barycentric coordinates


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barycentric coordinates

(ba-ră-sen -trik) See barycenter.

Barycentric Coordinates

 

the coordinates of a point M on a plane in relation to three basis points A1, A2, and A3 (not lying on the same line) of this plane—three numbers m1, m2, and m3 (which satisfy the condition m1 + m2 + m3 = 1), such that the point M represents the center of gravity of the system of three material points with masses m1, m2, and m3 located at the points A1, A2, and A3 respectively. (Here it is necessary to consider that the masses m1, m2, and m3 can be both positive and negative.) Barycentric coordinates in space are defined analogously. Barycentric coordinates are used in certain branches of mathematics and its applications.

barycentric coordinates

[‚bar·ə′sen·trik kō′ȯrd·ən‚əts]
(mathematics)
The coefficients in the representation of a point in a simplex as a linear combination of the vertices of the simplex.
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The keypoints on the mesh and their barycentric coordinates are extracted from a reference image in which the surface is in front of the camera without deformations.
i], it can be expressed in terms of its barycentric coordinate of the facet where this keypoint lies on, as:
A linear interpolation is used on tetrahedra for the soft tissue model, the displacement ut of a tissue constraint point placed inside a tetrahedron is given by the barycentric coordinates and the displacement [DELTA]qt of the 4 nodes ut = Jt[DELTA]qt.
i=1] are the symmetrical Gaussian quadrature positions in the lth triangle, whose Barycentric coordinates are [{([S.
i=1] are the Barycentric coordinates of the symmetrical Gaussian quadrature positions in a triangle.
Note that when computing Equation (2) in step (iii), [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] only needs to be computed once for all straight triangles since the barycentric coordinates of [([g.
We tested barycentric interpolation to adjust a skin mesh to the underlying anatomy (for more information on barycentric coordinates refer to Hansford [2007]).
This way, the feature points in the facial mesh would be interpolated to their counterparts and the remaining vertices would be adjusted through their barycentric coordinates (Figures 2D and 2E).
2] are the barycentric coordinates corresponding to the vertices of l and [[lambda].
The barycentric coordinates of a point x [element of] [Sigma] are real numbers [[Phi].
The barycenter of [Sigma] is the point b([Sigma]) with barycentric coordinates [[Phi].
i] define the barycentric coordinate corresponding to the i-th vartex [p.