Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Ray Ellipsoid intersections?

  1. Mar 23, 2008 #1
    So I have an array p(t) = e + td, where e is the start position, t is some parameter, and d is the direction of the ray

    For a sphere with center c and radius R, the vector form equation is (p-c).(p-c)-R^2=0

    This can be algebraically manipulated into:

    t = (-d.(e-c) +- sqrt((d.(e-c))^2 - (d.d)((e-c).(e-c)-R^2))) / (d.d)



    How can I express t for ellipsoids? I know there's an xRadius, yRadius, and a zRadius instead of radius R
     
  2. jcsd
  3. Mar 23, 2008 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    The most direct way is to transform the coordinates so that the ellipsoid is centered at the origin and its three axes coincide with the coordinate axes. The equation for the ellipsoid is then (x/a)2+(y/b)2+(z/c)2=1. Then substitute the components of p(t) for x,y,and z to get the equation for t.
     
  4. Mar 23, 2008 #3

    mgb_phys

    User Avatar
    Science Advisor
    Homework Helper

    Wouldn't that make a great name for a band "Ray Ellipsoid and the intersections"?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Ray Ellipsoid intersections?
  1. Volume of an ellipsoid (Replies: 5)

  2. Radius of Ellipsoid (Replies: 13)

  3. Is this an ellipsoid? (Replies: 5)

Loading...