Ray Ellipsoid intersections?

  • #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
 

Answers and Replies

  • #2
mathman
Science Advisor
8,021
526
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.
 
  • #3
mgb_phys
Science Advisor
Homework Helper
7,819
14
Wouldn't that make a great name for a band "Ray Ellipsoid and the intersections"?
 

Related Threads on Ray Ellipsoid intersections?

  • Last Post
Replies
13
Views
14K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
5
Views
19K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
1K
Replies
2
Views
4K
Replies
3
Views
936
Replies
1
Views
836
  • Last Post
Replies
6
Views
3K
Top