We use the standard equation to translate a barycentric coordinate
to cartesian coordinate, which we can then use within our estimation algorithm to drive the behavior of the MS[S.sup.sim] to behave like the MS[S.sup.ref].
The barycentric coordinate
of the rigid body is [[-36.7749, -6.2296, -208.3247].sup.T] in [o.sub.1]-[x.sub.1][y.sub.1][z.sub.1].
In 1827, the barycentric coordinate
was developed to characterize the relative position of a point with respect to other points [23-26].
We also denote [p.sub.1][p.sub.2][p.sub.3] to be the face containing [p.sup.*] and denote [alpha], [beta], gamma] to be the barycentric coordinate
of [p.sup.*] with respect to [p.sub.1][p.sub.2][p.sub.3]; that is, [p.sup.*] = [alpha][p.sub.1] + [beta][p.sub.2] + [gamma[p.sub.3].
Given a set of affine points u0, [u.sub.1], ..., [u.sub.p], p = 0, ..., 4 in 4-d spacetime, a p-simplex [[sigma].sub.p] is the region spanned by u = [[summation].sup.p.sub.i=0] [[lambda].sub.i][u.sub.i] for all possible values of [[lambda].sub.i] [member of] [0,1], where [[lambda].sub.i] is the barycentric coordinate
associated with [u.sub.i] such that [[summation].sup.p.sub.i=0] [[lambda].sub.i] = 1.
Let [[mu].sub.i] define the barycentric coordinate
corresponding to the i-th vartex [p.sub.i] of K as follows:
If a triangle with the barycentric coordinate
as the initial point can translate freely along any straight line where a edge of the triangle lies, then the triangle is deemed to be impending.
The oscillation can be minimized in most cases by using polar splines or splines based on barycentric coordinate
1) The moments of the universal mean time UT1 must be expressed in TT (Terrestrial Time), TCG (Geocentric Coordinate Time) and TCB (Barycentric Coordinate
Time) time scales.
In 1991 we also gained the relativity-based Geocentric Coordinate Time (TCG) and Barycentric Coordinate
Time (TCB), paralleling TT and TDB.
Assuming that a keypoint in the mesh in[x.sub.i], it can be expressed in terms of its barycentric coordinate
of the facet where this keypoint lies on, as:
where (s,t) is the Barycentric coordinate
of (x,y) in a triangle, and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are the Lagrangian interpolation positions in the triangle given by