面向立体光刻的有理曲面非网格化体素生成方法
Meshless Voxel Generation Method of Rational Surfaces towards Stereolithography
-
摘要: 随着激光立体光刻工艺的分辨率不断提升, 现有的基于网格化的三维流形体素化方法难以满足微纳乃至原子尺度的精度需求. 为此, 提出一种面向立体光刻的有理曲面非网格化体素生成(meshless voxel generation, MVG)方法, 可将非均匀有理B样条(non-uniform rational B-splines, NURBS)边界表示的实体直接转换为任意精度的体素化模型. 首先通过提出一种面向NURBS曲面的区域无隧道自适应采样方法, 利用边界标记填充算法获取修剪后NURBS曲面内部采样点; 然后将参数域内的采样点映射至体素空间, 生成基于区域无隧道采样的表面体素模型, 并采用广度优先搜索完成内部体素填充. 通过具有微米级结构的空间曲面桨叶进行实例验证, 证明了MVG方法在提升体素化精度方面的有效性; 与传统离散剖分采样方法进行对比实验的结果表明, MVG方法能够有效地提升有理曲面实体的体素化精度; 在高体素化分辨率下, 运用MVG方法, 有理实体在体素离散化过程中的平均体积误差可减少10.17%.Abstract: With the continuous improvement of laser stereolithography resolution, it’s difficult to meet the accuracy requirements of micro and nano scale and even atomic scale for the existing methods which commonly generate voxel of 3D manifold by meshing. Therefore, a meshless voxel generation (MVG) method of rational surfaces towards stereolithography is proposed to directly transform solids, represented by non-uniform rational B-splines (NURBS) surfaces, to voxel models of arbitrary precision. Initially, a regional tunnel-free adaptive sampling method targeted at NURBS surfaces is introduced. The trimming interior sample points are obtained by employing a boundary marking filling algorithm. Subsequently, the sampled points within the parameter domain are mapped to the voxel space and a surface voxel model is produced based on regional tunnel-free sampling. The internal voxel fill is thereby carried out using breadth-first search (BFS). Experimental validation, utilizing a micro-structured spatial surface propeller blade, testifies the effectiveness of the MVG method in terms of enhancing voxelization precision. Comparative experiments with traditional discrete subdivision sampling methods demonstrate the efficiency of MVG method in improving voxelization precision of rational surface solids. At high voxelization resolutions, through the MVG method, the mean volume error during the voxel discretization process of employed rational solid can be reduced by up to 10.17%.