## Uniform scale transformation of a ray

A ray \((O,\vec{d})\) in \(\mathbb{R}^3\) subjected to a uniform scale transformation represented by a scalar \(s \in \mathbb{R}\) yields a ray \((O',\vec{d}')\) where \(O' := s O\) and \(\vec{d}' := s (\vec{d} + O) - O'\).

## Scale transformation of a ray

An ray \((O,\vec{d})\) in \(\mathbb{R}^3\) subjected to a scale transformation represented by a vector \(\vec{s} \in \mathbb{R}^3\) yields a ray \((O', \vec{d})\) where \(O' := \vec{s} \cdot O \) and \(\vec{d}' := \vec{d} \cdot (\vec{d} + O) - O'\).

## Translate transformation of a ray

A ray \((O,\vec{d})\) in \(\mathbb{R}^3\) subjected to translate transformation represented by a vector \(\vec{t} \in \mathbb{R}^3\) yields a ray \((O',\vec{d}')\) where \(O' := O + \vec{t}\) and \(\vec{d}' := \vec{d}\).