For deformable objects modeled as a uniform grid of voxels connected by links, an octree for the voxels is constructed. Cutting is performed by disconnecting links swept by the cutting tool and reconstructing cut surface mesh using the dual contour method. The cubes of the voxel octree are not directly used because their edges generally do not remain straight when the objects deform. Instead, the voxel octree is used to mark active voxels and links and is therefore called “pseudo.” Voxels and links located in the interiors of voxel octree cubes are deactivated. For collision between the cutting tool and the deformable objects, only active voxels and links are considered. Then, voxel octree cubes with newly cut links on their boundaries are recursively subdivided, and new voxels and links are activated accordingly. These algorithms are implemented with multi-threading techniques. Simulation tests show that when compared to previous methods using a uniform grid of voxels, our voxel octree method can increase cutting tool collision speed by 11–96% and can increase overall simulation speed by 7–43%.

中文翻译：

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使用伪体素八叉树加速切割工具和建模为链接体素的可变形对象之间的碰撞

对于建模为由链接连接的统一体素网格的可变形对象，构建体素的八叉树。切割是通过断开切割工具扫过的链接并使用双轮廓方法重建切割面网格来执行的。不直接使用体素八叉树的立方体，因为它们的边缘在物体变形时通常不会保持笔直。相反，体素八叉树用于标记活动体素和链接，因此被称为“伪”。位于体素八叉树立方体内部的体素和链接被停用。对于切割工具和可变形对象之间的碰撞，仅考虑活动体素和链接。然后，递归地细分边界上具有新切割链接的体素八叉树立方体，并相应地激活新的体素和链接。这些算法是用多线程技术实现的。仿真测试表明，与以前使用统一体素网格的方法相比，我们的体素八叉树方法可以将刀具碰撞速度提高 11-96%，并将整体模拟速度提高 7-43%。