## Uniform scale transformation of an axis aligned box

An axis aligned box \((Min,Max)\) in \(\mathbb{R}^3\) subjected to a uniform scale transformation represented by a scalar \(s \in \mathbb{R}\) yields an axis aligned box \((Min',Max')\) where \(Min'_i = \min\{ s Min_i, s Max_i \}\) and \(Max'_i = \max\{ s Min_i, s Max_i \}\).

## Scale transformation of an axis aligned box

An axis aligned box \((Min,Max)\) in \(\mathbb{R}^3\) subjected to a scale transformation represented by a vector \(\vec{s} \in \mathbb{R}^3\) yields an axis aligned box \((Min',Max')\) where \(Min'_i = \min\{ s_i Min_i, s_i Max_i \}\) and \(Max'_i = \max\{ s_i Min_i, s_i Max_i \}\).

## Translate transformation of an axis aligned box

An axis aligned box \((Min,Max)\) in \(\mathbb{R}^3\) subjected to a translate transformation represented by a vector \(\vec{t} \in \mathbb{R}^3\) yields an axis aligned box \((Min',Max')\) where \(Min' = Min + t\) and \(Max' = Max + t\).