ui.internal.PaperPositionStorage
PaperTypeStorage	Object of class matlab.ui.internal.PaperPositionStorage
SerializableUIContextMenu	0 x 0 object of class matlab.graphics.GraphicsPlaceholder
CurrentAxesMode	Enum value: manual
NextPlotMode	Enum value: manual
DefaultTools_I	Enum value: menusandtoolbar
ScreenPixelsPerInchMode	Enum value: manual
TopLevelSerializedObject	Enum value: on
BeingDeleted	Enum value: off
Internal	Boolean flag
Copyable	Boolean flag
PointerShapeCData_IS	16 x 16 integer array
PointerShapeHotSpot_IS	1 x 2 integer array
CloseRequestFcn_IS	String: closereq
SerializableApplicationData	Empty struct
CustomThemePropertyMappings	Empty struct
SerializableTheme	Struct array with field ThemeMode
SerializableChildren	Object of class matlab.graphics.axis.Axes (contains the actual plot data)

[foreverallama]

So I suspect that MATLAB created this "subsystem" originally to load/save to their native .fig format. This package can read figures saved as both fig and mat files.

There's a whole lot of information stored in these files that tells a lot about MATLAB internals. There's like at least 42 unique classes with a whole bunch of properties in a fig file. This will take some time to analyze