function [t] = intersect(e,v,c,r)
%Computes the intersection of a sphere and a parametrically
%defined ray, given the center and radius of the sphere, the 
%ray originating point, and the ray direction.
temp(1) = sum(v.^2);     %a
temp(2) = v(1)*(e(1)-c(1)) + v(2)*(e(2)-c(2)) + v(3)*(e(3)-c(3));
temp(2) = 2*temp(2);     %b, and below, c.
temp(3) = sum(e.^2) + sum(c.^2) - 2*(e(1)*c(1) + e(2)*c(2) + e(3)*c(3)) - r^2;
%Now we plug into Descartes equation and find two t's.  Among the 
%real positive roots, the smaller is the front of the sphere's intersection
%with the ray, which is only a concern if the sphere is closest along that
%ray.
t(1) = (-temp(2) + sqrt(temp(2)^2 - 4*temp(1)*temp(3)))/(2*temp(1));
t(2) = (-temp(2) - sqrt(temp(2)^2 - 4*temp(1)*temp(3)))/(2*temp(1));