Spectral boundary conditions for volumetric frame fields design

TL;DR

This paper introduces a novel algebraic method for volumetric frame field design using spherical harmonics, enabling efficient constraint combination and hierarchical solving with immersed boundaries.

Contribution

It presents a simple algebraic technique for combining constraints into a quadratic penalty, facilitating hierarchical volumetric frame field design with immersed boundaries.

Findings

Effective combination of multiple constraints into a quadratic penalty.

Hierarchical solution approach on coarse-to-fine grids.

First presentation of these results at FRAMES 2023.

Abstract

Using the 4th and the 3rd degree spherical harmonics as the representations for volumetric frames, we describe a simple algebraic technique for combining multiple frame orientation constraints into a single quadratic penalty function. This technique allows to solve volumetric frame fields design problems using a coarse-to-fine strategy on hierarchical grids with immersed boundaries. These results were presented for the first time at the FRAMES 2023 European workshop on meshing.