areal coordinates

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Relative to a given triangle of reference A1A2A3 the areal coordinates of a point P inside, or on the boundary of, the triangle are (x1, x2, x3), where x1, x2, x3 are the areas of triangles PA2A3, PA3A1, PA1A2, respectively. In the usual case, where the triangle of reference is equilateral, the coordinates are called barycentric coordinates. The idea can be generalized to a tetrahedron of reference, using volumes, and to a simplex of reference.

Areal coordinates. The location of a point is specified by the areas of the component regions.

Subjects: Probability and Statistics.

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