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4.3.1 Some Details for 2-D Domains     continued...

Our expression for the shape functions is, in fact, a transformation from cartesian coordinates to a natural set of coordinates, often called area coordinates or barycentric coordinates. If we look at the transformation for for a point within the element with coordinates , we note that,

which is just a ratio of the areas of the triangles and .

Thus we have a transformation from a point inside an element in terms of its barycentric coordinates to the global cartesian system,