1. A method for evaluating a geometric patch for a tessellation operation when rendering a graphics image in a graphics processing pipeline, the method comprising: generating, with a processing unit a first fixed-point barycentric parameter corresponding to a first barycentric parameter; computing a second fixed-point barycentric parameter corresponding to a second barycentric parameter based on the first fixed-point barycentric parameter, wherein the second fixed-point barycentric parameter is computed by subtracting the first fixed-point barycentric parameter from 1; generating a floating-point barycentric coordinate for use in the tessellation operation based on the first fixed-point barycentric parameter and the second fixed-point barycentric parameter; and generating a vertex located on a boundary shared by a first geometric patch and a second geometric patch for use in the tessellation operation based on the floating-point barycentric coordinate.