3D Surface Representations
When we talk about geometry processing, it’s mostly about applying algorithms to the geometry models. There are multiple representations of the surface however if we see from the high-level view, there are two major representations.
# Parametric Representation
Formally, parametric surfaces are defined by a vector-valued parameterization function $f: \Omega \rightarrow S$ that maps a 2D parameter domain $\Omega \rightarrow \mathbb{R}^2$ to the surface $S = f(\Omega) \in \mathbb{R}^3$.
# Implicit Representation
While, implict surfaces surfaces are defined by a zero-level set of a scalar-valued function $F = \mathbb{R}^3 \rightarrow \mathbb{R}$, i.e., $S = { x \in \mathbb{R}^3 \mid F(x) = 0 }$