In real-world systems, in addition to optimizations that check if any member of a block is in the triangle, are there optimizations to prevent checking other blocks?
For example, if we were scanning 2x2 blocks, would seeing that a block whose top left corner is at (2,2) (going from left to right and top to bottom) negate the need to check a block whose top left corner is at (0,0)?
Interesting idea! I'm not sure if there are examples of what you're describing in the real world, but it's possible. In general, there are always going to be tradeoffs between theoretical optimization and the actual computational logic needed to implement that theory.