# How would one set up barycentric coordinates for a trapezoid?

Barycentric coordinates are great for triangles, but I'm interested in how to construct a barycentric coordinate system for an arbitrary trapezoid.

I've seen this done for an arbitrary quadrilateral, but it ought to be simpler in the case of a trapezoid because of the two parallel sides. There does not appear to be information on this specific case online.

This source has a good solution in general, but has this note: "Note that the special case $\vec{c}\times\vec{d}=0$ must be treated separately", but gives no explanation of how the special case must be treated. This special case turns out to be when two opposite sides are parallel — the definition of a trapezoid.

• By using the term barycenter, are you finding the center of mass if unequal weights are attached to the vertices? May 11 '18 at 19:20
• I know that's where the term originated, but it seems to have gone beyond that use, though I'm not sure how. My application is to interpolate values on a trapezoid. Similar, but slightly different! May 11 '18 at 21:56