37-Issue 5

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https://diglib.eg.org/handle/10.2312/2632598

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Browsing 37-Issue 5 by Subject "I.3.3 [Computer Graphics]"

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    Constructing 3D CSG Models from 3D Raw Point Clouds
    (The Eurographics Association and John Wiley & Sons Ltd., 2018) Wu, Qiaoyun; Xu, Kai; Wang, Jun; Ju, Tao and Vaxman, Amir
    The Constructive Solid Geometry (CSG) tree, encoding the generative process of an object by a recursive compositional structure of bounded primitives, constitutes an important structural representation of 3D objects. Therefore, automatically recovering such a compositional structure from the raw point cloud of an object represents a high-level reverse engineering problem, finding applications from structure and functionality analysis to creative redesign. We propose an effective method to construct CSG models and trees directly over raw point clouds. Specifically, a large number of hypothetical bounded primitive candidates are first extracted from raw scans, followed by a carefully designed pruning strategy. We then choose to approximate the target CSG model by the combination of a subset of these candidates with corresponding Boolean operations using a binary optimization technique, from which the corresponding CSG tree can be derived. Our method attempts to consider the minimal description length concept in the point cloud analysis setting, where the objective function is designed to minimize the construction error and complexity simultaneously. We demonstrate the effectiveness and robustness of our method with extensive experiments on real scan data with various complexities and styles.
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    An Explicit Structure-preserving Numerical Scheme for EPDiff
    (The Eurographics Association and John Wiley & Sons Ltd., 2018) Azencot, Omri; Vantzos, Orestis; Ben-Chen, Mirela; Ju, Tao and Vaxman, Amir
    We present a new structure-preserving numerical scheme for solving the Euler-Poincaré Differential (EPDiff) equation on arbitrary triangle meshes. Unlike existing techniques, our method solves the difficult non-linear EPDiff equation by constructing energy preserving, yet fully explicit, update rules. Our approach uses standard differential operators on triangle meshes, allowing for a simple and efficient implementation. Key to the structure-preserving features that our method exhibits is a novel numerical splitting scheme. Namely, we break the integration into three steps which rely on linear solves with a fixed sparse matrix that is independent of the simulation and thus can be pre-factored. We test our method in the context of simulating concentrated reconnecting wavefronts on flat and curved domains. In particular, EPDiff is known to generate geometrical fronts which exhibit wave-like behavior when they interact with each other. In addition, we also show that at a small additional cost, we can produce globally-supported periodic waves by using our simulated fronts with wavefronts tracking techniques. We provide quantitative graphs showing that our method exactly preserves the energy in practice. In addition, we demonstrate various interesting results including annihilation and recreation of a circular front, a wave splitting and merging when hitting an obstacle and two separate fronts propagating and bending due to the curvature of the domain.
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    Modular Latent Spaces for Shape Correspondences
    (The Eurographics Association and John Wiley & Sons Ltd., 2018) Ganapathi-Subramanian, Vignesh; Diamanti, Olga; Guibas, Leonidas J.; Ju, Tao and Vaxman, Amir
    We consider the problem of transporting shape descriptors across shapes in a collection in a modular fashion, in order to establish correspondences between them. A common goal when mapping between multiple shapes is consistency, namely that compositions of maps along a cycle of shapes should be approximately an identity map. Existing attempts to enforce consistency typically require recomputing correspondences whenever a new shape is added to the collection, which can quickly become intractable. Instead, we propose an approach that is fully modular, where the bulk of the computation is done on each shape independently. To achieve this, we use intermediate nonlinear embedding spaces, computed individually on every shape; the embedding functions use ideas from diffusion geometry and capture how different descriptors on the same shape inter-relate. We then establish linear mappings between the different embedding spaces, via a shared latent space. The introduction of nonlinear embeddings allows for more nuanced correspondences, while the modularity of the construction allows for parallelizable calculation and efficient addition of new shapes. We compare the performance of our framework to standard functional correspondence techniques and showcase the use of this framework to simple interpolation and extrapolation tasks.
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    Statistical Modeling of the 3D Geometry and Topology of Botanical Trees
    (The Eurographics Association and John Wiley & Sons Ltd., 2018) Wang, Guan; Laga, Hamid; Jia, Jinyuan; Xie, Ning; Tabia, Hedi; Ju, Tao and Vaxman, Amir
    We propose a framework for statistical modeling of the 3D geometry and topology of botanical trees. We treat botanical trees as points in a tree-shape space equipped with a proper metric that captures the geometric and the topological differences between trees. Geodesics in the tree-shape space correspond to the optimal sequence of deformations, i.e. bending, stretching, and topological changes, which align one tree onto another. In this way, the 3D tree modeling and synthesis problem becomes a problem of exploring the tree-shape space either in a controlled fashion, using statistical regression, or randomly by sampling from probability distributions fitted to populations in the tree-shape space. We show how to use this framework for (1) computing statistical summaries, e.g. the mean and modes of variations, of a population of botanical trees, (2) synthesizing random instances of botanical trees from probability distributions fitted to a population of botanical trees, and (3) modeling, interactively, 3D botanical trees using a simple sketching interface. The approach is fast and only requires as input 3D botanical tree models with a known upright orientation.