A method for determining whether a point is contained in a sub-volume of a digitized medical image, includes providing a tetrahedron volume mesh (TVM) representing a sub-volume of a digital image volume and a point M, finding a vertex P of said TVM that is closest to point M, finding a tetrahedron Ti in said TVM that defines a solid angle around point P where point M is located, wherein if M is inside Ti, then M is inside the TVM, if M is not inside Ti, finding a facet F of tetrahedron Ti through which a line PM connecting points M and P exits Ti, and determining whether a next tetrahedron Ti+1 of said TVM exists along line PM, wherein if no such tetrahedron Ti+1 exists, then point M is outside the TVM, and wherein if Ti+1 exists, determining whether point M is inside tetrahedron Ti+1.