We introduce carvable volume decomposition for efficient 3-axis CNC machining of 3D freeform objects, where our goal is to develop a fully automatic method to jointly optimize setup and path planning. We formulate our joint optimization as a volume decomposition problem which prioritizes minimizing the number of setup directions while striving for a minimum number of continuously carvable volumes, where a 3D volume is continuously carvable, or simply carvable, if it can be carved with the machine cutter traversing a single continuous path. Geometrically, carvability combines visibility and monotonicity and presents a new shape property which had not been studied before. Given a target 3D shape and the initial material block, our algorithm first finds the minimum number of carving directions by solving a set cover problem. Specifically, we analyze cutter accessibility and select the carving directions based on an assessment of how likely they would lead to a small carvable volume decomposition. Next, to obtain a minimum decomposition based on the selected carving directions efficiently, we narrow down the solution search by focusing on a special kind of points in the residual volume, single access or SA points, which are points that can be accessed from one and only one of the selected carving directions. Candidate carvable volumes are grown starting from the SA points. Finally, we devise an energy term to evaluate the carvable volumes and their combinations, leading to the final decomposition. We demonstrate the performance of our decomposition algorithm on a variety of 2D and 3D examples and evaluate it against the ground truth, where possible, and solutions provided by human experts. Physically machined models are produced where each carvable volume is continuously carved following a connected Fermat spiral toolpath.

中文翻译：

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VDAC

我们介绍可雕刻体积分解用于 3D 自由曲面对象的高效 3 轴 CNC 加工，我们的目标是开发一种全自动方法来联合优化设置和路径规划。我们将我们的联合优化表述为一个体积分解问题，该问题优先考虑最小化设置方向的数量，同时争取最小数量的可连续雕刻体积，其中 3D 体积是连续可雕刻的，或者简单地可雕刻，如果它可以用机器切割器遍历单连续小路。在几何上，可雕刻性结合了可见性和单调性，呈现出一种以前没有研究过的新的形状特性。给定目标 3D 形状和初始材料块，我们的算法首先通过求解设置封面问题。具体来说，我们分析刀具的可访问性并根据评估它们导致小可雕刻体积分解的可能性来选择雕刻方向。接下来，为了有效地获得基于所选雕刻方向的最小分解，我们通过关注剩余体积中的一种特殊点来缩小解决方案搜索范围，单次访问或 SA 点，这些点可以从一个，只有一个选择的雕刻方向。候选可雕刻卷是长大的从 SA 点开始。最后，我们设计了一个能量项来评估可雕刻的体积及其组合，从而进行最终分解。我们展示了我们的分解算法在各种 2D 和 3D 示例上的性能，并在可能的情况下根据基本事实和人类专家提供的解决方案对其进行评估。生产物理加工模型，其中每个可雕刻体积都按照连接的费马螺旋刀具路径连续雕刻。