We describe a GPU-based computational platform for six-dimensional configuration mapping, which is the description of the configuration space of rigid motions in terms of collision and contact constraints. The platform supports a wide range of computations in design and manufacturing, including three and six dimensional configuration space obstacle computations, Minkowski sums and differences, packaging problems, and sweep computations. We demonstrate dramatic performance improvements in the special case of configuration space operations that determine interference-free or containment-preserving configurations between moving solids. Our approach treats such operations as convolutions in the six dimensional configuration space that are efficiently computed using the Fast Fourier Transform (FFT). The inherent parallelism of FFT algorithms facilitates a straightforward implementation of convolution on GPUs with existing and freely available libraries, making all such six dimensional configuration space computations practical, and often interactive.

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