Create dynamic cities of perspective angle x with least amount of tiles

Question

I found you can create unique building sizes with perspective with six tiles using parallel projection, whose angles are always 45 degrees... this allows you to connect to the next tile without issue:

The issue with that is you're stuck to a 45 degree angle... I feel like a 75 degree angle better matches my game's overall perspective...

But doing anything other than 45 degrees limits how deep my building is (how far back the building top goes)... so this seems to force me to create additional buildings if I want to make the top reach back further... Which adds complexity

Question:

Is there a way to achieve what I'm doing for any angle I choose such that I can create one building tileset (of 6 tiles) and create dynamic cities?

Or, do I have to sacrifice the angle of my choosing and go with the simple 45 degrees?

Thanks

Answer 1

Sure. Make non-square tiles.

For 75 degrees, you want a tile that's tan(75) = 3.732 times as tall as it is wide.

(edit: You might want to use shorter tiles on the 'middle' area between ground and roof, so as to enable buildings of various heights.)

Answer 2

You can extend it as far as you want, but you will need tiles with different diagonal pieces (like a puzzle) if you don't use a 45 deg angle.

You can use an angle that lets the tiles repeat after 2,3,...,n tiles.

For example. 63.435 deg will require 2 diagonal tiles, but you can extend buildings by alternating between them like this:

[tile 1]

oxxx

xoxx

[tile 2]

xxox

xxxo

[together]

oxxx

xoxx

xxox

xxxo

____oxxx

____xoxx

the larger the angle the more complexity. here is a list of a few angles given by atan(n).

1 tile repeat, 45 deg

2 tile repeat, 63.435 deg

3 tile repeat, 71.57 deg

4 tile repeat, 75.96 deg