One major goal of mesh parameterization is to minimize the conformal distortion. Measured boundary parameterizations focus on lowering the distortion by setting the boundary free with the help of distance from a center vertex to all the boundary vertices. Hence these parameterizations strongly depend on the determination of the center vertex. In this paper

we introduce two methods to determine the center vertex automatically. Both of them can be used as necessary supplements to the existing measured boundary methods to minimize the common artifacts as a result of the obscure choice of the center vertex. In addition

we propose a simple and fast measured boundary parameterization method based on the Poisson’s equation. Our new approach generates less conformal distortion than the fixed boundary methods. It also generates more regular domain boundaries than other measured boundary methods. Moreover

it offers a good tradeoff between computation costs and conformal distortion compared with the fast and robust angle based flattening (ABF++).