Both and take longer than Sedna and to orbit the Sun using barycentric coordinates.
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Similarly, the third barycentric coordinate reads as
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An equation for the Euler line in barycentric coordinates \ alpha : \ beta : \ gamma is
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To do so, we first transform \ mathbf { r } into the barycentric coordinates of each triangle.
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Spatial functions include various intersection routines, conversion from / to barycentric coordinates and bounding box / sphere generators.
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The information recorded about each point includes its barycentric coordinates and its relation to lines joining other identified points.
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The triangle case can be solved easily by use of a barycentric coordinate system, parametric equation or dot product.
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Tetrahedral meshes are often used in finite element analysis because the use of barycentric coordinates can greatly simplify 3D interpolation.
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Practical examples include the International Atomic Time standard and its relationship with the Barycentric Coordinate Time standard used for interplanetary objects.
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Simplicial maps induce continuous maps between the underlying polyhedra of the simplicial complexes : one simply extends linearly using barycentric coordinates.
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