This paper proposes an anisotropic quad-dominant remeshing algorithm suitable for meshes of arbitrary topology. It takes an approach to the challenging problem of obtaining an anisotropic quad-dominant mesh. The method consists of operations that sample surface geometry by dense principle curvature lines and sort curvature-lines by variations of surface normal and volume related to them. The anisotropic sampling of curvature lines is then obtained by implementing a prioritization scheme of curvature lines elimination. The strategy is simple and straightforward to implement. It is flexible to produce anisotropic quad-dominant meshes ranging from dense to coarse too. The resulting meshes exhibit better anisotropic distribution than comparable methods while maintaining high geometric fidelity.