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In this paper, we present a novel fast Continuous Collision Detection (CCD) method using SIMD capacity of CPU and idea of dimension reduction. We apply a parallel linear filter culling performed in one-dimensional subspace followed by a parallel planar filter culling performed in two-dimensional subspace before each elementary test, which simultaneously and conservatively tests the relative motion of each primitive pairs in various selected subspace. CPU's SIMD capacity is utilized for parallelizing the projection and filtering process in each subspace. Parallel filter culling in subspace removes a large amount of redundant elementary tests with low cost, and improves the overall performance of collision query. We demonstrate the advantages of our approach when comparing with previous alternatives in various dynamic scenes as benchmarks. In experiments, we observe up to 99% removal of false positives, and a huge magnitude of speed improvement on elementary tests (over 3x). Since our method only correlates the elementary test, it is scalable and can be easily integrated with various available single or multicore CPU based CCD algorithm. In addition, the performance of our method is less sensitive to varying step time.