# Volumetric parametrization from a level set boundary representation with PHT Splines

## TL;DR

This paper introduces a method to generate volumetric spline representations from voxel data using level-set functions and hierarchical cubic splines, enabling accurate geometry modeling for isogeometric analysis.

## Contribution

The authors propose a novel approach to derive analysis-suitable volumetric meshes from voxel data using level-set boundaries and hierarchical splines without optimization.

## Key findings

- Effective boundary extraction via level-set functions
- Accurate C1 spline representation using geometric info
- Good performance on benchmark problems

## Abstract

A challenge in isogeometric analysis is constructing analysis-suitable volumetric meshes which can accurately represent the geometry of a given physical domain. In this paper, we propose a method to derive a spline-based representation of a domain of interest from voxel-based data. We show an efficient way to obtain a boundary representation of the domain by a level-set function. Then, we use the geometric information from the boundary (the normal vectors and curvature) to construct a matching C1 representation with hierarchical cubic splines. The approximation is done by a single template and linear transformations (scaling, translations and rotations) without the need for solving an optimization problem. We illustrate our method with several examples in two and three dimensions, and show good performance on some standard benchmark test problems.