Browsing by Author "Jacobson, Alec"
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Item 2018 Cover Image: Thingi10K(© 2018 The Eurographics Association and John Wiley & Sons Ltd., 2018) Zhou, Qingnan; Jacobson, Alec; Chen, Min and Benes, BedrichItem Fast Updates for Least-Squares Rotational Alignment(The Eurographics Association and John Wiley & Sons Ltd., 2021) Zhang, Jiayi Eris; Jacobson, Alec; Alexa, Marc; Mitra, Niloy and Viola, IvanAcross computer graphics, vision, robotics and simulation, many applications rely on determining the 3D rotation that aligns two objects or sets of points. The standard solution is to use singular value decomposition (SVD), where the optimal rotation is recovered as the product of the singular vectors. Faster computation of only the rotation is possible using suitable parameterizations of the rotations and iterative optimization. We propose such a method based on the Cayley transformations. The resulting optimization problem allows better local quadratic approximation compared to the Taylor approximation of the exponential map. This results in both faster convergence as well as more stable approximation compared to other iterative approaches. It also maps well to AVX vectorization. We compare our implementation with a wide range of alternatives on real and synthetic data. The results demonstrate up to two orders of magnitude of speedup compared to a straightforward SVD implementation and a 1.5-6 times speedup over popular optimized code.Item Geometry Processing 2020 CGF 39-5: Frontmatter(The Eurographics Association and John Wiley & Sons Ltd., 2020) Jacobson, Alec; Huang, Qixing; Jacobson, Alec and Huang, QixingItem Latent-space Dynamics for Reduced Deformable Simulation(The Eurographics Association and John Wiley & Sons Ltd., 2019) Fulton, Lawson; Modi, Vismay; Duvenaud, David; Levin, David I. W.; Jacobson, Alec; Alliez, Pierre and Pellacini, FabioWe propose the first reduced model simulation framework for deformable solid dynamics using autoencoder neural networks. We provide a data-driven approach to generating nonlinear reduced spaces for deformation dynamics. In contrast to previous methods using machine learning which accelerate simulation by approximating the time-stepping function, we solve the true equations of motion in the latent-space using a variational formulation of implicit integration. Our approach produces drastically smaller reduced spaces than conventional linear model reduction, improving performance and robustness. Furthermore, our method works well with existing force-approximation cubature methods.Item Levitating Rigid Objects with Hidden Rods and Wires(The Eurographics Association and John Wiley & Sons Ltd., 2021) Kushner, Sarah; Ulinski, Risa; Singh, Karan; Levin, David I. W.; Jacobson, Alec; Mitra, Niloy and Viola, IvanWe propose a novel algorithm to efficiently generate hidden structures to support arrangements of floating rigid objects. Our optimization finds a small set of rods and wires between objects and each other or a supporting surface (e.g., wall or ceiling) that hold all objects in force and torque equilibrium. Our objective function includes a sparsity inducing total volume term and a linear visibility term based on efficiently pre-computed Monte-Carlo integration, to encourage solutions that are as-hiddenas- possible. The resulting optimization is convex and the global optimum can be efficiently recovered via a linear program. Our representation allows for a user-controllable mixture of tension-, compression-, and shear-resistant rods or tension-only wires. We explore applications to theatre set design, museum exhibit curation, and other artistic endeavours.Item libigl: Prototyping Geometry Processing Research in C++(The Eurographics Association, 2019) Panozzo, Daniele; Jacobson, Alec; Jakob, Wenzel and Puppo, EnricoModern geometry processing algorithms depend on an ever-growing toolbox of fundamental sub-routines and data structures. Prototyping from scratch requires much time building basic tools rather than focusing on the novel research idea. Many existing code libraries have unsatisfactory APIs and the time spent implementing sub-routines is often replaced with time spent learning complex, templated object hierarchies or memory layouts. Libigl is a C++ library of geometry processing algorithms designed for and by researchers. Its wide functionality includes construction of common sparse discrete differential geometry operators (such as the cotangent Laplacian), simple facet- and edge-based topology data structures, mesh-viewing utilities for OpenGL and GLSL, and many core functions for matrix manipulation which make Eigen feel a lot more like MATLAB. Libigl places extreme importance on ease of use and experimentation. To this end, algorithms are directly exposed as functions taking simple matrix types as inputs and outputs. Libigl is a "header only" library and compiles on Windows, Mac, and Linux. In this course, we will walk through an introduction of libigl via readymade examples spanning the gamut of geometry processing applications and tasks. Attendees will be able to follow along on their laptops. We will explain the core functionality of libigl, how to piece together complex algorithms from library functions, and how to interface to libigl from Python and MATLAB. We will highlight some of libigl’'s most powerul features: including mesh booleans, quad remeshing, parameterization, and shape deformation. We will conclude with live coding sessions demonstrating libigl's effectiveness and ease-of-use.Item Normal-Driven Spherical Shape Analogies(The Eurographics Association and John Wiley & Sons Ltd., 2021) Liu, Hsueh-Ti Derek; Jacobson, Alec; Digne, Julie and Crane, KeenanThis paper introduces a new method to stylize 3D geometry. The key observation is that the surface normal is an effective instrument to capture different geometric styles. Centered around this observation, we cast stylization as a shape analogy problem, where the analogy relationship is defined on the surface normal. This formulation can deform a 3D shape into different styles within a single framework. One can plug-and-play different target styles by providing an exemplar shape or an energy-based style description (e.g., developable surfaces). Our surface stylization methodology enables Normal Captures as a geometric counterpart to material captures (MatCaps) used in rendering, and the prototypical concept of Spherical Shape Analogies as a geometric counterpart to image analogies in image processing.Item OptCtrlPoints: Finding the Optimal Control Points for Biharmonic 3D Shape Deformation(The Eurographics Association and John Wiley & Sons Ltd., 2023) Kim, Kunho; Uy, Mikaela Angelina; Paschalidou, Despoina; Jacobson, Alec; Guibas, Leonidas J.; Sung, Minhyuk; Chaine, Raphaëlle; Deng, Zhigang; Kim, Min H.We propose OPTCTRLPOINTS, a data-driven framework designed to identify the optimal sparse set of control points for reproducing target shapes using biharmonic 3D shape deformation. Control-point-based 3D deformation methods are widely utilized for interactive shape editing, and their usability is enhanced when the control points are sparse yet strategically distributed across the shape. With this objective in mind, we introduce a data-driven approach that can determine the most suitable set of control points, assuming that we have a given set of possible shape variations. The challenges associated with this task primarily stem from the computationally demanding nature of the problem. Two main factors contribute to this complexity: solving a large linear system for the biharmonic weight computation and addressing the combinatorial problem of finding the optimal subset of mesh vertices. To overcome these challenges, we propose a reformulation of the biharmonic computation that reduces the matrix size, making it dependent on the number of control points rather than the number of vertices. Additionally, we present an efficient search algorithm that significantly reduces the time complexity while still delivering a nearly optimal solution. Experiments on SMPL, SMAL, and DeformingThings4D datasets demonstrate the efficacy of our method. Our control points achieve better template-to-target fit than FPS, random search, and neural-network-based prediction. We also highlight the significant reduction in computation time from days to approximately 3 minutes.Item Pacific Graphics 2020 - CGF 39-7: Frontmatter(The Eurographics Association and John Wiley & Sons Ltd., 2020) Eisemann, Elmar; Jacobson, Alec; Zhang, Fang-Lue; Eisemann, Elmar and Jacobson, Alec and Zhang, Fang-LueItem RodSteward: A Design-to-Assembly System for Fabrication using 3D-Printed Joints and Precision-Cut Rods(The Eurographics Association and John Wiley & Sons Ltd., 2019) Jacobson, Alec; Lee, Jehee and Theobalt, Christian and Wetzstein, GordonWe present RodSteward, a design-to-assembly system for creating furniture-scale structures composed of 3D-printed joints and precision-cut rods. The RodSteward systems consists of: RSDesigner, a fabrication-aware design interface that visualizes accurate geometries during edits and identifies infeasible designs; physical fabrication of parts automatically generated 3Dprintable joint geometries and cutting plans for rods; and RSAssembler, a guided-assembly interface that prompts the user to place parts in order while showing a focus+context visualization of the assembly in progress. We demonstrate the effectiveness of our tools with a number of example constructions of varying complexity, style and parameter choices.Item Seamless Reconstruction of Part-Based High-Relief Models from Hand-Drawn Images(ACM, 2018) Dvorožnák, Marek; Nejad, Saman Sepehri; Jamriška, Ondřej; Jacobson, Alec; Kavan, Ladislav; Sýkora, Daniel; Aydın, Tunç and Sýkora, DanielWe present a new approach to reconstruction of high-relief models from hand-made drawings. Our method is tailored to an interactive modeling scenario where the input drawing can be separated into a set of semantically meaningful parts of which relative depth order is known beforehand. For this kind of input, our technique allows inflating individual components to have a semi-elliptical profile, position them to satisfy prescribed depth order, and provide their seamless interconnection. As compared to previous similar frameworks our approach is the first that formulates this reconstruction process as a joint non-linear optimization problem. Although its direct optimization is computationally demanding we propose an approximative solution which delivers comparable results orders of magnitude faster enabling an interactive response. We evaluate our approach on various hand-made drawings and demonstrate that it provides stateof-the-art quality in comparison with previous methods which require comparable user intervention.Item A Simple Discretization of the Vector Dirichlet Energy(The Eurographics Association and John Wiley & Sons Ltd., 2020) Stein, Oded; Wardetzky, Max; Jacobson, Alec; Grinspun, Eitan; Jacobson, Alec and Huang, QixingWe present a simple and concise discretization of the covariant derivative vector Dirichlet energy for triangle meshes in 3D using Crouzeix-Raviart finite elements. The discretization is based on linear discontinuous Galerkin elements, and is simple to implement, without compromising on quality: there are two degrees of freedom for each mesh edge, and the sparse Dirichlet energy matrix can be constructed in a single pass over all triangles using a short formula that only depends on the edge lengths, reminiscent of the scalar cotangent Laplacian. Our vector Dirichlet energy discretization can be used in a variety of applications, such as the calculation of Killing fields, parallel transport of vectors, and smooth vector field design. Experiments suggest convergence and suitability for applications similar to other discretizations of the vector Dirichlet energy.Item Solid Geometry Processing on Deconstructed Domains(© 2019 The Eurographics Association and John Wiley & Sons Ltd., 2019) Sellán, Silvia; Cheng, Herng Yi; Ma, Yuming; Dembowski, Mitchell; Jacobson, Alec; Chen, Min and Benes, BedrichMany tasks in geometry processing are modelled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh. Unfortunately, tetrahedral meshing remains an open challenge and existing methods either struggle to conform to complex boundary surfaces or require manual intervention to prevent failure. Rather than create a single volumetric mesh for the entire shape, we advocate for solid geometry processing on , where a large and complex shape is composed of overlapping solid subdomains. As each smaller and simpler part is now easier to tetrahedralize, the question becomes how to account for overlaps during problem modelling and how to couple solutions on each subdomain together . We explore how and why previous coupling methods fail, and propose a method that couples solid domains only along their boundary surfaces. We demonstrate the superiority of this method through empirical convergence tests and qualitative applications to solid geometry processing on a variety of popular second‐order and fourth‐order partial differential equations.Many tasks in geometry processing are modelled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh. Unfortunately, tetrahedral meshing remains an open challenge and existing methods either struggle to conform to complex boundary surfaces or require manual intervention to prevent failure. Rather than create a single volumetric mesh for the entire shape, we advocate for solid geometry processing on , where a large and complex shape is composed of overlapping solid subdomains. As each smaller and simpler part is now easier to tetrahedralize, the question becomes how to account for overlaps during problem modelling and how to couple solutions on each subdomain together . We explore how and why previous coupling methods fail, and propose a method that couples solid domains only along their boundary surfaces. We demonstrate the superiority of this method through empirical convergence tests and qualitative applications to solid geometry processing on a variety of popular second‐order and fourth‐order partial differential equations.Item Spectral Mesh Simplification(The Eurographics Association and John Wiley & Sons Ltd., 2020) Lescoat, Thibault; Liu, Hsueh-Ti Derek; Thiery, Jean-Marc; Jacobson, Alec; Boubekeur, Tamy; Ovsjanikov, Maks; Panozzo, Daniele and Assarsson, UlfThe spectrum of the Laplace-Beltrami operator is instrumental for a number of geometric modeling applications, from processing to analysis. Recently, multiple methods were developed to retrieve an approximation of a shape that preserves its eigenvectors as much as possible, but these techniques output a subset of input points with no connectivity, which limits their potential applications. Furthermore, the obtained Laplacian results from an optimization procedure, implying its storage alongside the selected points. Focusing on keeping a mesh instead of an operator would allow to retrieve the latter using the standard cotangent formulation, enabling easier processing afterwards. Instead, we propose to simplify the input mesh using a spectrum-preserving mesh decimation scheme, so that the Laplacian computed on the simplified mesh is spectrally close to the one of the input mesh. We illustrate the benefit of our approach for quickly approximating spectral distances and functional maps on low resolution proxies of potentially high resolution input meshes.