Explict representations often don't exist (e.g.,
a circle around the origin with radius \(r\)
requires two functions, \(y = \sqrt{r^2 - x^2}\)
and \(y = -\sqrt{r^2 - x^2}\), and they only
hold when \(0 \leq |x| \leq r\))
Implicit Form:
We can use implicit representations (e.g.,
a circle around the origin with radius \(r\)
can be represented as \(x^2 + y^2 - r^2 = 0\))
But, we must use a scanning algorithm
(i.e., check each point to see
if it is on the curve)
In addition, curves in 3D are difficult to represent in
implicit form (it is possible to use the intersection of
surfaces but it is difficult)