Abstract: Signed distance field based on triangle meshes can efficiently perform operations such as Boolean operations and conformal gradient lattice generation that are difficult to handle with triangular mesh models,and there are important uses in the field of additive manufacturing.However it is time-consuming to construct signed distance field.The concept and the constructing method for the exact signed distance field and the Hybrid Signed Distance from triangle meshes based on multi-information voxel were introduced.The space of the triangle meshes was divided into boxes Parallel to the axes,and the approximate distance field was established using the fast distance transform method.According to the approximate signed distance field,the exact signed distance field in every box could be constructed by extracting the related triangles,which was a hundredfold increase in efficiency.In hybrid signed distance field,the exact distance field near the boundary was constructed selectively using the approximate signed distance field,and other positions in the space were estimated by the approximate distance field,which improved the efficiency on the promise of ensuring the resolution inside.Finally,the proposed method was verified by generating several conformal lattice with gradient.

Key words: signed distance field, triangle meshes, additive manufacturing, distance transform, triply periodic minimal surface

摘要： 基于三维实体模型的符号距离场可高效进行诸如布尔运算和随形梯度点阵结构生成等三角网格模型难以处理的操作,在增材制造领域有着重要的用途,但复杂三角网格模型符号距离场的生成效率非常低。提出了基于多信息体素的三角网格模型精确符号距离场和混合距离场的概念及其生成算法。精确距离场算法将包含三角网格模型的有限空间平行于坐标轴等距分割成多个体素,对三维体素空间进行快速距离变换,生成粗糙符号距离场,依据粗糙符号距离场将相关三角面片划分到每个体素中,过滤无关的三角形,生成精确符号距离场,在效率上有百倍的提升;混合距离场算法利用粗糙符号距离场选择性构建边界附近的精确符号距离场,空间内其他位置用粗糙符号距离场表示,在保证内部符号距离场分辨率的前提下的提高了距离场的生成效率。最后通过生成随形的梯度点阵结构对算法进行验证。

关键词: 符号距离场, 三角网格模型, 增材制造, 距离变换, 三周期极小曲面