To clarify why the Boolean union corresponds to the minimum: If d is the distance function for the union of A and B, we want d(x) < 0 when x is in A or x is in B, d(x) = 0 when x is on the boundary of (A union B), and d(x) > 0 when x is neither in A nor B. If d1 and d2 are the distance functions of A and B, then if d1(x) < 0 or d2(x) < 0 we should say that d(x) < 0. The best way to detect if at least one of two quantities is zero is to take the minimum! The other cases can be checked similarly.
coolbreeze
What's the difference between algebraic surface and distance function? I think they are similar
jesshuifeng
I am still a little confused how this minimum function will perform a boolean union of d1x and d2x?
haotingl
Looks like a very convenient function to use for rendering water
fullkeyboardalchemist
I didn't quite understand the answer. Why taking the minimum = a Boolean union of them?
idkLinearAlgebra
Didn't quite understand+1.
yumz
although d1, d2 are distance functions, f(x) = min(d1, d2) is not.
To clarify why the Boolean union corresponds to the minimum: If d is the distance function for the union of A and B, we want d(x) < 0 when x is in A or x is in B, d(x) = 0 when x is on the boundary of (A union B), and d(x) > 0 when x is neither in A nor B. If d1 and d2 are the distance functions of A and B, then if d1(x) < 0 or d2(x) < 0 we should say that d(x) < 0. The best way to detect if at least one of two quantities is zero is to take the minimum! The other cases can be checked similarly.
What's the difference between algebraic surface and distance function? I think they are similar
I am still a little confused how this minimum function will perform a boolean union of d1x and d2x?
Looks like a very convenient function to use for rendering water
I didn't quite understand the answer. Why taking the minimum = a Boolean union of them?
Didn't quite understand+1.
although d1, d2 are distance functions, f(x) = min(d1, d2) is not.