Abstract: Blended barycentric coordinates based on derived polygons were proposed based on the existing
barycentric coordinates by triangulating the initial polygon, and deriving the point polygons, the edge polygons, and
the face polygons of the triangle using a triangular mesh. First, the derived polygons were obtained using a triangular
mesh. Then, the derived polygons’ vertices, which are about the initial polygons’ vertices, could be calculated by
referring to harmonic coordinates, local barycentric coordinates, or iterative coordinates. Next, a point as an affine
combination of the derived polygons’ vertices could be represented using iterative coordinates. The most important
step was to represent the point as an affine combination of the initial polygon’s vertices using a suited mixing
coefficient. Taking all the instances into consideration, the conclusion can be naturally drawn that the proposed
construction of barycentric coordinates are local, non-negative, and smooth.

Key words: derived polygons, harmonic coordinates, local barycentric coordinates, iterative coordinates, mixing
function