Our multiresolution method can be applied to many existing cloth simulation methods, since our method works on a general linear system. In order to demonstrate benefits of our method, we apply our method into four largescale cloth benchmarks that consist of tens or hundreds of thousands of triangles. Because of the reduced computations, we achieve a performance improvement by a factor of up to one order of magnitude, with a little loss of simulation quality. While animation using Links of London R Charm coordinates or other automatic weight assignment methods has become a popular method for shape deformation, the global nature of the weights limits their use for realtime applications. We present a method that reduces the number of control points influencing a vertex to a userspecified number such that the deformations created by the reduced weight set resemble that of the original deformation. To do so we show how to set up a Poisson minimization problem to solve for a reduced weight set and illustrate its advantages over other weight reduction methods. Not only does weight reduction lower the amount of storage space necessary to deform these models but also allows GPU acceleration of the resulting deformations. Our experiments show that we can achieve a factor of increase in speed over CPU deformations using the full weight set, which makes realtime deformations of large models possible. PUBLICATION ABSTRACT Strange attractors of D vector field flows sometimes have a fractal geometric structure in one dimension, and smooth surface behavior in the other two. General flow visualization methods show the links of london sale dynamics well, but not the fractal structure. Here we approximate the attractor by polygonal surfaces, which reveal the fractal geometry. We start with a polygonal approximation which neglects the fractal dimension, and then deform it by the flow to create multiple sheets of the fractal structure. We use adaptive subdivision, mesh decimation, and retiling methods to preserve the quality of the polygonal surface in the face of extreme stretching, bending, and creasing caused by the flow. A GPU implementation provides efficient visualization, which we also apply to other turbulent flows. Spectral methods for mesh processing and analysis rely on the eigenvalues, eigenvectors, or eigenspace projections derived from appropriately defined mesh operators to carry out desired tasks. Early work in this area can be traced back to the seminal paper by Taubin in , where spectral analysis of mesh geometry based on a combinatorial Laplacian aids our understanding of the lowpass filtering approach to mesh smoothing. Over the past years, the list of applications in the area of geometry processing which utilize the eigenstructures of a variety of mesh operators in different manners have valentines Day pendants growing steadily. Many works presented so far draw parallels from developments in fields such as graph theory, computer vision, machine learning, graph drawing, numerical linear algebra, and highperformance computing. This paper aims to provide a comprehensive survey on the spectral approach, focusing on its power and versatility in solving geometry processing problems and attempting to bridge the gap between relevant research in computer graphics and other fields.
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