面向多轴制造的可达性深度神经隐式表示
Deep Neural Implicit Representation of Accessibility for Multi-Axis Manufacturing
AI总结：
本文提出用深度神经网络隐式表示多轴制造中的碰撞度量场，以低内存开销从稀疏旋转采样中精确插值，并支持通过微调高效更新以适应几何增量变化。
摘要：
多轴增材与减材制造的设计与工艺规划中的一个主要关注点是运动物体（例如刀具组件）与静止物体（例如与夹具固定在一起的零件）之间的碰撞避免。两个点集之间各种相对刚体平移和旋转组合的碰撞度量可以通过6D非欧几里得配置空间上的一个紧支撑标量场来概念化。该场的显式表示和计算在时间和空间上代价都很高。如果我们固定O(m)个稀疏采样的旋转（例如刀具方向），那么通过快速傅里叶变换（FFTs）在分辨率为O(n^3)的均匀网格（即体素化几何）上计算碰撞度量场，作为3D点集指示函数的卷积，其时间复杂度为O(mn^3 log n)，空间复杂度为O(mn^3)。在本文中，我们通过深度神经网络（DNNs）开发了碰撞度量场的隐式表示。我们表明，我们的方法能够从稀疏采样的旋转中精确插值碰撞度量，并且能够以较小的内存占用表示碰撞度量场。此外，我们表明，该表示可以通过微调高效更新，从而更有效地在多分辨率数据上训练网络，并适应几何的增量变化（例如在受CNC刀具可达性约束的零件拓扑优化等迭代过程中可能出现的变化）。
英文摘要：
One of the main concerns in design and process planning for multi-axis additive and subtractive manufacturing is collision avoidance between moving objects (e.g., tool assemblies) and stationary objects (e.g., a part unified with fixtures). The collision measure for various pairs of relative rigid translations and rotations between the two pointsets can be conceptualized by a compactly supported scalar field over the 6D non-Euclidean configuration space. Explicit representation and computation of this field is costly in both time and space. If we fix $O(m)$ sparsely sampled rotations (e.g., tool orientations), computation of the collision measure field as a convolution of indicator functions of the 3D pointsets over a uniform grid (i.e., voxelized geometry) of resolution $O(n^3)$ via fast Fourier transforms (FFTs) scales as in $O(mn^3 \log n)$ in time and $O(mn^3)$ in space. In this paper, we develop an implicit representation of the collision measure field via deep neural networks (DNNs). We show that our approach is able to accurately interpolate the collision measure from a sparse sampling of rotations, and can represent the collision measure field with a small memory footprint. Moreover, we show that this representation can be efficiently updated through fine-tuning to more efficiently train the network on multi-resolution data, as well as accommodate incremental changes to the geometry (such as might occur in iterative processes such as topology optimization of the part subject to CNC tool accessibility constraints).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
