# Modified PHT-splines

## TL;DR

This paper introduces modified PHT-splines using split-in-half mesh refinement to enhance flexibility and efficiency in surface fitting and isogeometric analysis, especially for anisotropic features.

## Contribution

The paper proposes modified hierarchical T-meshes and PHT-splines with split-in-half refinement to improve local refinement and flexibility over traditional methods.

## Key findings

- Enhanced surface fitting accuracy with modified PHT-splines.
- Improved isogeometric analysis performance on anisotropic features.
- Numerical examples demonstrate the advantages of the new splines.

## Abstract

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.