An Implicit Representation of Swept Volumes based on Local Shapes and Movements

Abstract: 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.