HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

Comrades, is it possible to achieve the following through a mod: set the game's resolution, for example, to 1680*1050, and make the battle window display in 800*600 resolution or stretch to the entire screen?

I recommend choosing the resolution 1062x664 (or 960x600 as a last resort).
In the latest beta (3.808 beta 2) (installed on top of 3.807), with the 32-bit True (stretchable) Nx renderer and xBRZ + Bilinear Sharper / xBRZ + Bicubic SharperX2 filters, the picture will be excellent.

xBRZ + Bicubic SharperX2 is the most resource-intensive (CPU speed, memory, number of cores).
xBRZ + Bilinear Sharper is faster (visually, I wouldn't say it's worse, just slightly different).

If your computer turns out to be too weak for these filters, then you can use the faster alternative UltraSaI + Bilinear Sharper.

With the suggested resolutions for the town and battle windows, they will be as large as possible. With 1062x664, 100% of the HD functionality is preserved; with 960x600, it is not.

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I will not implement different resizing for different windows. Different scaling/quality of the same interface elements is not aesthetically pleasing.