P. Voglreiter, B. Kerbl, A. Weinrauch, J. H. Mueller, Thomas Neff, M. Steinberger, D. Schmalstieg
Visibility computation is a key element in computer graphics applications. More specifically, a from-region potentially visible set (PVS) is an established tool in rendering acceleration, but its high computational cost means a from-region PVS is almost always precomputed. Precomputation restricts the use of PVS to static scenes and leads to high storage cost, in particular, if we need fine-grained regions. For dynamic applications, such as streaming content over a variable-bandwidth network, online PVS computation with configurable region size is required. We address this need with trim regions, a new method for generating from-region PVS for arbitrary scenes in real time. Trim regions perform controlled erosion of object silhouettes in image space, implicitly applying the shrinking theorem known from previous work. Our algorithm is the first that applies automatic shrinking to unconstrained 3D scenes, including non-manifold meshes, and does so in real time using an efficient GPU execution model. We demonstrate that our algorithm generates a tight PVS for complex scenes and outperforms previous online methods for from-viewpoint and from-region PVS. It runs at 60 Hz for realistic game scenes consisting of millions of triangles and computes PVS with a tightness matching or surpassing existing approaches.
{"title":"Trim Regions for Online Computation of From-Region Potentially Visible Sets","authors":"P. Voglreiter, B. Kerbl, A. Weinrauch, J. H. Mueller, Thomas Neff, M. Steinberger, D. Schmalstieg","doi":"10.1145/3592434","DOIUrl":"https://doi.org/10.1145/3592434","url":null,"abstract":"Visibility computation is a key element in computer graphics applications. More specifically, a from-region potentially visible set (PVS) is an established tool in rendering acceleration, but its high computational cost means a from-region PVS is almost always precomputed. Precomputation restricts the use of PVS to static scenes and leads to high storage cost, in particular, if we need fine-grained regions. For dynamic applications, such as streaming content over a variable-bandwidth network, online PVS computation with configurable region size is required. We address this need with trim regions, a new method for generating from-region PVS for arbitrary scenes in real time. Trim regions perform controlled erosion of object silhouettes in image space, implicitly applying the shrinking theorem known from previous work. Our algorithm is the first that applies automatic shrinking to unconstrained 3D scenes, including non-manifold meshes, and does so in real time using an efficient GPU execution model. We demonstrate that our algorithm generates a tight PVS for complex scenes and outperforms previous online methods for from-viewpoint and from-region PVS. It runs at 60 Hz for realistic game scenes consisting of millions of triangles and computes PVS with a tightness matching or surpassing existing approaches.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"23 1","pages":"1 - 15"},"PeriodicalIF":0.0,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85847917","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}
L. Lan, Minchen Li, Chenfanfu Jiang, Huamin Wang, Yin Yang
In this paper, we present a GPU algorithm for finite element hyperelastic simulation. We show that the interior-point method, known to be effective for robust collision resolution, can be coupled with non-Newton procedures and be massively sped up on the GPU. Newton's method has been widely chosen for the interior-point family, which fully solves a linear system at each step. After that, the active set associated with collision/contact constraints is updated. Mimicking this routine using a non-Newton optimization (like gradient descent or ADMM) unfortunately does not deliver expected accelerations. This is because the barrier functions employed in an interior-point method need to be updated at every iteration to strictly confine the search to the feasible region. The associated cost (e.g., per-iteration CCD) quickly overweights the benefit brought by the GPU, and a new parallelism modality is needed. Our algorithm is inspired by the domain decomposition method and designed to move interior-point-related computations to local domains as much as possible. We minimize the size of each domain (i.e., a stencil) by restricting it to a single element, so as to fully exploit the capacity of modern GPUs. The stencil-level results are integrated into a global update using a novel hybrid sweep scheme. Our algorithm is locally second-order offering better convergence. It enables simulation acceleration of up to two orders over its CPU counterpart. We demonstrate the scalability, robustness, efficiency, and quality of our algorithm in a variety of simulation scenarios with complex and detailed collision geometries.
{"title":"Second-order Stencil Descent for Interior-point Hyperelasticity","authors":"L. Lan, Minchen Li, Chenfanfu Jiang, Huamin Wang, Yin Yang","doi":"10.1145/3592104","DOIUrl":"https://doi.org/10.1145/3592104","url":null,"abstract":"In this paper, we present a GPU algorithm for finite element hyperelastic simulation. We show that the interior-point method, known to be effective for robust collision resolution, can be coupled with non-Newton procedures and be massively sped up on the GPU. Newton's method has been widely chosen for the interior-point family, which fully solves a linear system at each step. After that, the active set associated with collision/contact constraints is updated. Mimicking this routine using a non-Newton optimization (like gradient descent or ADMM) unfortunately does not deliver expected accelerations. This is because the barrier functions employed in an interior-point method need to be updated at every iteration to strictly confine the search to the feasible region. The associated cost (e.g., per-iteration CCD) quickly overweights the benefit brought by the GPU, and a new parallelism modality is needed. Our algorithm is inspired by the domain decomposition method and designed to move interior-point-related computations to local domains as much as possible. We minimize the size of each domain (i.e., a stencil) by restricting it to a single element, so as to fully exploit the capacity of modern GPUs. The stencil-level results are integrated into a global update using a novel hybrid sweep scheme. Our algorithm is locally second-order offering better convergence. It enables simulation acceleration of up to two orders over its CPU counterpart. We demonstrate the scalability, robustness, efficiency, and quality of our algorithm in a variety of simulation scenarios with complex and detailed collision geometries.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"132 1","pages":"1 - 16"},"PeriodicalIF":0.0,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85743647","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}
A method is presented to compute volumetric maps and parametrizations of objects over 3D domains. As a key feature, continuity and bijectivity are ensured by construction. Arbitrary objects of ball topology, represented as tetrahedral meshes, are supported. Arbitrary convex as well as star-shaped domains are supported. Full control over the boundary mapping is provided. The method is based on the technique of simplicial foliations, generalized to a broader class of domain shapes and applied adaptively in a novel localized manner. This increases flexibility as well as efficiency over the state of the art, while maintaining reliability in guaranteeing map bijectivity.
{"title":"Galaxy Maps: Localized Foliations for Bijective Volumetric Mapping","authors":"Steffen Hinderink, M. Campen","doi":"10.1145/3592410","DOIUrl":"https://doi.org/10.1145/3592410","url":null,"abstract":"A method is presented to compute volumetric maps and parametrizations of objects over 3D domains. As a key feature, continuity and bijectivity are ensured by construction. Arbitrary objects of ball topology, represented as tetrahedral meshes, are supported. Arbitrary convex as well as star-shaped domains are supported. Full control over the boundary mapping is provided. The method is based on the technique of simplicial foliations, generalized to a broader class of domain shapes and applied adaptively in a novel localized manner. This increases flexibility as well as efficiency over the state of the art, while maintaining reliability in guaranteeing map bijectivity.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"23 1","pages":"1 - 16"},"PeriodicalIF":0.0,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91222365","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}
This paper proposes a method to model masonry shell structures where the shell elements fall into a set of discrete equivalence classes. Such shell structure can reduce the fabrication cost and simplify the physical construction due to reuse of a few template shell elements. Given a freeform surface, our goal is to generate a small set of template shell elements that can be reused to produce a seamless and buildable structure that closely resembles the surface. The major technical challenge in this process is balancing the desire for high reusability of template elements with the need for a seamless and buildable final structure. To address the challenge, we define three error metrics to measure the seamlessness and buildability of shell structures made from discrete equivalence classes and develop a hierarchical cluster-and-optimize approach to generate a small set of template elements that produce a structure closely approximating the surface with low error metrics. We demonstrate the feasibility of our approach on various freeform surfaces and geometric patterns, and validate buildability of our results with four physical prototypes. Code and data of this paper are at https://github.com/Linsanity81/TileableShell.
{"title":"Masonry Shell Structures with Discrete Equivalence Classes","authors":"Rulin Chen, Pengyun Qiu, Peng Song, Bailin Deng, Ziqi Wang, Ying He","doi":"10.1145/3592095","DOIUrl":"https://doi.org/10.1145/3592095","url":null,"abstract":"This paper proposes a method to model masonry shell structures where the shell elements fall into a set of discrete equivalence classes. Such shell structure can reduce the fabrication cost and simplify the physical construction due to reuse of a few template shell elements. Given a freeform surface, our goal is to generate a small set of template shell elements that can be reused to produce a seamless and buildable structure that closely resembles the surface. The major technical challenge in this process is balancing the desire for high reusability of template elements with the need for a seamless and buildable final structure. To address the challenge, we define three error metrics to measure the seamlessness and buildability of shell structures made from discrete equivalence classes and develop a hierarchical cluster-and-optimize approach to generate a small set of template elements that produce a structure closely approximating the surface with low error metrics. We demonstrate the feasibility of our approach on various freeform surfaces and geometric patterns, and validate buildability of our results with four physical prototypes. Code and data of this paper are at https://github.com/Linsanity81/TileableShell.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"55 7 1","pages":"1 - 12"},"PeriodicalIF":0.0,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85820453","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}
Real-life flows exhibit complex and visually appealing behaviors such as bubbling, splashing, glugging and wetting that simulation techniques in graphics have attempted to capture for years. While early approaches were not capable of reproducing multiphase flow phenomena due to their excessive numerical viscosity and low accuracy, kinetic solvers based on the lattice Boltzmann method have recently demonstrated the ability to simulate water-air interaction at high Reynolds numbers in a massively-parallel fashion. However, robust and accurate handling of fluid-solid coupling has remained elusive: be it for CG or CFD solvers, as soon as the motion of immersed objects is too fast or too sudden, pressures near boundaries and interfacial forces exhibit spurious oscillations leading to blowups. Built upon a phase-field and velocity-distribution based lattice-Boltzmann solver for multiphase flows, this paper spells out a series of numerical improvements in momentum exchange, interfacial forces, and two-way coupling to drastically reduce these typical artifacts, thus significantly expanding the types of fluid-solid coupling that we can efficiently simulate. We highlight the numerical benefits of our solver through various challenging simulation results, including comparisons to previous work and real footage.
{"title":"Fluid-Solid Coupling in Kinetic Two-Phase Flow Simulation","authors":"Wei Li, M. Desbrun","doi":"10.1145/3592138","DOIUrl":"https://doi.org/10.1145/3592138","url":null,"abstract":"Real-life flows exhibit complex and visually appealing behaviors such as bubbling, splashing, glugging and wetting that simulation techniques in graphics have attempted to capture for years. While early approaches were not capable of reproducing multiphase flow phenomena due to their excessive numerical viscosity and low accuracy, kinetic solvers based on the lattice Boltzmann method have recently demonstrated the ability to simulate water-air interaction at high Reynolds numbers in a massively-parallel fashion. However, robust and accurate handling of fluid-solid coupling has remained elusive: be it for CG or CFD solvers, as soon as the motion of immersed objects is too fast or too sudden, pressures near boundaries and interfacial forces exhibit spurious oscillations leading to blowups. Built upon a phase-field and velocity-distribution based lattice-Boltzmann solver for multiphase flows, this paper spells out a series of numerical improvements in momentum exchange, interfacial forces, and two-way coupling to drastically reduce these typical artifacts, thus significantly expanding the types of fluid-solid coupling that we can efficiently simulate. We highlight the numerical benefits of our solver through various challenging simulation results, including comparisons to previous work and real footage.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"21 1","pages":"1 - 14"},"PeriodicalIF":0.0,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82719914","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 juxtaform, a novel approach to the interactive summarization of large shape collections for conceptual shape design. We conduct a formative study to ascertain design goals for creative shape exploration tools. Motivated by a mathematical formulation of these design goals, juxtaform integrates the exploration, analysis, selection, and refinement of large shape collections to support an interactive divergence-convergence shape design workflow. We exploit sparse, segmented sketch-stroke visual abstractions of shape and a novel visual summarization algorithm to balance the needs of shape understanding, in-situ shape juxtaposition, and visual clutter. Our evaluation is three-fold: we show that existing shape and stroke clustering algorithms do not address our design goals compared to our proposed shape corpus summarization algorithm; we compare juxtaform against a structured image gallery interface for various shape design and analysis tasks; and we present multiple compelling 2D/3D applications using juxtaform.
{"title":"Juxtaform: interactive visual summarization for exploratory shape design","authors":"Karran Pandey, Fanny Chevalier, Karan Singh","doi":"10.1145/3592436","DOIUrl":"https://doi.org/10.1145/3592436","url":null,"abstract":"We present juxtaform, a novel approach to the interactive summarization of large shape collections for conceptual shape design. We conduct a formative study to ascertain design goals for creative shape exploration tools. Motivated by a mathematical formulation of these design goals, juxtaform integrates the exploration, analysis, selection, and refinement of large shape collections to support an interactive divergence-convergence shape design workflow. We exploit sparse, segmented sketch-stroke visual abstractions of shape and a novel visual summarization algorithm to balance the needs of shape understanding, in-situ shape juxtaposition, and visual clutter. Our evaluation is three-fold: we show that existing shape and stroke clustering algorithms do not address our design goals compared to our proposed shape corpus summarization algorithm; we compare juxtaform against a structured image gallery interface for various shape design and analysis tasks; and we present multiple compelling 2D/3D applications using juxtaform.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"42 6 1","pages":"1 - 14"},"PeriodicalIF":0.0,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90274193","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}
Computation of injective (or inversion-free) maps is a key task in geometry processing, physical simulation, and shape optimization. Despite being a longstanding problem, it remains challenging due to its highly nonconvex and combinatoric nature. We propose computation of variational quasi-harmonic maps to obtain smooth inversion-free maps. Our work is built on a key observation about inversion-free maps: A planar map is a diffeomorphism if and only if it is quasi-harmonic and satisfies a special Cauchy boundary condition. We hence equate the inversion-free mapping problem to an optimal control problem derived from our theoretical result, in which we search in the space of parameters that define an elliptic PDE. We show that this problem can be solved by minimizing within a family of functionals. Similarly, our discretized functionals admit exactly injective maps as the minimizers, empirically producing inversion-free discrete maps of triangle meshes. We design efficient numerical procedures for our problem that prioritize robust convergence paths. Experiments show that on challenging examples our methods can achieve up to orders of magnitude improvement over state-of-the-art, in terms of speed or quality. Moreover, we demonstrate how to optimize a generic energy in our framework while restricting to quasi-harmonic maps.
{"title":"Variational quasi-harmonic maps for computing diffeomorphisms","authors":"Yu Wang, Minghao Guo, J. Solomon","doi":"10.1145/3592105","DOIUrl":"https://doi.org/10.1145/3592105","url":null,"abstract":"Computation of injective (or inversion-free) maps is a key task in geometry processing, physical simulation, and shape optimization. Despite being a longstanding problem, it remains challenging due to its highly nonconvex and combinatoric nature. We propose computation of variational quasi-harmonic maps to obtain smooth inversion-free maps. Our work is built on a key observation about inversion-free maps: A planar map is a diffeomorphism if and only if it is quasi-harmonic and satisfies a special Cauchy boundary condition. We hence equate the inversion-free mapping problem to an optimal control problem derived from our theoretical result, in which we search in the space of parameters that define an elliptic PDE. We show that this problem can be solved by minimizing within a family of functionals. Similarly, our discretized functionals admit exactly injective maps as the minimizers, empirically producing inversion-free discrete maps of triangle meshes. We design efficient numerical procedures for our problem that prioritize robust convergence paths. Experiments show that on challenging examples our methods can achieve up to orders of magnitude improvement over state-of-the-art, in terms of speed or quality. Moreover, we demonstrate how to optimize a generic energy in our framework while restricting to quasi-harmonic maps.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"613 1","pages":"1 - 26"},"PeriodicalIF":0.0,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76199255","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}
Subdividing non-conforming T-mesh layouts into conforming quadrangular meshes is a core component of state-of-the-art (re-)meshing methods. Typically, the required constrained assignment of integer lengths to T-Mesh edges is left to generic branch-and-cut solvers, greedy heuristics, or a combination of the two. This either does not scale well with input complexity or delivers suboptimal result quality. We introduce the Minimum-Deviation-Flow Problem in bi-directed networks (Bi-MDF) and demonstrate its use in modeling and efficiently solving a variety of T-Mesh quantization problems. We develop a fast approximate solver as well as an iterative refinement algorithm based on matching in graphs that solves Bi-MDF exactly. Compared to the state-of-the-art QuadWild [Pietroni et al. 2021] implementation on the authors' 300 dataset, our exact solver finishes after only 0.49% (total 17.06s) of their runtime (3491s) and achieves 11% lower energy while an approximation is computed after 0.09% (3.19s) of their runtime at the cost of 24% increased energy. A novel half-arc-based T-Mesh quantization formulation extends the feasible solution space to include previously unattainable quad meshes. The Bi-MDF problem is more general than our application in layout quantization, potentially enabling similar speedups for other optimization problems that fit into the scheme, such as quad mesh refinement.
将不一致的t形网格划分为一致的四边形网格是最先进的(重新)网格划分方法的核心组成部分。通常，对T-Mesh边的整数长度的约束分配留给一般的分支-切割求解器、贪婪启发式算法或两者的组合。这要么不能很好地扩展输入复杂性，要么提供次优的结果质量。我们介绍了双向网络中的最小偏差流问题(Bi-MDF)，并演示了它在建模和有效解决各种T-Mesh量化问题中的应用。我们开发了一种快速近似求解器和一种基于图中匹配的迭代优化算法，可以精确地求解Bi-MDF。与最先进的QuadWild [Pietroni et al. 2021]在作者的300个数据集上的实现相比，我们的精确求解器仅在运行时(3491秒)的0.49%(总计17.06秒)后完成，能耗降低11%，而在运行时的0.09%(3.19秒)后计算近似，能耗增加24%。一种新的基于半弧的t网格量化公式扩展了可行的解空间，包括以前无法实现的四元网格。Bi-MDF问题比我们在布局量化中的应用更普遍，潜在地为适合该方案的其他优化问题提供类似的加速，例如四网格细化。
{"title":"Min-Deviation-Flow in Bi-directed Graphs for T-Mesh Quantization","authors":"Martin Heistermann, Jethro Warnett, D. Bommes","doi":"10.1145/3592437","DOIUrl":"https://doi.org/10.1145/3592437","url":null,"abstract":"Subdividing non-conforming T-mesh layouts into conforming quadrangular meshes is a core component of state-of-the-art (re-)meshing methods. Typically, the required constrained assignment of integer lengths to T-Mesh edges is left to generic branch-and-cut solvers, greedy heuristics, or a combination of the two. This either does not scale well with input complexity or delivers suboptimal result quality. We introduce the Minimum-Deviation-Flow Problem in bi-directed networks (Bi-MDF) and demonstrate its use in modeling and efficiently solving a variety of T-Mesh quantization problems. We develop a fast approximate solver as well as an iterative refinement algorithm based on matching in graphs that solves Bi-MDF exactly. Compared to the state-of-the-art QuadWild [Pietroni et al. 2021] implementation on the authors' 300 dataset, our exact solver finishes after only 0.49% (total 17.06s) of their runtime (3491s) and achieves 11% lower energy while an approximation is computed after 0.09% (3.19s) of their runtime at the cost of 24% increased energy. A novel half-arc-based T-Mesh quantization formulation extends the feasible solution space to include previously unattainable quad meshes. The Bi-MDF problem is more general than our application in layout quantization, potentially enabling similar speedups for other optimization problems that fit into the scheme, such as quad mesh refinement.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"44 1","pages":"1 - 25"},"PeriodicalIF":0.0,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79468597","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}
Computing the intersection between two parametric surfaces (SSI) is one of the most fundamental problems in geometric and solid modeling. Maintaining the SSI topology is critical to its computation robustness. We propose a topology-driven hybrid symbolic-numeric framework to approximate rational parametric surface-surface intersection (SSI) based on a concept of interval algebraic topology analysis (IATA), which configures within a 4D interval box the SSI topology. We map the SSI topology to an algebraic system's solutions within the framework, classify and enumerate all topological cases as a mixture of four fundamental cases (or their specific sub-cases). Various complicated topological situations are covered, such as cusp points or curves, tangent points (isolated or not) or curves, tiny loops, self-intersections, or their mixtures. The theoretical formulation is also implemented numerically using advanced real solution isolation techniques, and computed within a topology-driven framework which maximally utilizes the advantages of the topology maintenance of algebraic analysis, the robustness of iterative subdivision, and the efficiency of forward marching. The approach demonstrates improved robustness under benchmark topological cases when compared with available open-source and commercial solutions, including IRIT, SISL, and Parasolid.
{"title":"Topology driven approximation to rational surface-surface intersection via interval algebraic topology analysis","authors":"Jin-San Cheng, Bingwei Zhang, Yikun Xiao, Ming Li","doi":"10.1145/3592452","DOIUrl":"https://doi.org/10.1145/3592452","url":null,"abstract":"Computing the intersection between two parametric surfaces (SSI) is one of the most fundamental problems in geometric and solid modeling. Maintaining the SSI topology is critical to its computation robustness. We propose a topology-driven hybrid symbolic-numeric framework to approximate rational parametric surface-surface intersection (SSI) based on a concept of interval algebraic topology analysis (IATA), which configures within a 4D interval box the SSI topology. We map the SSI topology to an algebraic system's solutions within the framework, classify and enumerate all topological cases as a mixture of four fundamental cases (or their specific sub-cases). Various complicated topological situations are covered, such as cusp points or curves, tangent points (isolated or not) or curves, tiny loops, self-intersections, or their mixtures. The theoretical formulation is also implemented numerically using advanced real solution isolation techniques, and computed within a topology-driven framework which maximally utilizes the advantages of the topology maintenance of algebraic analysis, the robustness of iterative subdivision, and the efficiency of forward marching. The approach demonstrates improved robustness under benchmark topological cases when compared with available open-source and commercial solutions, including IRIT, SISL, and Parasolid.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"31 1","pages":"1 - 16"},"PeriodicalIF":0.0,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76927941","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}
Kangrui Xue, Ryan M. Aronson, Jui-Hsien Wang, Timothy R. Langlois, Doug L. James
We introduce a practical framework for synthesizing bubble-based water sounds that captures the rich inter-bubble coupling effects responsible for low-frequency acoustic emissions from bubble clouds. We propose coupled-bubble oscillator models with regularized singularities, and techniques to reduce the computational cost of time stepping with dense, time-varying mass matrices. Airborne acoustic emissions are estimated using finite-difference time-domain (FDTD) methods. We propose a simple, analytical surface-acceleration model, and a sample-and-hold GPU wavesolver that is simple and faster than prior CPU wavesolvers. Sound synthesis results are demonstrated using bubbly flows from incompressible, two-phase simulations, as well as procedurally generated examples using single-phase FLIP fluid animations. Our results demonstrate sound simulations with hundreds of thousands of bubbles, and perceptually significant frequency transformations with fuller low-frequency content.
{"title":"Improved Water Sound Synthesis using Coupled Bubbles","authors":"Kangrui Xue, Ryan M. Aronson, Jui-Hsien Wang, Timothy R. Langlois, Doug L. James","doi":"10.1145/3592424","DOIUrl":"https://doi.org/10.1145/3592424","url":null,"abstract":"We introduce a practical framework for synthesizing bubble-based water sounds that captures the rich inter-bubble coupling effects responsible for low-frequency acoustic emissions from bubble clouds. We propose coupled-bubble oscillator models with regularized singularities, and techniques to reduce the computational cost of time stepping with dense, time-varying mass matrices. Airborne acoustic emissions are estimated using finite-difference time-domain (FDTD) methods. We propose a simple, analytical surface-acceleration model, and a sample-and-hold GPU wavesolver that is simple and faster than prior CPU wavesolvers. Sound synthesis results are demonstrated using bubbly flows from incompressible, two-phase simulations, as well as procedurally generated examples using single-phase FLIP fluid animations. Our results demonstrate sound simulations with hundreds of thousands of bubbles, and perceptually significant frequency transformations with fuller low-frequency content.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"29 1","pages":"1 - 13"},"PeriodicalIF":0.0,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83639049","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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