Barycentric coordinates can additionally be used for interpolation of vertex data, such as color. So we can use the barycentric coordinates to determine whether a point is in the triangle, then additionally use the coordinates we calculated as coefficients on the color of each vertex to interpolate the color of the point p.
I found barycentric coordinates quite intriguing, so I found this presentation on it potential applications that was a fun read:
https://web.ma.utexas.edu/users/drp/files/Spring2020Projects/Barycentric_Coordinate - Mark.pdf
The article gives details of barycentric coordinates, and demonstrates the color interpolation. Very useful link.
Find some computation for barycentric coordinates. https://mathworld.wolfram.com/BarycentricCoordinates.html
A simple question, but in CS248, we had to use Barycentric Coordinates in addition to Homogeneous Coordinates (and its conversions); will we be going over Homogeneous 3D Coordinate transforms in the future?