equation of the object

equation of the object

I am using ray tracing and at the beginning I assumed a plane surface so I
used the equation of the plane surface which is :
Ax + BY + CZ +d = 0
while A,B and C are the component of the normal vector of the Plane Normal
= [A B C] and using the Ray equation : Ray = Source + t*Direction And then
solve it for t and I can find the intersection points.
My question now that I have function in matlab to read the surface of the
object but the object may not be plane surface and I am getting the data
of the surface [X Y Z] of the surface but I don't know which equation
should I use to find t and then the intersection point. And I even have a
function to give me the normal vector at each point
If you can edit the tags the get the right ones please do it. Any one has
suggestion please.
Thanks