Giving the view selection gizmo some thought. Excuse the fugly mockups, but I’m hoping it will show the idea…
The thought is to start with sphere. Add the three axes, along with six locations for each major view labeled “FBLRUD”. You can drag the sphere around like a trackball or you can click anywhere on it to change views. Preselection highlighting will show hotspots on the sphere before you click. Selecting a labeled area obviously takes you to that major face view, but selecting different areas between them will take you to a view that is in between.
When you select one of the six major face views the ball will shrink a bit and an outer ring fades into view. Clicking the top, bottom, right, left sections of that ring will take you to the other major views. Clicking on diagonal sections will take you out of major face view mode (removing the ring) and take you to a 3/4 view. Clicking on the face that is selected (so the “F” when already in Front view) will toggle between Orthographic and Perspective. You can also rotate the ring to roll the view.
By default it would be faded out in the corner, and probably smaller than this:
Hovering over it then becomes active and the buttons around it become visible:
The button shown at the top-left takes you to your default (customizable) “home” view. A long press of it brings up a list of important and saved views. The button on the top-right shows the status of, and allows you to switch between, Ortho and Persp. The button at the bottom-right brings up a menu for configuration and customization of the gizmo.
This may seem similar to Autodesk’s Viewcube. But reading that patent document they are very explicit about it only applying to a cube in particular.