Ray-tracing

badatcode123

Raytracing is a method of 3D rendering that uses ray-surface intersection functions to find the nearest intersection distance to an object, “t”, if the ray hits the object. A simple ray-surface intersection is the ray-sphere intersection, shown below.

define Ray-sphere intersection|sphere pos (x) (y) (z) radius (rad) color (r) (g) (b)
    set [nx v] to ((ray origin x) - (x))
    set [ny v] to ((ray origin y) - (y))
    set [nz v] to ((ray origin z) - (z))
    set [b v] to ((((ray dir x) * (nx)) + ((ray dir y) * (ny))) + ((ray dir z) * (nz)))
    set [c v] to (((((nx) * (nx)) + ((ny) * (ny))) + ((nz) * (nz))) - ((rad) * (rad)))
    set [t v] to ((b) * (b) - (c))
    if <((t) > (0))> then
        set [t v] to (((0) - (b)) - ([sqrt v] of (t)))
        check if intersecting (t) object color (r) (g) (b) :: custom
    end

define check if intersecting (t) object color (r) (g) (b)
    if <<(t) > (0)> and <(t) < (ray t)>> then
        set [ray t v] to (t)
        set [object color R v] to (r)
        set [object color G v] to (g)
        set [object color B v] to (b)
    end

Now we can test intersections with every object in the scene and then color that pixel the color of the object (reminder that the color of the object is from 0-1 not 0-255) that has the smallest t value or the background color if there are no intersections. Do the ray-sphere intersection right after defining the ray origin and direction.

Expected output (circle radius of 25 and positioned at 0,0,100)