Help questions about rendering ellipsoids

[josemendez]

I  got confused on this part too. And I also think it should be the square of \widetilde{r}. So which one is correct? Please let me know of the progress.

Quoting the paper:

By dividing the coordinates by r, the in this way normalized x- and y- coordinates need to be inside the easier to handle unit circle.

That's why r2 is divided by mapping.w (which is the radius, r). This equation:

square(q) = 1/r * (x*x + y*y);

in code:

Code:

float r2 = dot(mapping.xy, mapping.xy);
float iq = 1 - r2/mapping.w;

r2 is the sum of the squares of x and y. then, we multiply it by 1/r: r2/mapping.w

So iq = 1- square(q)., used in the denominator of equation (11) - the one that calculates lambda. In the IntersectEllipsoid function you can see it being used:

Code:

float lambda = 1/(1 + mapping.z * sqrt(iq));

Hope this clarifies it. let me know if you need further help!

cheers,