Barycentric coordinate expresses the location of any point coplanar with a triangle in three scale , , and . The position of that point is at where are the coordinates of the three vertices of the triangle.

The three coordinates satisfy the relationship and if a point is inside a triangle, . Notice that from two of the coordinates we can find the third one .

Barycentric coordinates are proportion to area of sub-triangles. For example, . Below is a visualization: barycentric.png

Barycentric coordinates are useful in both rasterization and ray-triangle intersection.

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