md`The ray intersects a box at upto two points. If we assume the ray parameters of the intersections to be t_near and t_far, then [t_near, t_far] defines the parameter range of all the points of the ray that lie inside the box. It also implies that if the range [t_near, t_far] is null, i.e. t_near< t_far, then there is no ray point of intersection, or in other words, there is no intersection.

The intersection algorithm extends the ray-plane intersection to compute the intersection of the ray with the planes parallel to three pairs of the sides as (t_xmin,t_xmax), (t_ymin,t_ymax), and (t_zmin,t_zmax). As the normals to these planes are vectors parallel to the primary axes, two of the components of the normals are zeros, and thus the ray-plane intersection equation simplifies to a scalar subtraction and a division. So the expression for t's are as follows.
t_xmin = (x_min-x_O)/x_d, t_ymin = (y_min-y_O)/y_d and t_zmin = (z_min-z_O)/z_d,
t_xmax = (x_max-x_O)/x_d, t_ymax = (y_max-y_O)/y_d and t_zmax = (z_max-z_O)/z_d.
Each of these pairs define a scalar range and the range must be non-null. So the algorithm orders the intersection pairs to guaranty validity of the range by swapping them as necessary.
For ex: if (t_xmin > t_xmax) then swap(t_xmin , t_xmax), and so on.
From these ranges the algorithm computes the actual intersection range [t_near,t_far] as
t_near = max(max(t_xmin,t_ymin),t_zmin), and t_far = min(min(t_xmax,t_ymax),t_zmax)
If t_near > t_far then the ray does not intersect the box.`

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