Jan 13, 2019 9:13 PM
Rational rendering and floating bar
"So, what would happen if we replaced floating point numbers with rational numbers and tried to render an image?"
This was the question I posed to myself after some pondering around a tweet by Morgan McGuire, a computer graphics researcher and educator. He was reflecting on how computer science students get surprised when they first learn that the nature floating point numbers in our current computers have precision tradeoffs that makes simple things like checking whether a point belongs to a triangle difficult. The problem of course is that checking for the coplanarity of four points through a determinant or some cross products (same thing really) will never result in a value of exactly zero, which those mathematical methods require. Even if the actual coplanarity computations were exact, the same precision trade-off would guarantee with almost probability 1.0 that the four points themselves would not coplanar.