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We present fast CCD algorithm for general rigid and articulated models based on conservative advancement. We have implemented the CCD algorithm with two different acceleration techniques which can handle rigid models, and have extended one of them to articulated models. The resulting algorithms take a few milliseconds for rigid models with tens of thousands of triangles, and a few milliseconds for articulated models with tens of links. We show that the performance of our algorithms is much faster than existing CCD algorithms for polygon-soup models and it is also comparable to competing CCD algorithms that are limited to manifold models. The preliminary version of this paper appeared in .