Case of implicit surfaces

Undeformed implicit surface \(S=\{p\in\mathbb{R}^3\;|\;\;g(p)=0\}\)

Given a volume deformation \(f:p\to f(p)\)
The implicit surface \(S'\) deformed by \(f\) is defined by
- \(S'=\{p\in\mathbb{R}^3\;|\;\;(g\circ f^{-1})(p)=0\}\)

\(p\in S' \Rightarrow f^{-1}(p)\in S \Rightarrow g(f^{-1}(p))=0\)

assets/implicit_surface.png