We introduce a new way to implicitly represent swept volumes in 3D. We first implicitize the base volume and then apply the time-dependent rigid transformation to build an implicit representation of the swept volume. This way, we build a fitting representation, where geometric details generated by the rigid transformation and details of the base volume itself are both taken into account. This representation relies on a partition of a boundary box of the swept volume according to portions of the space related either to parts of the base volume or to time span of the transformation.

中文翻译：

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基于局部形状和运动的扫描体积的隐式表示

我们引入了一种在 3D 中隐式表示扫描体积的新方法。我们首先隐式基本体积，然后应用时间相关的刚性变换来构建扫描体积的隐式表示。通过这种方式，我们构建了一个拟合表示，其中由刚性变换生成的几何细节和基础体积本身的细节都被考虑在内。该表示依赖于根据与基础体积的部分或与变换的时间跨度相关的空间部分对扫描体积的边界框的划分。