Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data

in finite element analysis, and in these applications it is desirable to have as few obtuse

triangles as possible to reduce the discretization error. We present a variational approach to

suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal

Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of

the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant

properties of the CVT method with the newly introduced metric. Experiments show that

our algorithm produces anisotropic meshes with much fewer obtuse triangles than using

existing methods while maintaining mesh anisotropy.