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The Sutherland-Hodgman clipping algorithm is used here to compute the intersection of two Delaunay triangulations with one another. Sutherland-Hodgman implementation by Joy Patel.
This algorithm can be used to intersect the decomposition of one triangle with a decomposition coming from another triangle of equal area.
For a decomposition of two triangles of equal area that uses Sutherland-Hodgman clipping, see this example.
See d3-equidecompose.
Any polygon can be decomposed into a finite (though possibly large) number of polygons that can be rearranged through rotations and translations to form another polygon of equal area. This is known as equidecomposition.
The first step in one well-known algorithm for accomplishing this involves decomposing a triangle into a square.
In order to decompose a triangle into another triangle of equal area, it is necessary to intersect collections of polygons contained in a square common to both triangles.
See d3-equidecompose.
