the 3d orthogonal grid intersections a flowchart of a shape tree construction algorithm according to an embodiment of the invention is presented in fig6 referring now to the figure and referring also to fig4 and 5 a shape tree construction algorithm begins at step 60 by computing the binary segmented 3d volume v bseg for the target area at step 61 a sphere s r is inflated where r represents the radius at a location p until its surface hits the boundary of v bseg in the voxel grid space where the boundary is defined as the exterior voxels of v bseg and p can be a manual input or be provided from another application at step 62 one searches for a center location p u2032 within s r that maximize the radius and let s m be the maximum radius sphere at p u2032 if two or more spheres have the same radius the nearest sphere to the center of s r is selected fig4 a illustrates how the initial sphere s r is inflated from the given point p until its surface hits the boundary of the binary segmented image v bseg at step 63 assign all voxels of v s m.