Abstract: In this paper we present an easy computation of a generalized form of barycentric coordinates for irrecular, convex n-sided polygons. Triangular barycentric coordinates have had many classical applications in computer graphics, from texture mapping to ray tracing. Our new equations preserve many of the familiar properties of the traingular barycentric coordinates with an equally simple calculation, contrary to the previous formulations. We illustrate the properties and behavior of these new generalized barycentric coordinates through several example applications.