  The local refinement of PHT-splines (polynomial splines over hierarchical
T-meshes) is achieved by a simple cross insertion, which may introduce
superfluous control points or coefficients. By allowing split-in-half in mesh
refinement, modified hierarchical T-meshes are defined. Using this approach,
polynomial splines defined over the modified hierarchical T-meshes (modified
PHT-splines) are introduced to increase the flexibility of PHT-splines.
Numerical examples demonstrate the advantages of our new splines when applied
to surface fitting and isogeometric analysis problems with anisotropic
features.
