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Item Fabrication-aware Design with Intersecting Planar Pieces(The Eurographics Association and Blackwell Publishing Ltd., 2013) Schwartzburg, Yuliy; Pauly, Mark; I. Navazo, P. PoulinWe propose a computational design approach to generate 3D models composed of interlocking planar pieces. We show how intricate 3D forms can be created by sliding the pieces into each other along straight slits, leading to a simple construction that does not require glue, screws, or other means of support. To facilitate the design process, we present an abstraction model that formalizes the main geometric constraints imposed by fabrication and assembly, and incorporates conditions on the rigidity of the resulting structure.We show that the tight coupling of constraints makes manual design highly nontrivial and introduce an optimization method to automate constraint satisfaction based on an analysis of the constraint relation graph. This algorithm ensures that the planar parts can be fabricated and assembled. We demonstrate the versatility of our approach by creating 3D toy models, an architectural design study, and several examples of functional furniture.Item Primitive Trees for Precomputed Distance Queries(The Eurographics Association and Blackwell Publishing Ltd., 2013) Lee, Sung-Ho; Park, Taejung; Kim, Chang-Hun; I. Navazo, P. PoulinWe propose the primitive tree, a novel and compact space-partition method that samples and reconstructs a distance field with high accuracy, even for regions far from the surfaces. The primitive tree is based on the octree and stores the indices of the nearest primitives in its leaf nodes. Most previous approaches have involved a trade-off between accuracy and speed in distance queries, but our method can improve both aspects simultaneously. In addition, our method can sample unsigned distance fields effectively, even for self-intersecting and nonmanifold models. We present test results showing that our method can sample and represent large scenes, with more than ten million triangles, rapidly and accurately.Item Coupled Quasi-harmonic Bases(The Eurographics Association and Blackwell Publishing Ltd., 2013) Kovnatsky, Artiom; Bronstein, Michael M.; Bronstein, Alexander M.; Glashoff, Klaus; Kimmel, Ron; I. Navazo, P. PoulinThe use of Laplacian eigenbases has been shown to be fruitful in many computer graphics applications. Today, state-of-the-art approaches to shape analysis, synthesis, and correspondence rely on these natural harmonic bases that allow using classical tools from harmonic analysis on manifolds. However, many applications involving multiple shapes are obstacled by the fact that Laplacian eigenbases computed independently on different shapes are often incompatible with each other. In this paper, we propose the construction of common approximate eigenbases for multiple shapes using approximate joint diagonalization algorithms, taking as input a set of corresponding functions (e.g. indicator functions of stable regions) on the two shapes. We illustrate the benefits of the proposed approach on tasks from shape editing, pose transfer, correspondence, and similarity.Item Bilateral Hermite Radial Basis Functions for Contour-based Volume Segmentation(The Eurographics Association and Blackwell Publishing Ltd., 2013) Ijiri, Takashi; Yoshizawa, Shin; Sato, Yu; Ito, Masaaki; Yokota, Hideo; I. Navazo, P. PoulinIn this paper, we propose a novel contour-based volume image segmentation technique. Our technique is based on an implicit surface reconstruction strategy, whereby a signed scalar field is generated from user-specified contours. The key idea is to compute the scalar field in a joint spatial-range domain (i.e., bilateral domain) and resample its values on an image manifold. We introduce a new formulation of Hermite radial basis function (HRBF) interpolation to obtain the scalar field in the bilateral domain. In contrast to previous implicit methods, bilateral HRBF (BHRBF) generates a segmentation boundary that passes through all contours, fits high-contrast image edges if they exist, and has a smooth shape in blurred areas of images. We also propose an acceleration scheme for computing B-HRBF to support a real-time and intuitive segmentation interface. In our experiments, we achieved high-quality segmentation results for regions of interest with high-contrast edges and blurred boundaries.Item Mutable Elastic Models for Sculpting Structured Shapes(The Eurographics Association and Blackwell Publishing Ltd., 2013) Milliez, Antoine; Wand, Michael; Cani, Marie-Paule; Seidel, Hans-Peter; I. Navazo, P. PoulinIn this paper, we propose a new paradigm for free-form shape deformation. Standard deformable models minimize an energy measuring the distance to a single target shape. We propose a new, ''mutable'' elastic model. It represents complex geometry by a collection of parts and measures the distance of each part measures to a larger set of alternative rest configurations. By detecting and reacting to local switches between best-matching rest states, we build a 3D sculpting system: It takes a structured shape consisting of parts and replacement rules as input. The shape can subsequently be elongated, compressed, bent, cut, and merged within a constraints-based free-form editing interface, where alternative rest-states model to such changes. In practical experiments, we show that the approach yields a surprisingly intuitive and easy to implement interface for interactively designing objects described by such discrete shape grammars, for which direct shape control mechanisms were typically lacking.Item Reconstructing Complex Indoor Environments with Arbitrary Wall Orientations(The Eurographics Association, 2014) Mura, Claudio; Villanueva, Alberto Jaspe; Mattausch, Oliver; Gobbetti, Enrico; Pajarola, Renato; Mathias Paulin and Carsten DachsbacherReconstructing the architectural shape of interiors is a problem that is gaining increasing attention in the field of computer graphics. Some solutions have been proposed in recent years, but cluttered environments with multiple rooms and non-vertical walls still represent a challenge for state-of-the-art methods. We propose an occlusionsaware pipeline that extends current solutions to work with complex environments with arbitrary wall orientations.Item Quantifying 3D Shape Similarity Using Maps: Recent Trends, Applications and Perspectives(The Eurographics Association, 2014) Biasotti, S.; Cerri, A.; Bronstein, A.; Bronstein, M.; Sylvain Lefebvre and Michela SpagnuoloShape similarity is an acute issue in Computer Vision and Computer Graphics that involves many aspects of human perception of the real world, including judged and perceived similarity concepts, deterministic and probabilistic decisions and their formalization. 3D models carry multiple information with them (e.g., geometry, topology, texture, time evolution, appearance), which can be thought as the filter that drives the recognition process. Assessing and quantifying the similarity between 3D shapes is necessary to explore large dataset of shapes, and tune the analysis framework to the user's needs. Many efforts have been done in this sense, including several attempts to formalize suitable notions of similarity and distance among 3D objects and their shapes. In the last years, 3D shape analysis knew a rapidly growing interest in a number of challenging issues, ranging from deformable shape similarity to partial matching and view-point selection. In this panorama, we focus on methods which quantify shape similarity (between two objects and sets of models) and compare these shapes in terms of their properties (i.e., global and local, geometric, differential and topological) conveyed by (sets of) maps. After presenting in detail the theoretical foundations underlying these methods, we review their usage in a number of 3D shape application domains, ranging from matching and retrieval to annotation and segmentation. Particular emphasis will be given to analyse the suitability of the different methods for specific classes of shapes (e.g. rigid or isometric shapes), as well as the flexibility of the various methods at the different stages of the shape comparison process. Finally, the most promising directions for future research developments are discussed.Item Transfinite Surface Patches Using Curved Ribbons(The Eurographics Association, 2013) Várady, Tamás; Salvi, Péter; Rockwood, Alyn; M.- A. Otaduy and O. SorkineAn important problem in Computer Aided Design is to create digital representations for complex free-form objects that produce nice, predictable shapes and facilitate real-time editing in 3D. The clue to curve network-based design is the construction of smoothly connected multi-sided patches. A new type of transfinite surface, called Composite Ribbon (CR) patch is introduced, that is a combination of curved ribbons and ensures G1 continuity over non-regular, convex polygonal domains. After discussing the construction and the preferred parameterization scheme, a few simple examples conclude the paper.Item Geometry-Aware Volume-of-Fluid Method(The Eurographics Association and Blackwell Publishing Ltd., 2013) Cho, Junghyun; Ko, Hyeong-Seok; I. Navazo, P. PoulinWe present a new framework to simulate moving interfaces in viscous incompressible two phase flows. The goal is to achieve both conservation of the fluid volume and a detailed reconstruction of the fluid surface. To these ends, we incorporate sub-grid refinement of the level set with the volume-of-fluid method. In the context of this refined level set grid we propose the algorithms needed for the coupling of the level set and the volume-of-fluid, which include techniques for computing volume, redistancing the level set, and handling surface tension. We report the experimental results produced with the proposed method via simulations of the two phase fluid phenomena such as air-cushioning and deforming large bubbles.Item A Particle-Grid Method for Opaque Ice Formation(The Eurographics Association and Blackwell Publishing Ltd., 2013) Im, Jaeho; Park, Hanwook; Kim, Jong-Hyun; Kim, Chang-Hun; I. Navazo, P. PoulinThis paper presents a particle-grid method to simulate the generation of opaque ice which has air bubbles in it. Water temperature is diffused over a grid, and the exchange of dissolved air between ice and water particles is simulated. We render a particle as an air bubble if it has sufficient air. Otherwise, it is treated as a cloudy volume by distributing air into dissolved air field when the final state has been reached. In addition, our method includes a model in which heat transfer rate may change across the grid. Unlike previous models which could generate an ice volume of only fixed shapes, our approach uses signed distance function (SDF) to generate opaque ice volumes stored in containers of various geometric shapes and can render needle-shaped or egg-shaped bubbles.