This paper presents and analyzes improved algorithms for clustering bigram and trigram word equivalence classes, and their respective results: 1) We give a detailed time complexity analysis of bigram clustering algorithms. 2) We present an improved implementation of bigram clustering so that large corpora (38 million words and more) can be clustered within a small number of days or even hours. 3) We extend the clustering approach from bigrams to trigrams. 4) We present experimental results on a 38 million word training corpus.
Figure 1: A result of our method: given a character rig and a set of keyframes for some of its parameters, our method automatically produces animation curves for the remaining parameters by solving the equations of motion in the space of deformations defined by the rig. The resulting motion is physically plausible, maintains the original artistic intent, and is easily editable.
AbstractWe present a method that brings the benefits of physics-based simulations to traditional animation pipelines. We formulate the equations of motions in the subspace of deformations defined by an animator's rig. Our framework fits seamlessly into the workflow typically employed by artists, as our output consists of animation curves that are identical in nature to the result of manual keyframing. Artists can therefore explore the full spectrum between handcrafted animation and unrestricted physical simulation. To enhance the artist's control, we provide a method that transforms stiffness values defined on rig parameters to a non-homogeneous distribution of material parameters for the underlying FEM model. In addition, we use automatically extracted high-level rig parameters to intuitively edit the results of our simulations, and also to speed up computation. To demonstrate the effectiveness of our method, we create compelling results by adding rich physical motions to coarse input animations. In the absence of artist input, we create realistic passive motion directly in rig space.
Finite element simulations in computer graphics are typically based on tetrahedral or hexahedral elements, which enables simple and efficient implementations, but in turn requires complicated remeshing in case of topological changes or adaptive refinement. We propose a flexible finite element method for arbitrary polyhedral elements, thereby effectively avoiding the need for remeshing. Our polyhedral finite elements are based on harmonic basis functions, which satisfy all necessary conditions for FEM simulations and seamlessly generalize both linear tetrahedral and trilinear hexahedral elements. We discretize harmonic basis functions using the method of fundamental solutions, which enables their flexible computation and efficient evaluation. The versatility of our approach is demonstrated on cutting and adaptive refinement within a simulation framework for corotated linear elasticity.
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