Continuous toolpath planning in a graphical framework for sparse infill additive manufacturing

We develop a framework that creates a new polygonal mesh representation of the sparse infill domain of a layer-by-layer 3D printing job. We guarantee the existence of a single, continuous tool path covering each connected piece of the domain in every layer in this graphical model. We also present a tool path algorithm that traverses each such continuous tool path with no crossovers.The key construction at the heart of our framework is a novel Euler transformation which converts a 2-dimensional cell complex K into a new 2-complex (K) over cap such that every vertex in the 1-skeleton (G) over cap of (K) over cap has even degree. Hence (G) over cap is Eulerian, and an Eulerian tour can be followed to print all edges in a continuous fashion without stops.We start with a mesh K of the union of polygons obtained by projecting all layers to the plane. First we compute its Euler transformation (K) over cap. In the slicing step, we clip (K) over cap at each layer using its polygon to obtain a complex that may not necessarily be Euler. We then patch this complex by adding edges such that any odd-degree nodes created by slicing are transformed to have even degrees again. We print extra support edges in place of any segments left out to ensure there are no edges without support in the next layer above. These support edges maintain the Euler nature of the complex. Finally, we describe a tree-based search algorithm that builds the continuous tool path by traversing "concentric'' cycles in the Euler complex. Our algorithm produces a tool path that avoids material collisions and crossovers, and can be printed in a continuous fashion irrespective of complex geometry or topology of the domain (e.g., holes).We implement our test our framework on several 3D objects. Apart from standard geometric shapes including a nonconvex star, we demonstrate the framework on the Stanford bunny. Several intermediate layers in the bunny have multiple components as well as complicated geometries. (C) 2020 Elsevier Ltd. All rights reserved.

我们开发了一个框架，该框架为逐层3D打印作业的稀疏填充区域创建了一种新的多边形网格表示。我们保证在这个图形模型的每一层中，存在一条单一的、连续的刀具路径，覆盖该区域的每个连通部分。我们还提出了一种刀具路径算法，该算法可以无交叉地遍历每条这样的连续刀具路径。我们框架核心的关键构造是一种新颖的欧拉变换，它将一个二维胞腔复形\(K\)转换为一个新的二维复形\(\hat{K}\)，使得\(\hat{K}\)的1 - 骨架\(\hat{G}\)中的每个顶点都具有偶数度。因此\(\hat{G}\)是欧拉图，可以沿着一条欧拉回路以连续的方式打印所有边而无需停顿。 我们从通过将所有层投影到平面而获得的多边形并集的网格\(K\)开始。首先我们计算它的欧拉变换\(\hat{K}\)。在切片步骤中，我们使用其多边形在每层对\(\hat{K}\)进行裁剪，以获得一个不一定是欧拉图的复形。然后我们通过添加边来修补这个复形，使得由切片产生的任何奇数度节点再次变为偶数度。我们打印额外的支撑边来替代任何遗漏的线段，以确保在上一层中没有无支撑的边。这些支撑边保持了复形的欧拉性质。最后，我们描述了一种基于树的搜索算法，该算法通过遍历欧拉复形中的“同心”循环来构建连续的刀具路径。我们的算法生成的刀具路径避免了材料碰撞和交叉，并且无论区域（例如，孔洞）的复杂几何形状或拓扑结构如何，都可以以连续的方式进行打印。 我们在几个3D对象上实现并测试了我们的框架。除了包括非凸星在内的标准几何形状外，我们还在斯坦福兔子模型上演示了该框架。兔子模型中的几个中间层具有多个组件以及复杂的几何形状。（C）2020爱思唯尔有限公司。保留所有权利。