When transforming [[Normal Vector|Normals]] between spaces (*ex.* [[../Computer Science/Object Space|Object Space]] $\to$ [[../Computer Science/World Space]]), special care is needed to ensure [[Orthogonal|orthogonality]]. [[Universal Quantifier|For any]] normal $n$ of a face $F$, the [[Image]] of $n$ must be a [[Normal Vector|Normal]] of the image of $F$. Given an [[Triangle]] that we are trying to convert between [[Linear Subspace|Spaces]] $A \to B$, with $\mathcal C$ being the [[Change of Basis Matrix]] of $A\to B$. $\huge \begin{align} F &\perp \vec n \\ F' &\perp \vec n' \end{align} $ To preserve [[Orthogonal|orthogonality]], we need to convert the [[Change of Basis Matrix]] $\mathcal C$ into an [[Orthogonal Matrix]]. To do this in this context, we can take the [[Inverse Matrices|Inverse]] [[Matrix Transpose|Transpose]]. $\huge N = \pa{\mathcal C^{-1}}^\intercal $