Quote:Original post by Zipster
Actually, you just remove the the sum restriction u + t ≤ 1 completely to get the full quadrilateral (keep 0 ≤ u/t ≤ 1). But it describes the entire inner area. You would have more logic to get just the edges.
Quote:Original post by TheAdmiralQuote:Original post by erissian
It's discontinuous (it has corners)
Not quite. A square is continuous (there are certainly no gaps), but it isn't smooth. If one were to describe it piecewise-implicitly or parametrically, then it's the first derivatives (and hence all that follow) that would be discontinuous. </unnecessary aside>
Admiral
Quote:Original post by MerlzThat's a filled square though (or a filled diamond if you prefer)
Here's another one, just for fun:
abs(x) + abs(y) <= 1
Although this one is at 45 degrees rotation to the axis, it's of max radius 1 :-)
Quote:Original post by iMalcTry:
A more generic unfilled version of that would be:
abs(x) + abs(y) = r
Of course you could probably rotate that by 45 degrees, which would probably look something like this:
abs(x*sin(45)+y*cos(45)) + abs(x*cos(45)-y*sin(45)) = r
sawtooth(x){
abs((x-4*floor(0.25*x))-2)-1
}
infcos(x){
min(1,max(-1,sawtooth(0.5*x)*2))
}
infsin(x){
infcos(x-2)
}
abscos(x){
x*=sqrt(2)*0.5;
sawtooth(x)
}
abssin(x){
x*=sqrt(2)*0.5;
sawtooth(x-1)
}
