Optimized Pht-to-Nurbs Conversion: A Weighted Rectangle Partition Approach

Abstract

This study addresses the conversion of Polynomial Splines over Hierarchical T-meshes (PHT-splines) to Non-Uniform Rational BSplines (NURBS). We reformulate this conversion as a weighted rectangle partition problem, introducing a coarser grid, referred to as base rectangles, to minimize the search space while ensuring optimal solutions. Our systematic framework facilitates the lossless conversion of PHT-splines to NURBS, effectively balancing the number of patches and control points. Extensive experiments on 109 2D and 118 3D subjects demonstrate reductions in control points by up to 48.94% for 2D cases and 78.35% for 3D cases. Moreover, our approach is versatile and adaptable to fixed-patch partition scenarios, highlighting its potential to bridge PHT-splines and NURBS.

Keywords: T-mesh, PHT-spline, NURBS, Weighted rectangle partition