Results 1 to 3 of 3

Math Help - Intersection of a ray and a curved surface

  1. #1
    Member
    Joined
    May 2008
    Posts
    87

    Intersection of a ray and a curved surface

    Hi,
    I'd like to write a ray tracing program but I have some issues with the mathematics thereof, I'm trying to do some exercises in a book to help me as such but I don't know how to solve e.g. problems of the form:

    Find where (if at all) the ray ray(t) = (5, -1, 0)^T + t(-1, 1,  1)^T intersects the curved surface z(x, y) = (x - 2)(y - 3) + 4, if there is more than one intersection, which is the first?

    As far as I understand I should set the two equations equal to each other and try solve them for the unknown parameter t? I've tried this but I can't get anywhere.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Failure's Avatar
    Joined
    Jul 2009
    From
    Zürich
    Posts
    555
    Quote Originally Posted by posix_memalign View Post
    Hi,
    I'd like to write a ray tracing program but I have some issues with the mathematics thereof, I'm trying to do some exercises in a book to help me as such but I don't know how to solve e.g. problems of the form:

    Find where (if at all) the ray ray(t) = (5, -1, 0)^T + t(-1, 1,  1)^T intersects the curved surface z(x, y) = (x - 2)(y - 3) + 4, if there is more than one intersection, which is the first?
    The one that is closer to the source of the ray, of course! For, you see, a ray is not a line: a ray has a source from which it originates. Once a ray hits a surface it gets reflected - and the reflected ray may, in principle, hit the same or another surface at some other point.

    As far as I understand I should set the two equations equal to each other and try solve them for the unknown parameter t? I've tried this but I can't get anywhere.
    I find that surprising: why, you just replace the coordinates x,y,z in the equation for the surface with terms expressed with t, i.e. x=5-t, y=-1+t and z=t, based on the equation of the ray, then solve for t.
    In your example this gives the two solutions t1=2 and t2=4, if I am not mistaken (check it for yourself). Now plug these two values of t back into the equation of the ray and you have found the points of intersection.
    Last edited by Failure; August 30th 2010 at 11:53 AM. Reason: typo corrected
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member mfetch22's Avatar
    Joined
    Feb 2010
    From
    Columbus, Ohio, USA
    Posts
    168
    I agree
    Last edited by mfetch22; August 30th 2010 at 11:46 AM. Reason: SOLVED
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: September 19th 2011, 07:10 AM
  2. Replies: 2
    Last Post: February 10th 2011, 07:06 PM
  3. Replies: 4
    Last Post: April 27th 2010, 02:52 PM
  4. terminology to describe curved surface
    Posted in the Geometry Forum
    Replies: 1
    Last Post: December 1st 2009, 12:32 PM
  5. Line-Surface intersection
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 24th 2008, 08:56 PM

Search Tags


/mathhelpforum @mathhelpforum