Martin Kilian, Anthony S Ramos Cisneros, Christian Müller, Helmut Pottmann
Discrete surfaces with spherical faces are interesting from a simplified manufacturing viewpoint when compared to other double curved face shapes. Furthermore, by the nature of their definition they are also appealing from the theoretical side leading to a Möbius invariant discrete surface theory. We therefore systematically describe so called sphere meshes with spherical faces and circular arcs as edges where the Möbius transformation group acts on all of its elements. Driven by aspects important for manufacturing, we provide the means to cluster spherical panels by their radii. We investigate the generation of sphere meshes which allow for a geometric support structure and characterize all such meshes with triangular combinatorics in terms of non-Euclidean geometries. We generate sphere meshes with hexagonal combinatorics by intersecting tangential spheres of a reference surface and let them evolve - guided by the surface curvature - to visually convex hexagons, even in negatively curved areas. Furthermore, we extend meshes with circular faces of all combinatorics to sphere meshes by filling its circles with suitable spherical caps and provide a remeshing scheme to obtain quadrilateral sphere meshes with support structure from given sphere congruences. By broadening polyhedral meshes to sphere meshes we exploit the additional degrees of freedom to minimize intersection angles of neighboring spheres enabling the use of spherical panels that provide a softer perception of the overall surface.
{"title":"Meshes with Spherical Faces","authors":"Martin Kilian, Anthony S Ramos Cisneros, Christian Müller, Helmut Pottmann","doi":"10.1145/3618345","DOIUrl":"https://doi.org/10.1145/3618345","url":null,"abstract":"Discrete surfaces with spherical faces are interesting from a simplified manufacturing viewpoint when compared to other double curved face shapes. Furthermore, by the nature of their definition they are also appealing from the theoretical side leading to a Möbius invariant discrete surface theory. We therefore systematically describe so called sphere meshes with spherical faces and circular arcs as edges where the Möbius transformation group acts on all of its elements. Driven by aspects important for manufacturing, we provide the means to cluster spherical panels by their radii. We investigate the generation of sphere meshes which allow for a geometric support structure and characterize all such meshes with triangular combinatorics in terms of non-Euclidean geometries. We generate sphere meshes with hexagonal combinatorics by intersecting tangential spheres of a reference surface and let them evolve - guided by the surface curvature - to visually convex hexagons, even in negatively curved areas. Furthermore, we extend meshes with circular faces of all combinatorics to sphere meshes by filling its circles with suitable spherical caps and provide a remeshing scheme to obtain quadrilateral sphere meshes with support structure from given sphere congruences. By broadening polyhedral meshes to sphere meshes we exploit the additional degrees of freedom to minimize intersection angles of neighboring spheres enabling the use of spherical panels that provide a softer perception of the overall surface.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"31 16","pages":"1 - 19"},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138604139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Zhang, Jérémie Dumas, Yun (Raymond) Fei, Alec Jacobson, Doug L. James, Danny M. Kaufman
Thin shell structures exhibit complex behaviors critical for modeling and design across wide-ranging applications. Capturing their mechanical response requires finely detailed, high-resolution meshes. Corresponding simulations for predicting equilibria with these meshes are expensive, whereas coarse-mesh simulations can be fast but generate unacceptable artifacts and inaccuracies. The recently proposed progressive simulation framework [Zhang et al. 2022] offers a promising avenue to address these limitations with consistent and progressively improving simulation over a hierarchy of increasingly higher-resolution models. Unfortunately, it is currently severely limited in application to meshes and shapes generated via Loop subdivision. We propose Progressive Shells Quasistatics to extend progressive simulation to the high-fidelity modeling and design of all input shell (and plate) geometries with unstructured (as well as structured) triangle meshes. To do so, we construct a fine-to-coarse hierarchy with a novel nonlinear prolongation operator custom-suited for curved-surface simulation that is rest-shape preserving, supports complex curved boundaries, and enables the reconstruction of detailed geometries from coarse-level meshes. Then, to enable convergent, high-quality solutions with robust contact handling, we propose a new, safe, and efficient shape-preserving upsampling method that ensures non-intersection and strain limits during refinement. With these core contributions, Progressive Shell Quasistatics enables, for the first time, wide generality for progressive simulation, including support for arbitrary curved-shell geometries, progressive collision objects, curved boundaries, and unstructured triangle meshes - all while ensuring that preview and final solutions remain free of intersections. We demonstrate these features across a wide range of stress-tests where progressive simulation captures the wrinkling, folding, twisting, and buckling behaviors of frictionally contacting thin shells with orders-of-magnitude speed-up in examples over direct fine-resolution simulation.
薄壳结构表现出复杂的行为，对广泛应用的建模和设计至关重要。捕捉它们的机械反应需要非常详细的高分辨率网格。用这些网格预测平衡的相应模拟是昂贵的，而粗网格模拟可以很快，但会产生不可接受的工件和不准确性。最近提出的渐进式模拟框架[Zhang et al. 2022]提供了一个有希望的途径，通过在越来越高分辨率模型的层次结构上一致和逐步改进的模拟来解决这些限制。不幸的是，它目前在通过循环细分生成的网格和形状的应用中受到严重限制。我们提出渐进式壳准静力学将渐进式模拟扩展到具有非结构化(以及结构化)三角形网格的所有输入壳(和板)几何形状的高保真建模和设计。为此，我们构建了一个精细到粗糙的层次结构，其中包含一种适合于曲面模拟的新型非线性扩展算子，该算子具有静止形状保持功能，支持复杂的弯曲边界，并能够从粗级网格重建详细的几何形状。然后，为了实现具有鲁棒接触处理的收敛，高质量的解决方案，我们提出了一种新的，安全，高效的形状保持上采样方法，以确保精化过程中的无相交和应变限制。有了这些核心贡献，渐进式壳准静力学首次实现了渐进式模拟的广泛通用性，包括支持任意弯曲壳几何形状、渐进式碰撞对象、弯曲边界和非结构化三角形网格，同时确保预览和最终解决方案没有交集。我们通过广泛的压力测试展示了这些特征，其中渐进模拟捕获了摩擦接触薄壳的起皱、折叠、扭曲和屈曲行为，在直接精细模拟的例子中，速度提高了几个数量级。
{"title":"Progressive Shell Qasistatics for Unstructured Meshes","authors":"J. Zhang, Jérémie Dumas, Yun (Raymond) Fei, Alec Jacobson, Doug L. James, Danny M. Kaufman","doi":"10.1145/3618388","DOIUrl":"https://doi.org/10.1145/3618388","url":null,"abstract":"Thin shell structures exhibit complex behaviors critical for modeling and design across wide-ranging applications. Capturing their mechanical response requires finely detailed, high-resolution meshes. Corresponding simulations for predicting equilibria with these meshes are expensive, whereas coarse-mesh simulations can be fast but generate unacceptable artifacts and inaccuracies. The recently proposed progressive simulation framework [Zhang et al. 2022] offers a promising avenue to address these limitations with consistent and progressively improving simulation over a hierarchy of increasingly higher-resolution models. Unfortunately, it is currently severely limited in application to meshes and shapes generated via Loop subdivision. We propose Progressive Shells Quasistatics to extend progressive simulation to the high-fidelity modeling and design of all input shell (and plate) geometries with unstructured (as well as structured) triangle meshes. To do so, we construct a fine-to-coarse hierarchy with a novel nonlinear prolongation operator custom-suited for curved-surface simulation that is rest-shape preserving, supports complex curved boundaries, and enables the reconstruction of detailed geometries from coarse-level meshes. Then, to enable convergent, high-quality solutions with robust contact handling, we propose a new, safe, and efficient shape-preserving upsampling method that ensures non-intersection and strain limits during refinement. With these core contributions, Progressive Shell Quasistatics enables, for the first time, wide generality for progressive simulation, including support for arbitrary curved-shell geometries, progressive collision objects, curved boundaries, and unstructured triangle meshes - all while ensuring that preview and final solutions remain free of intersections. We demonstrate these features across a wide range of stress-tests where progressive simulation captures the wrinkling, folding, twisting, and buckling behaviors of frictionally contacting thin shells with orders-of-magnitude speed-up in examples over direct fine-resolution simulation.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"85 7","pages":"1 - 17"},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138604422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Discontinuous visibility changes at object boundaries remain a persistent source of difficulty in the area of differentiable rendering. Left untreated, they bias computed gradients so severely that even basic optimization tasks fail. Prior path-space methods addressed this bias by decoupling boundaries from the interior, allowing each part to be handled using specialized Monte Carlo sampling strategies. While conceptually powerful, the full potential of this idea remains unrealized since existing methods often fail to adequately sample the boundary proportional to its contribution. This paper presents theoretical and algorithmic contributions. On the theoretical side, we transform the boundary derivative into a remarkably simple local integral that invites present and future developments. Building on this result, we propose a new strategy that projects ordinary samples produced during forward rendering onto nearby boundaries. The resulting projections establish a variance-reducing guiding distribution that accelerates convergence of the subsequent differential phase. We demonstrate the superior efficiency and versatility of our method across a variety of shape representations, including triangle meshes, implicitly defined surfaces, and cylindrical fibers based on Bézier curves.
{"title":"Projective Sampling for Differentiable Rendering of Geometry","authors":"Ziyi Zhang, Nicolas Roussel, Wenzel Jakob","doi":"10.1145/3618385","DOIUrl":"https://doi.org/10.1145/3618385","url":null,"abstract":"Discontinuous visibility changes at object boundaries remain a persistent source of difficulty in the area of differentiable rendering. Left untreated, they bias computed gradients so severely that even basic optimization tasks fail. Prior path-space methods addressed this bias by decoupling boundaries from the interior, allowing each part to be handled using specialized Monte Carlo sampling strategies. While conceptually powerful, the full potential of this idea remains unrealized since existing methods often fail to adequately sample the boundary proportional to its contribution. This paper presents theoretical and algorithmic contributions. On the theoretical side, we transform the boundary derivative into a remarkably simple local integral that invites present and future developments. Building on this result, we propose a new strategy that projects ordinary samples produced during forward rendering onto nearby boundaries. The resulting projections establish a variance-reducing guiding distribution that accelerates convergence of the subsequent differential phase. We demonstrate the superior efficiency and versatility of our method across a variety of shape representations, including triangle meshes, implicitly defined surfaces, and cylindrical fibers based on Bézier curves.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"43 14","pages":"1 - 14"},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138602194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Boundary layer flow plays a very important role in shaping the entire flow feature near and behind obstacles inside fluids. Thus, boundary treatment methods are crucial for a physically consistent fluid simulation, especially when turbulence occurs at a high Reynolds number, in which accurately handling thin boundary layer becomes quite challenging. Traditional Navier-Stokes solvers usually construct multi-resolution body-fitted meshes to achieve high accuracy, often together with near-wall and sub-grid turbulence modeling. However, this could be time-consuming and computationally intensive even with GPU accelerations. An alternative and much faster approach is to switch to a kinetic solver, such as the lattice Boltzmann model, but boundary treatment has to be done in a cut-cell manner, sacrificing accuracy unless grid resolution is much increased. In this paper, we focus on simulating the boundary-dominated turbulent flow phenomena with an efficient kinetic solver. In order to significantly improve the cut-cell-based boundary treatment for higher accuracy without excessively increasing the simulation resolution, we propose a novel parametric boundary treatment model, including a semi-Lagrangian scheme at the wall for non-equilibrium distribution functions, together with a purely link-based near-wall analytical mesoscopic model by analogy with the macroscopic wall modeling approach, which is yet simple to compute. Such a new method is further extended to handle moving boundaries, showing increased accuracy. Comprehensive analyses are conducted, with a variety of simulation results that are both qualitatively and quantitatively validated with experiments and real life scenarios, and compared to existing methods, to indicate superiority of our method. We highlight that our method not only provides a more accurate way for boundary treatment, but also a valuable tool to control boundary layer behaviors. This has not been achieved and demonstrated before in computer graphics, which we believe will be very useful in practical engineering.
{"title":"A Parametric Kinetic Solver for Simulating Boundary-Dominated Turbulent Flow Phenomena","authors":"Mengyun Liu, Xiaopei Liu","doi":"10.1145/3618313","DOIUrl":"https://doi.org/10.1145/3618313","url":null,"abstract":"Boundary layer flow plays a very important role in shaping the entire flow feature near and behind obstacles inside fluids. Thus, boundary treatment methods are crucial for a physically consistent fluid simulation, especially when turbulence occurs at a high Reynolds number, in which accurately handling thin boundary layer becomes quite challenging. Traditional Navier-Stokes solvers usually construct multi-resolution body-fitted meshes to achieve high accuracy, often together with near-wall and sub-grid turbulence modeling. However, this could be time-consuming and computationally intensive even with GPU accelerations. An alternative and much faster approach is to switch to a kinetic solver, such as the lattice Boltzmann model, but boundary treatment has to be done in a cut-cell manner, sacrificing accuracy unless grid resolution is much increased. In this paper, we focus on simulating the boundary-dominated turbulent flow phenomena with an efficient kinetic solver. In order to significantly improve the cut-cell-based boundary treatment for higher accuracy without excessively increasing the simulation resolution, we propose a novel parametric boundary treatment model, including a semi-Lagrangian scheme at the wall for non-equilibrium distribution functions, together with a purely link-based near-wall analytical mesoscopic model by analogy with the macroscopic wall modeling approach, which is yet simple to compute. Such a new method is further extended to handle moving boundaries, showing increased accuracy. Comprehensive analyses are conducted, with a variety of simulation results that are both qualitatively and quantitatively validated with experiments and real life scenarios, and compared to existing methods, to indicate superiority of our method. We highlight that our method not only provides a more accurate way for boundary treatment, but also a valuable tool to control boundary layer behaviors. This has not been achieved and demonstrated before in computer graphics, which we believe will be very useful in practical engineering.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"8 3","pages":"1 - 20"},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138602266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a set of operators to perform modifications, in particular collapses and splits, in volumetric cell complexes which are discretely embedded in a background mesh. Topological integrity and geometric embedding validity are carefully maintained. We apply these operators strategically to volumetric block decompositions, so-called T-meshes or base complexes, in the context of hexahedral mesh generation. This allows circumventing the expensive and unreliable global volumetric remapping step in the versatile meshing pipeline based on 3D integer-grid maps. In essence, we reduce this step to simpler local cube mapping problems, for which reliable solutions are available. As a consequence, the robustness of the mesh generation process is increased, especially when targeting coarse or block-structured hexahedral meshes. We furthermore extend this pipeline to support feature alignment constraints, and systematically respect these throughout, enabling the generation of meshes that align to points, curves, and surfaces of special interest, whether on the boundary or in the interior of the domain.
{"title":"Collapsing Embedded Cell Complexes for Safer Hexahedral Meshing","authors":"Hendrik Brückler, M. Campen","doi":"10.1145/3618384","DOIUrl":"https://doi.org/10.1145/3618384","url":null,"abstract":"We present a set of operators to perform modifications, in particular collapses and splits, in volumetric cell complexes which are discretely embedded in a background mesh. Topological integrity and geometric embedding validity are carefully maintained. We apply these operators strategically to volumetric block decompositions, so-called T-meshes or base complexes, in the context of hexahedral mesh generation. This allows circumventing the expensive and unreliable global volumetric remapping step in the versatile meshing pipeline based on 3D integer-grid maps. In essence, we reduce this step to simpler local cube mapping problems, for which reliable solutions are available. As a consequence, the robustness of the mesh generation process is increased, especially when targeting coarse or block-structured hexahedral meshes. We furthermore extend this pipeline to support feature alignment constraints, and systematically respect these throughout, enabling the generation of meshes that align to points, curves, and surfaces of special interest, whether on the boundary or in the interior of the domain.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"37 15","pages":"1 - 24"},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138602468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Artificial light sources make our daily life convenient, but cause a severe problem called light pollution. We propose a novel system for efficient visualization of light pollution in the night sky. Numerous methods have been proposed for rendering the sky, but most of these focus on rendering of the daytime or the sunset sky where the sun is the only, or dominant light source. For the visualization of the light pollution, however, we must consider many city light sources on the ground, resulting in excessive computational cost. We address this problem by precomputing a set of intensity distributions for the sky illuminated by city light at various locations and with different atmospheric conditions. We apply a principal component analysis and fast Fourier transform to the precomputed distributions, allowing us to efficiently visualize the extent of the light pollution. Using this method, we can achieve one to two orders of magnitudes faster computation compared to a naive approach that simply accumulates the scattered intensity for each viewing ray. Furthermore, the fast computation allows us to interactively solve the inverse problem that determines the city light intensity needed to reduce light pollution. Our system provides the user with both a forward and inverse investigation tool for the study and minimization of light pollution.
{"title":"Efficient Visualization of Light Pollution for the Night Sky","authors":"Y. Dobashi, Naoto Ishikawa, Kei Iwasaki","doi":"10.1145/3618337","DOIUrl":"https://doi.org/10.1145/3618337","url":null,"abstract":"Artificial light sources make our daily life convenient, but cause a severe problem called light pollution. We propose a novel system for efficient visualization of light pollution in the night sky. Numerous methods have been proposed for rendering the sky, but most of these focus on rendering of the daytime or the sunset sky where the sun is the only, or dominant light source. For the visualization of the light pollution, however, we must consider many city light sources on the ground, resulting in excessive computational cost. We address this problem by precomputing a set of intensity distributions for the sky illuminated by city light at various locations and with different atmospheric conditions. We apply a principal component analysis and fast Fourier transform to the precomputed distributions, allowing us to efficiently visualize the extent of the light pollution. Using this method, we can achieve one to two orders of magnitudes faster computation compared to a naive approach that simply accumulates the scattered intensity for each viewing ray. Furthermore, the fast computation allows us to interactively solve the inverse problem that determines the city light intensity needed to reduce light pollution. Our system provides the user with both a forward and inverse investigation tool for the study and minimization of light pollution.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"19 8","pages":"1 - 11"},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138602894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The surface/surface intersection technique serves as one of the most fundamental functions in modern Computer Aided Design (CAD) systems. Despite the long research history and successful applications of surface intersection algorithms in various CAD industrial software, challenges still exist in balancing computational efficiency, accuracy, as well as topology correctness. Specifically, most practical intersection algorithms fail to guarantee the correct topology of the intersection curve(s) when two surfaces are in near-critical positions, which brings instability to CAD systems. Even in one of the most successfully used commercial geometry engines ACIS, such complicated intersection topology can still be a tough nut to crack. In this paper, we present a practical topology guaranteed algorithm for computing the intersection loci of two B-spline surfaces. Our algorithm well treats all types of common and complicated intersection topology with practical efficiency, including those intersections with multiple branches or cross singularities, contacts in several isolated singular points or highorder contacts along a curve, as well as intersections along boundary curves. We present representative examples of these hard topology situations that challenge not only the open-source geometry engine OCCT but also the commercial engine ACIS. We compare our algorithm in both efficiency and topology correctness on plenty of common and complicated models with the open-source intersection package in SISL, OCCT, and the commercial engine ACIS.
{"title":"Topology Guaranteed B-Spline Surface/Surface Intersection","authors":"Jieyin Yang, Xiaohong Jia, Dong-Ming Yan","doi":"10.1145/3618349","DOIUrl":"https://doi.org/10.1145/3618349","url":null,"abstract":"The surface/surface intersection technique serves as one of the most fundamental functions in modern Computer Aided Design (CAD) systems. Despite the long research history and successful applications of surface intersection algorithms in various CAD industrial software, challenges still exist in balancing computational efficiency, accuracy, as well as topology correctness. Specifically, most practical intersection algorithms fail to guarantee the correct topology of the intersection curve(s) when two surfaces are in near-critical positions, which brings instability to CAD systems. Even in one of the most successfully used commercial geometry engines ACIS, such complicated intersection topology can still be a tough nut to crack. In this paper, we present a practical topology guaranteed algorithm for computing the intersection loci of two B-spline surfaces. Our algorithm well treats all types of common and complicated intersection topology with practical efficiency, including those intersections with multiple branches or cross singularities, contacts in several isolated singular points or highorder contacts along a curve, as well as intersections along boundary curves. We present representative examples of these hard topology situations that challenge not only the open-source geometry engine OCCT but also the commercial engine ACIS. We compare our algorithm in both efficiency and topology correctness on plenty of common and complicated models with the open-source intersection package in SISL, OCCT, and the commercial engine ACIS.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"2 25","pages":"1 - 16"},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138603893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Zhehao Li, Qingyu Xu, Xiaohan Ye, Bo-Ning Ren, Ligang Liu
Differentiable physics simulation has shown its efficacy in inverse design problems. Given the pervasiveness of the diverse interactions between fluids and solids in life, a differentiable simulator for the inverse design of the motion of rigid objects in two-way fluid-rigid coupling is also demanded. There are two main challenges to develop a differentiable two-way fluid-solid coupling simulator for rigid body control tasks: the ubiquitous, discontinuous contacts in fluid-solid interactions, and the high computational cost of gradient formulation due to the large number of degrees of freedom (DoF) of fluid dynamics. In this work, we propose a novel differentiable SPH-based two-way fluid-rigid coupling simulator to address these challenges. Our purpose is to provide a differentiable simulator for SPH which incorporates a unified representation for both fluids and solids using particles. However, naively differentiating the forward simulation of the particle system encounters gradient explosion issues. We investigate the instability in differentiating the SPH-based fluid-rigid coupling simulator and present a feasible gradient computation scheme to address its differentiability. In addition, we also propose an efficient method to compute the gradient of fluid-rigid coupling without incurring the high computational cost of differentiating the entire high-DoF fluid system. We show the efficacy, scalability, and extensibility of our method in various challenging rigid body control tasks with diverse fluid-rigid interactions and multi-rigid contacts, achieving up to an order of magnitude speedup in optimization compared to baseline methods in experiments.
{"title":"DiffFR: Differentiable SPH-Based Fluid-Rigid Coupling for Rigid Body Control","authors":"Zhehao Li, Qingyu Xu, Xiaohan Ye, Bo-Ning Ren, Ligang Liu","doi":"10.1145/3618318","DOIUrl":"https://doi.org/10.1145/3618318","url":null,"abstract":"Differentiable physics simulation has shown its efficacy in inverse design problems. Given the pervasiveness of the diverse interactions between fluids and solids in life, a differentiable simulator for the inverse design of the motion of rigid objects in two-way fluid-rigid coupling is also demanded. There are two main challenges to develop a differentiable two-way fluid-solid coupling simulator for rigid body control tasks: the ubiquitous, discontinuous contacts in fluid-solid interactions, and the high computational cost of gradient formulation due to the large number of degrees of freedom (DoF) of fluid dynamics. In this work, we propose a novel differentiable SPH-based two-way fluid-rigid coupling simulator to address these challenges. Our purpose is to provide a differentiable simulator for SPH which incorporates a unified representation for both fluids and solids using particles. However, naively differentiating the forward simulation of the particle system encounters gradient explosion issues. We investigate the instability in differentiating the SPH-based fluid-rigid coupling simulator and present a feasible gradient computation scheme to address its differentiability. In addition, we also propose an efficient method to compute the gradient of fluid-rigid coupling without incurring the high computational cost of differentiating the entire high-DoF fluid system. We show the efficacy, scalability, and extensibility of our method in various challenging rigid body control tasks with diverse fluid-rigid interactions and multi-rigid contacts, achieving up to an order of magnitude speedup in optimization compared to baseline methods in experiments.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"22 4","pages":"1 - 17"},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138604107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ziyin Qu, Minchen Li, Yin Yang, Chenfanfu Jiang, Fernando de Goes
We present a novel hybrid Lagrangian/Eulerian method for simulating inelastic flows that generates high-quality particle distributions with adaptive volumes. At its core, our approach integrates an updated Lagrangian time discretization of continuum mechanics with the Power Particle-In-Cell geometric representation of deformable materials. As a result, we obtain material points described by optimized density kernels that precisely track the varying particle volumes both spatially and temporally. For efficient CFL-rate simulations, we also propose an implicit time integration for our system using a non-linear Gauss-Seidel solver inspired by X-PBD, viewing Eulerian nodal velocities as primal variables. We demonstrate the versatility of our method with simulations of mesoscale bubbles, sands, liquid, and foams.
{"title":"Power Plastics: A Hybrid Lagrangian/Eulerian Solver for Mesoscale Inelastic Flows","authors":"Ziyin Qu, Minchen Li, Yin Yang, Chenfanfu Jiang, Fernando de Goes","doi":"10.1145/3618344","DOIUrl":"https://doi.org/10.1145/3618344","url":null,"abstract":"We present a novel hybrid Lagrangian/Eulerian method for simulating inelastic flows that generates high-quality particle distributions with adaptive volumes. At its core, our approach integrates an updated Lagrangian time discretization of continuum mechanics with the Power Particle-In-Cell geometric representation of deformable materials. As a result, we obtain material points described by optimized density kernels that precisely track the varying particle volumes both spatially and temporally. For efficient CFL-rate simulations, we also propose an implicit time integration for our system using a non-linear Gauss-Seidel solver inspired by X-PBD, viewing Eulerian nodal velocities as primal variables. We demonstrate the versatility of our method with simulations of mesoscale bubbles, sands, liquid, and foams.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"75 17","pages":"1 - 11"},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138604571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Physics-based differentiable rendering is becoming increasingly crucial for tasks in inverse rendering and machine learning pipelines. To address discontinuities caused by geometric boundaries and occlusion, two classes of methods have been proposed: 1) the edge-sampling methods that directly sample light paths at the scene discontinuity boundaries, which require nontrivial data structures and precomputation to select the edges, and 2) the reparameterization methods that avoid discontinuity sampling but are currently limited to hemispherical integrals and unidirectional path tracing. We introduce a new mathematical formulation that enjoys the benefits of both classes of methods. Unlike previous reparameterization work that focused on hemispherical integral, we derive the reparameterization in the path space. As a result, to estimate derivatives using our formulation, we can apply advanced Monte Carlo rendering methods, such as bidirectional path tracing, while avoiding explicit sampling of discontinuity boundaries. We show differentiable rendering and inverse rendering results to demonstrate the effectiveness of our method.
{"title":"Warped-Area Reparameterization of Differential Path Integrals","authors":"Peiyu Xu, S. Bangaru, Tzu-Mao Li, Shuang Zhao","doi":"10.1145/3618330","DOIUrl":"https://doi.org/10.1145/3618330","url":null,"abstract":"Physics-based differentiable rendering is becoming increasingly crucial for tasks in inverse rendering and machine learning pipelines. To address discontinuities caused by geometric boundaries and occlusion, two classes of methods have been proposed: 1) the edge-sampling methods that directly sample light paths at the scene discontinuity boundaries, which require nontrivial data structures and precomputation to select the edges, and 2) the reparameterization methods that avoid discontinuity sampling but are currently limited to hemispherical integrals and unidirectional path tracing. We introduce a new mathematical formulation that enjoys the benefits of both classes of methods. Unlike previous reparameterization work that focused on hemispherical integral, we derive the reparameterization in the path space. As a result, to estimate derivatives using our formulation, we can apply advanced Monte Carlo rendering methods, such as bidirectional path tracing, while avoiding explicit sampling of discontinuity boundaries. We show differentiable rendering and inverse rendering results to demonstrate the effectiveness of our method.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"27 20","pages":"1 - 18"},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138601632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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