The ray marching (naïve) algorithm is to march a ray by a fixed step size, check if a ray intersection occurs at each step, until the ray reaches a maximum distance or step count.
Formally, the root found by ray marching (naïve) is the limit point of the sequence defined by the recurrence equation
\[t_{i+1} = t_i + \Delta t\]
where \(t_0 = 0\) and \(\Delta t\) is the fixed step size.
At each step, the ray marches to \(\boldsymbol {r}(t_i)\), which is usually denoted \(\boldsymbol {r}_i\).