mercredi 25 novembre 2015

reflection vector on a sphere ?

Hello I've an exercice in mathematics (actually I study openGl (the light and reflection on objects) but this one is pure mathematics) and I'm stuck here all day ... I don't know how to solve it. I would like at least any explanation. the exercice says : ( I translated it from french to english so please if there's anything wrong just correct me)

    we have the cartesian equation of a sphere  :

    (x − h)^2 + (y − k)^2 + (z − l)^2 = r^2

    where ( h, k , l) is its center and its radius r

    A light ray direction (vector) v = (a, b, c) strikes a sphere 
    at the point ( x0, y0 , z0 ) and is reflected at the same angle as that it 
    forms with the normal vector to the sphere at the point (x0, y0, z0 ) 
    in the direction of a vector v'

    Give a formula for the vector v' as a function of (h, k, l) , r, (a, b, c) 
    and (x0, y0, z0 )

the vector v' is the reflected ray??

I'm sorry for the tags I don't know what to put. anyway I really can't solve it that,s why I didn't put here any solution :( I'Ll appreciate any help. thank you.





Aucun commentaire:

Enregistrer un commentaire