So,

normal vector field and unit

normal vector field of M are

Thus, after allocation of the points forming cutting line using (2), and obtaining their spatial coordinates it is necessary to solve a problem of calculation of

normal vector to surface of parts in all points of this line.

i]) is calculated by the inner product of the unit direction vector (i) of the incidence photons and the unit

normal vector ([[vector].

i] in the normal direction of the surface is obtained by projecting following a unitary

normal vector (shown as [[vector].

We shall assume that M is oriented (so that a unit

normal vector field [xi] is defined on the whole M)and that the type number k(x) is greater than 0 everywhere on M.

w] is the unit

normal vector directed into the wall, and [[[vector].

m]), the

normal vector of reflection (N), the ideal reflection vector ([R.

g] is the

normal vector for cutter surfaces of segment a; Eq.

Where denotes the dot product and W the (not necessarily normalized)

normal vector to the hyper plane.

For an affine hyperplane H and a

normal vector direction, let [H.

y]) is the solution of the boundary of the

normal vector field, [OMEGA] is the solution domain, [partial derivative][OMEGA] is the boundary outward

normal vector.

An additional condition, verified in the described procedure, analyzes the values of angle deviations of every

normal vector of the respective triangles, from the direction of the resultant vector.