Output: the largest inscribed circle in P.
1. Compute h1, h2, ...,
hn, determined by edges of P and
O(x0, y0, z0).
2. Compute normal vectors V1, V2,
..., Vn to h1, h2, ...,
3. Compute lines l1,l2,...,
ln , determined by O(x0, y0, z0)
and V1, V2, ..., Vn .
4. Compute points Q(Q1, Q2, ...,
Qn) as the intersection of l1,l2,...,
ln with the sphere.
5. Compute planes h'1, h'2, ...,
h'n tangent to the sphere at points Q(Q1, Q2, ...,
6. Compute the vertex K of the polyhedral
region as the intersection of h'1, h'2, ...,
7. Compute the line l0 , determined
by K(xk, yk, zk) and
O(x0, y0, z0) .
8. Compute the center of the minimum circle Cmin
containing Q(Q1, Q2, ...,Qn) .
9. Compute the largest inscribed circle Cmax by using the relation between the aperture angles of the cone defined by Cmax , O(x0, y0, z0) and the polar cone defined by Cmin , O(x0, y0, z0)