I recently stumbled over quad menus and found perfect for usage in complex editors and for staying "in flow" while modelling. However, this pattern is only rarely used, as most editors use very long, cascaded context menus.
Are these good to use from a UX perspective or do they only "surprise" the user in a negative way? Does it compare favourable to the older radial menus?
There may be some legitimate uses for a quad menu pattern though here are the reasons why I would almost always opt for the accordion pattern.
Even if the little squares that light up aren't the target of the expand/collapse operation the four tiny root level words seem too close to each other for high accuracy interaction.
I would probably go for a single vertical accordion where the 4 sub-sections could all be expanded/collapsed independently and have a little more vertical space for each root level item when collapsed.
Humans are really good at filtering out noise without even realizing it. Tasks like driving a car would be almost impossible if we noticed every little mark on the windshield and every little inconsistency on the road. Because of this it is hard for us to quickly scan and target the item we need from lists that are exceptionally large. At least the quad menu is chunked into different sections that don't all have to be opened at once but again I would choose the vertical accordion pattern to handle this chunking.
The only benefit I see that this pattern has over an accordion is that it requires less vertical space. There is plenty of research showing that scrolling vertically is preferred to scrolling horizontally (mouse wheel, touch screens, etc.) so until this is no longer the case I think that a simple vertical accordion interaction would be more familiar as well as usable.
This menu looks like a nightmare to me but I could see it living in a 3D modeling app.
Is there any benefit to your users seeing all the open menus at once? As in, are they choosing 'attach' or maybe 'select' or 'divide' but need to see those options at the same time? If not, I would suggest a standard context menu with 4 main options, 1 for each sub-menu.
In the shown menu, I assume each menu is ordered from top to bottom but this destroys the benefit of "most important is closest" for the 2 top menus. If you want around this you have to reverse their order which probably conflicts with a duplication of this menu in a toolbar somewhere.
Also note, Tools 1/2 are not very descriptive names.
