which is why games like Doom in the 90s only had textured horizontal and vertical surfaces, no slopes.
So in each horizontal or vertical line of pixels you only need one division by z-distance, which can be optimised out of the loop
division is 20-40 CPU cycles. multiplication is 4. if you're dividing by the same constant in a loop, you're paying that tax a million times for no reason.
one reciprocal. computed once. everything else is multiplication.
In fact, given subset S of ℝ, it is possible to construct a continuous nowhere constant
f: ℝ → ℝ
with extrema attained at exactly the points of S if and only if S is countable.
So, using (un)countability in the proof seems natural.
In fact, given subset S of ℝ, it is possible to construct a continuous nowhere constant
f: ℝ → ℝ
with extrema attained at exactly the points of S if and only if S is countable.
So, using (un)countability in the proof seems natural.
@subcountability I meant to use f\colon throughout, but stately typed f: in the preamble. And lemma as plural was just a typo. I did spot it at the last moment before posting but too lazy to fix, thinking no-one would notice or comment
Our teams are working hard to clean up after yesterday’s @Arsenal parade – and what a day it was!
With over a million people attending, it’s a major clean-up. We’re getting through it as quickly as we can, so please bear with us while we get the borough back to its best ✨ (1/2)