For a front f : [M.sup.n] [right arrow] [R.sup.n+1] with a (possibly locally defined)

unit normal vector field v,

In the RobotStudio, the scroll bar tools can indicate all the points around the surface for selection, the API function Edge.GetTangent(*) is able to get the tangent vector on point [P.sub.0] and the API function Faces.GetNormalToSurface(*) can get the

unit normal vector of a polygon.

The inner product of reflected wave [r.sub.m] from subreflector and subreflector's

unit normal vector is

where ( )' = d/ds, [??] denotes the

unit normal of [gamma] in M and K is the Gaussian curvature of M.

The outward

unit normal vector on the surface of any ellipsoid [rho] = const., given through

where ([n.sub.ix],[n.sub.iy],[n.sub.iz]) are the components of the

unit normal to the external surface of the PDL (here, the subscripts i = 1 and i = 2 correspond to PDL in the form of a circular paraboloid and hyperboloid, respectively), p is the parameter characterizing the rounding rate of the apex (the tooth root passes through a circular cone at p = 0); in this case p = 0.4.

Nomenclature C: Color function (-) [f.sub.sv]: Total external force per volume on the fluid (N/[m.sup.3]) h: The width of microchannel ([micro]m) l: The length of the lateral channel ([micro]m) L: The length of the slug ([micro]m) [bar.L]: The ratio between organic slug length and water slug length (-) n: Normal vector to the interface (-) [??]:

Unit normal vector to the interface (-) t: Time (s) [DELTA]t: Time interval (s) [??]: Velocity vector (m/s) u: Velocity component in x direction (m/s) [bar.u]: [bar.u] = [absolute value of [[??].sub.02]]/ [absolute value of [[??].sub.01]](-) v: Velocity component in y direction (m/s) xl: The length of solution domain (m) yl: The width of solution domain (m).

For a regular parameter surface r(u, v) = (x(u, v), y(u, v), z(u, v)), its two unit tangent vectors in the directions of u and v and its

unit normal vector are given by [17]

where n is the

unit normal vector of the flame front, which can be obtained by

Following that control, the next step was the construction of

unit normal variance matrix (Z).

[GAMMA] denotes the surface of the object with the

unit normal vector n, and the parameter c depends on the location of observation point.

Let M be a semi-Riemannian hypersurface in [R.sup.3.sub.1], D and N represent Levi-Civita connection and

unit normal vector field of M, respectively.