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Graph."],"published-print":{"date-parts":[[2014,7,27]]},"abstract":"<jats:p>\n            We propose a new algorithm for random-access evaluation of\n            <jats:italic>diffusion curve images<\/jats:italic>\n            (DCIs) using the\n            <jats:italic>fast multipole method<\/jats:italic>\n            . Unlike all previous methods, our algorithm achieves\n            <jats:italic>real-time<\/jats:italic>\n            performance for rasterization and texture-mapping DCIs of up to millions of curves. After precomputation, computing the color at a single pixel takes nearly constant time. We also incorporate Gaussian radial basis functions into our\n            <jats:italic>fast multipole representation<\/jats:italic>\n            using the fast Gauss transform. The fast multipole representation is not only a data structure for fast color evaluation, but also a framework for vector graphics analogues of bitmap editing operations. 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