一种快速3D打印分层方向确定算法
A Fast Determination Algorithm for Slicing Direction of 3D Printing

针对减少3D打印等分层制造应用中成型的模型实体与理论模型之间的体积偏差,提出一种快速精确的分层方向确定算法。通过分析体积偏差的产生原因和理论模型,明确了统一分层厚度下使体积偏差最小的分层方向,是与模型面片面积加权法向量内积绝对值之和最小的单位向量,将最优方向选取问题转化为最小绝对偏差线性回归问题。用最小二乘准则近似最小绝对偏差准则,并用基于该准则的主成分分析方法,对加权法向量的散列矩阵进行特征值分解,从特征向量中快速确定最优的分层方向。针对多个不同复杂程度的模型进行评估实验,结果表明,该算法能在保证精度的前提下将运算量减少80％,适合于复杂精细模型的分层制造应用。
An efficient determination algorithm on slicing direction is proposed to reduce the volume deviation between fabrication entity and its theoretical model in layered manufacturing applications such as 3D printing. The cause of volume deviation and its mathematical model are analyzed, and the results show that the optimal slicing direction with the least volume deviation is a unit vector with the minimum value in the sum of absolute inner products of the vector and the area weighted normal vector of model facets. Thus, the problem to determine the optimal direction is converted into a linear regression problem with the least absolute deviation. The least absolute deviation norm is approximated by using the least squares norm and the principal component analysis method is used to process eigenvalue decomposition on the scatter matrix of weighted normal vecter. The optimal direction is then efficiently determined from the eigenvectors. Experiments on several models with different complexity show that the proposed algorithm reduces 80% of the computation load on the premise of guarantee accuracy, and is suitable for layered manufacturing of complex models