barycentric coordinates sentence in Hindi

Examples

1. Using the previously given conversion between barycentric and trilinear coordinates, the various other equations given in Trilinear coordinates # Formulas can be rewritten in terms of barycentric coordinates.
2. However, in the situations where the important points of the studied problem are affinity independent, barycentric coordinates may lead to simpler computation, as in the following example.
3. Instead, it is often easier to make a change of variables to any two barycentric coordinates, e . g . \ lambda _ 1, \ lambda _ 2.
4. J . M . Tienstra ( 1895-1951 ) was a professor of the Delft university of Technology where he taught the use of barycentric coordinates in solving the resection problem.
5. The barycentric coordinates define an affine isomorphism between the affine space and the affine subspace of defined by the equation \ lambda _ 0 + \ cdots + \ lambda _ n = 1.
6. In particular, if a point lies on the opposite side of a sideline from the vertex opposite that sideline, then that point's barycentric coordinate corresponding to that vertex is negative.
7. This is again a linear transformation, and we may extend the above procedure for triangles to find the barycentric coordinates of a point \ mathbf { r } with respect to a tetrahedron:
8. That is, the Cartesian coordinates of any point are a weighted average of the Cartesian coordinates of the triangle's vertices, with the weights being the point's barycentric coordinates summing to unity.
9. Thus if and only if two of the vertex angles differ from each other by more than 90? one of the barycentric coordinates is negative and so the nine-point center is outside the triangle.
10. This result follows from the fact that a rectangle in barycentric coordinates corresponds to a quadrilateral in cartesian coordinates, and the ratio of the areas of the corresponding shapes in the corresponding coordinate systems is given by 2A.