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.

翻译：我们以四阶和三阶球谐函数作为体积帧的表征，描述了一种将多个帧取向约束组合为单一二次惩罚函数的简单代数技术。该技术允许在具有浸入边界的层次化网格上采用由粗到精的策略求解体积帧场设计问题。这些成果首次于2023年欧洲网格划分研讨会FRAMES上公布。