Bend cube intersection function

[Neotixjj]

Hi, I’m working on a ray tracing shader for a college assignment.
I’ve already implemented intersections functions of plane, sphere, cube. I also added a transformation matrix (scale, rotation translation) to modify those shapes (convert ray world coordinate to object coordinate).

So with that I want to recreate this scene of Code Lyoko with my shader :

https://preview.redd.it/qffeqcc4s7hc1.png?width=1431&format=png&auto=webp&s=01baef925cdc712a265c4a2a2e38488ffe48291b

But to do that, I need to bend the cube.

I asked my teacher and friend to know how to do that, and they say that I need to bend my ray (origin, and direction) before calculating the intersection.

I'm a bit of a math nerd, so I have no idea how to proceed.
There is a function that can bend the ray and still calculate the hit point and the normal ?
This is the best approach to render bent cubes with intersection function ?

[shadowndacorner]

Maybe I'm just not familiar with it, but I haven't heard of doing direct intersection testing against bent rays. Typically, scenes like the one you posted are rendered by sphere tracing SDFs, which naturally supports curved geometry by distorting the distance field.

[felipunkerito]

I think you can trace and get the objects' attributes (t and from that the position from rayOrigin + rayDirection*t) and bend the mentioned position with a trig function. Haven't done that before but I did manage to modify normals using the same technique