We propose a new algorithm for random-access evaluation of diffusion curve images (DCIs) using the fast multipole method. Unlike all previous methods, our algorithm achieves real-time 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 fast multipole representation 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. We exhibit this capability by devising new tools for fast diffusion curve Poisson cloning and composition with masks.

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Timothy Sun, Papoj Thamjaroenporn, Changxi Zheng, Fast Multipole Representation of Diffusion Curves and Points, ACM Transactions on Graphics 33(4) (Proc. SIGGRAPH 2014), Aug, 2014.

We thank the anonymous reviewers for their feedback. We also thank Orzan et al. for making their DCIs publicly accessible, Dingzeyu Li and Henrique Maia for help with revising an earlier draft, and Yun Fei and Angela Wei for assistance in video and figure editing. This research was supported in part by Columbia Junior Faculty Startup Fund as well as donations from Intel. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of funding agencies or others.