This paper presents an easy-to-control volume peeling method for multi-axis machining based on the computation taken on vector fields. The current scalar field based methods are not flexible and the vector-field based methods do not guarantee the satisfaction of the constraints in the final results. We first conduct an optimization formulation to compute an initial vector field that is well aligned with those anchor vectors specified by users according to different manufacturing requirements. The vector field is further optimized to be an irrotational field so that it can be completely realized by a scalar field's gradients. Iso-surfaces of the scalar field will be employed as the layers of working surfaces for multi-axis volume peeling in the rough machining. Algorithms are also developed to remove and process singularities of the fields. Our method has been tested on a variety of models and verified by physical experimental machining.

翻译：本文提出一种基于矢量场计算的、易于控制的多轴加工体积剥离方法。当前基于标量场的方法缺乏灵活性，而基于矢量场的方法无法保证最终结果满足约束条件。我们首先通过优化公式计算初始矢量场，使其与用户根据不同制造需求指定的锚定矢量良好对齐。随后进一步优化矢量场为无旋场，使其可完全由标量场的梯度实现。标量场的等值面将作为粗加工中多轴体积剥离的工作曲面层。我们还开发了去除与处理场奇异点的算法。该方法已在多种模型上经过测试，并通过物理实验加工验证。