The target of the occluder is to use very few faces to maintain similar occlusion properties of the original 3D model. In this paper, we present DR-Occluder, a novel coarse-to-fine framework for occluder generation that leverages differentiable rendering to optimize a triangle set to an occluder. Unlike prior work, which has not utilized differentiable rendering for this task, our approach provides the ability to optimize a 3D shape to defined targets. Given a 3D model as input, our method first projects it to silhouette images, which are then processed by a convolution network to output a group of vertex offsets. These offsets are used to transform a group of distributed triangles into a preliminary occluder, which is further optimized by differentiable rendering. Finally, triangles whose area is smaller than a threshold are removed to obtain the final occluder. Our extensive experiments demonstrate that DR-Occluder significantly outperforms state-of-the-art methods in terms of occlusion quality. Furthermore, we compare the performance of our method with other approaches in a commercial engine, providing compelling evidence of its effectiveness.
{"title":"DR-Occluder: Generating Occluders Using Differentiable Rendering","authors":"Jiaxian Wu, Yue Lin, Dehui Lu","doi":"10.1145/3618346","DOIUrl":"https://doi.org/10.1145/3618346","url":null,"abstract":"The target of the occluder is to use very few faces to maintain similar occlusion properties of the original 3D model. In this paper, we present DR-Occluder, a novel coarse-to-fine framework for occluder generation that leverages differentiable rendering to optimize a triangle set to an occluder. Unlike prior work, which has not utilized differentiable rendering for this task, our approach provides the ability to optimize a 3D shape to defined targets. Given a 3D model as input, our method first projects it to silhouette images, which are then processed by a convolution network to output a group of vertex offsets. These offsets are used to transform a group of distributed triangles into a preliminary occluder, which is further optimized by differentiable rendering. Finally, triangles whose area is smaller than a threshold are removed to obtain the final occluder. Our extensive experiments demonstrate that DR-Occluder significantly outperforms state-of-the-art methods in terms of occlusion quality. Furthermore, we compare the performance of our method with other approaches in a commercial engine, providing compelling evidence of its effectiveness.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"58 23","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":"138604952","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}
Haitao Yang, Bo Sun, Liyan Chen, Amy Pavel, Qixing Huang
We study how to optimize the latent space of neural shape generators that map latent codes to 3D deformable shapes. The key focus is to look at a deformable shape generator from a differential geometry perspective. We define a Riemannian metric based on as-rigid-as-possible and as-conformal-as-possible deformation energies. Under this metric, we study two desired properties of the latent space: 1) straight-line interpolations in latent codes follow geodesic curves; 2) latent codes disentangle pose and shape variations at different scales. Strictly enforcing the geometric interpolation property, however, only applies if the metric matrix is a constant. We show how to achieve this property approximately by enforcing that geodesic interpolations are axis-aligned, i.e., interpolations along coordinate axis follow geodesic curves. In addition, we introduce a novel approach that decouples pose and shape variations via generalized eigendecomposition. We also study efficient regularization terms for learning deformable shape generators, e.g., that promote smooth interpolations. Experimental results on benchmark datasets show that our approach leads to interpretable latent codes, improves the generalizability of synthetic shapes, and enhances performance in geodesic interpolation and geodesic shooting.
{"title":"GeoLatent: A Geometric Approach to Latent Space Design for Deformable Shape Generators","authors":"Haitao Yang, Bo Sun, Liyan Chen, Amy Pavel, Qixing Huang","doi":"10.1145/3618371","DOIUrl":"https://doi.org/10.1145/3618371","url":null,"abstract":"We study how to optimize the latent space of neural shape generators that map latent codes to 3D deformable shapes. The key focus is to look at a deformable shape generator from a differential geometry perspective. We define a Riemannian metric based on as-rigid-as-possible and as-conformal-as-possible deformation energies. Under this metric, we study two desired properties of the latent space: 1) straight-line interpolations in latent codes follow geodesic curves; 2) latent codes disentangle pose and shape variations at different scales. Strictly enforcing the geometric interpolation property, however, only applies if the metric matrix is a constant. We show how to achieve this property approximately by enforcing that geodesic interpolations are axis-aligned, i.e., interpolations along coordinate axis follow geodesic curves. In addition, we introduce a novel approach that decouples pose and shape variations via generalized eigendecomposition. We also study efficient regularization terms for learning deformable shape generators, e.g., that promote smooth interpolations. Experimental results on benchmark datasets show that our approach leads to interpretable latent codes, improves the generalizability of synthetic shapes, and enhances performance in geodesic interpolation and geodesic shooting.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"32 25","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":"138601407","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}
Xingqiao Li, Xingyu Ni, Bo Zhu, Bin Wang, Bao Chen
This paper presents a novel level-set method that combines gradient augmentation and reference mapping to enable high-fidelity interface tracking and surface tension flow simulation, preserving small-scale volumes and interface features comparable to the grid size. At the center of our approach is a novel reference-map algorithm to concurrently convect level-set values and gradients, both of which are crucial for reconstructing a dynamic surface exhibiting small-scale volumes. In addition, we develop a full pipeline for the new level-set scheme by incorporating a novel extrapolation algorithm and an enhanced reinitialization procedure into our reference-map method. We test our algorithm by simulating complex surface tension flow phenomena such as raindrop collision, merging, and splashing. We also showcase the efficacy of our approach by performing validation tests and comparing it to a broad range of existing level-set algorithms.
{"title":"GARM-LS: A Gradient-Augmented Reference-Map Method for Level-Set Fluid Simulation","authors":"Xingqiao Li, Xingyu Ni, Bo Zhu, Bin Wang, Bao Chen","doi":"10.1145/3618377","DOIUrl":"https://doi.org/10.1145/3618377","url":null,"abstract":"This paper presents a novel level-set method that combines gradient augmentation and reference mapping to enable high-fidelity interface tracking and surface tension flow simulation, preserving small-scale volumes and interface features comparable to the grid size. At the center of our approach is a novel reference-map algorithm to concurrently convect level-set values and gradients, both of which are crucial for reconstructing a dynamic surface exhibiting small-scale volumes. In addition, we develop a full pipeline for the new level-set scheme by incorporating a novel extrapolation algorithm and an enhanced reinitialization procedure into our reference-map method. We test our algorithm by simulating complex surface tension flow phenomena such as raindrop collision, merging, and splashing. We also showcase the efficacy of our approach by performing validation tests and comparing it to a broad range of existing level-set algorithms.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"20 8","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":"138601966","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}
Kinetic solvers for incompressible fluid simulation were designed to run efficiently on massively parallel architectures such as GPUs. While these lattice Boltzmann solvers have recently proven much faster and more accurate than the macroscopic Navier-Stokes-based solvers traditionally used in graphics, it systematically comes at the price of a very large memory requirement: a mesoscopic discretization of statistical mechanics requires over an order of magnitude more variables per grid node than most fluid solvers in graphics. In order to open up kinetic simulation to gaming and simulation software packages on commodity hardware, we propose a HighOrder Moment-Encoded Lattice-Boltzmann-Method solver which we coined HOME-LBM, requiring only the storage of a few moments per grid node, with little to no loss of accuracy in the typical simulation scenarios encountered in graphics. We show that our lightweight and lightspeed fluid solver requires three times less memory and runs ten times faster than state-of-the-art kinetic solvers, for a nearly-identical visual output.
{"title":"High-Order Moment-Encoded Kinetic Simulation of Turbulent Flows","authors":"Wei Li, Tongtong Wang, Zherong Pan, Xifeng Gao, Kui Wu, Mathieu Desbrun","doi":"10.1145/3618341","DOIUrl":"https://doi.org/10.1145/3618341","url":null,"abstract":"Kinetic solvers for incompressible fluid simulation were designed to run efficiently on massively parallel architectures such as GPUs. While these lattice Boltzmann solvers have recently proven much faster and more accurate than the macroscopic Navier-Stokes-based solvers traditionally used in graphics, it systematically comes at the price of a very large memory requirement: a mesoscopic discretization of statistical mechanics requires over an order of magnitude more variables per grid node than most fluid solvers in graphics. In order to open up kinetic simulation to gaming and simulation software packages on commodity hardware, we propose a HighOrder Moment-Encoded Lattice-Boltzmann-Method solver which we coined HOME-LBM, requiring only the storage of a few moments per grid node, with little to no loss of accuracy in the typical simulation scenarios encountered in graphics. We show that our lightweight and lightspeed fluid solver requires three times less memory and runs ten times faster than state-of-the-art kinetic solvers, for a nearly-identical visual output.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"10 8","pages":"1 - 13"},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138602110","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 method for the generation of higher-order tetrahedral meshes. In contrast to previous methods, the curved tetrahedral elements are guaranteed to be free of degeneracies and inversions while conforming exactly to prescribed piecewise polynomial surfaces, such as domain boundaries or material interfaces. Arbitrary polynomial order is supported. Algorithmically, the polynomial input surfaces are first covered by a single layer of carefully constructed curved elements using a recursive refinement procedure that provably avoids degeneracies and inversions. These tetrahedral elements are designed such that the remaining space is bounded piecewise linearly. In this way, our method effectively reduces the curved meshing problem to the classical problem of linear mesh generation (for the remaining space).
{"title":"3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing","authors":"Payam Khanteimouri, M. Campen","doi":"10.1145/3618332","DOIUrl":"https://doi.org/10.1145/3618332","url":null,"abstract":"We present a method for the generation of higher-order tetrahedral meshes. In contrast to previous methods, the curved tetrahedral elements are guaranteed to be free of degeneracies and inversions while conforming exactly to prescribed piecewise polynomial surfaces, such as domain boundaries or material interfaces. Arbitrary polynomial order is supported. Algorithmically, the polynomial input surfaces are first covered by a single layer of carefully constructed curved elements using a recursive refinement procedure that provably avoids degeneracies and inversions. These tetrahedral elements are designed such that the remaining space is bounded piecewise linearly. In this way, our method effectively reduces the curved meshing problem to the classical problem of linear mesh generation (for the remaining space).","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"3 1","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":"138603892","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 method for interactively authoring and simulating meandering river networks. Starting from a terrain with an initial low-resolution network encoded as a directed graph, we simulate the evolution of the path of the different river channels using a physically-based migration equation augmented with control terms. The curvature-based terms in the equation allow us to reproduce phenomena identified in geomorphology, such as downstream migration of bends. Control terms account for the influence of the landscape topography and user-defined river trajectory constraints. Our model implements abrupt events that shape meandering networks, such as cutoffs forming oxbow lakes and avulsions. We visually show the effectiveness of our method and compare the generated networks quantitatively to river data by analyzing sinuosity and wavelength metrics. Our vector-based model runs at interactive rates, allowing for efficient authoring of large-scale meandering networks.
{"title":"Authoring and Simulating Meandering Rivers","authors":"A. Paris, É. Guérin, Pauline Collon, E. Galin","doi":"10.1145/3618350","DOIUrl":"https://doi.org/10.1145/3618350","url":null,"abstract":"We present a method for interactively authoring and simulating meandering river networks. Starting from a terrain with an initial low-resolution network encoded as a directed graph, we simulate the evolution of the path of the different river channels using a physically-based migration equation augmented with control terms. The curvature-based terms in the equation allow us to reproduce phenomena identified in geomorphology, such as downstream migration of bends. Control terms account for the influence of the landscape topography and user-defined river trajectory constraints. Our model implements abrupt events that shape meandering networks, such as cutoffs forming oxbow lakes and avulsions. We visually show the effectiveness of our method and compare the generated networks quantitatively to river data by analyzing sinuosity and wavelength metrics. Our vector-based model runs at interactive rates, allowing for efficient authoring of large-scale meandering networks.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"20 16","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":"138604225","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}
Autonomous surface reconstruction of 3D scenes has been intensely studied in recent years, however, it is still difficult to accurately reconstruct all the surface details of complex scenes with complicated object relations and severe occlusions, which makes the reconstruction results not suitable for direct use in applications such as gaming and virtual reality. Therefore, instead of reconstructing the detailed surfaces, we aim to recompose the scene with CAD models retrieved from a given dataset to faithfully reflect the object geometry and arrangement in the given scene. Moreover, unlike most of the previous works on scene CAD recomposition requiring an offline reconstructed scene or captured video as input, which leads to significant data redundancy, we propose a novel online scene CAD recomposition method with autonomous scanning, which efficiently recomposes the scene with the guidance of automatically optimized Next-Best-View (NBV) in a single online scanning pass. Based on the key observation that spatial relation in the scene can not only constrain the object pose and layout optimization but also guide the NBV generation, our system consists of two key modules: relation-guided CAD recomposition module that uses relation-constrained global optimization to get accurate object pose and layout estimation, and relation-aware NBV generation module that makes the exploration during the autonomous scanning tailored for our composition task. Extensive experiments have been conducted to show the superiority of our method over previous methods in scanning efficiency and retrieval accuracy as well as the importance of each key component of our method.
{"title":"Online Scene CAD Recomposition via Autonomous Scanning","authors":"Changhao Li, Junfu Guo, Ruizhen Hu, Ligang Liu","doi":"10.1145/3618339","DOIUrl":"https://doi.org/10.1145/3618339","url":null,"abstract":"Autonomous surface reconstruction of 3D scenes has been intensely studied in recent years, however, it is still difficult to accurately reconstruct all the surface details of complex scenes with complicated object relations and severe occlusions, which makes the reconstruction results not suitable for direct use in applications such as gaming and virtual reality. Therefore, instead of reconstructing the detailed surfaces, we aim to recompose the scene with CAD models retrieved from a given dataset to faithfully reflect the object geometry and arrangement in the given scene. Moreover, unlike most of the previous works on scene CAD recomposition requiring an offline reconstructed scene or captured video as input, which leads to significant data redundancy, we propose a novel online scene CAD recomposition method with autonomous scanning, which efficiently recomposes the scene with the guidance of automatically optimized Next-Best-View (NBV) in a single online scanning pass. Based on the key observation that spatial relation in the scene can not only constrain the object pose and layout optimization but also guide the NBV generation, our system consists of two key modules: relation-guided CAD recomposition module that uses relation-constrained global optimization to get accurate object pose and layout estimation, and relation-aware NBV generation module that makes the exploration during the autonomous scanning tailored for our composition task. Extensive experiments have been conducted to show the superiority of our method over previous methods in scanning efficiency and retrieval accuracy as well as the importance of each key component of our method.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"53 16","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":"138602325","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 introduce an adaptive level-of-detail technique for ray tracing triangle meshes that aims to reduce the memory bandwidth used during ray traversal, which can be the bottleneck for rendering time with large scenes and the primary consumer of energy. We propose a specific data structure for hierarchically representing triangle meshes, allowing localized decisions for the desired mesh resolution per ray. Starting with the lowest-resolution triangle mesh level, higher-resolution levels are generated by tessellating each triangle into four via splitting its edges with arbitrarily-placed vertices. We fit the resulting mesh hierarchy into a specialized acceleration structure to perform on-the-fly tessellation level selection during ray traversal. Our structure reduces both storage cost and data movement during rendering, which are the main consumers of energy. It also allows continuous transitions between detail levels, while locally adjusting the mesh resolution per ray and preserving watertightness. We present how this structure can be used with both primary and secondary rays for reflections and shadows, which can intersect with different tessellation levels, providing consistent results. We also propose specific hardware units to cover the cost of additional compute needed for level-of-detail operations. We evaluate our method using a cycle-accurate simulation of a custom ray tracing hardware architecture. Our results show that, as compared to traditional bounding volume hierarchies, our method can provide more than an order of magnitude reduction in energy use and render time, given sufficient computational resources.
{"title":"Locally-Adaptive Level-of-Detail for Hardware-Accelerated Ray Tracing","authors":"Jacob Haydel, Cem Yuksel, Larry Seiler","doi":"10.1145/3618359","DOIUrl":"https://doi.org/10.1145/3618359","url":null,"abstract":"We introduce an adaptive level-of-detail technique for ray tracing triangle meshes that aims to reduce the memory bandwidth used during ray traversal, which can be the bottleneck for rendering time with large scenes and the primary consumer of energy. We propose a specific data structure for hierarchically representing triangle meshes, allowing localized decisions for the desired mesh resolution per ray. Starting with the lowest-resolution triangle mesh level, higher-resolution levels are generated by tessellating each triangle into four via splitting its edges with arbitrarily-placed vertices. We fit the resulting mesh hierarchy into a specialized acceleration structure to perform on-the-fly tessellation level selection during ray traversal. Our structure reduces both storage cost and data movement during rendering, which are the main consumers of energy. It also allows continuous transitions between detail levels, while locally adjusting the mesh resolution per ray and preserving watertightness. We present how this structure can be used with both primary and secondary rays for reflections and shadows, which can intersect with different tessellation levels, providing consistent results. We also propose specific hardware units to cover the cost of additional compute needed for level-of-detail operations. We evaluate our method using a cycle-accurate simulation of a custom ray tracing hardware architecture. Our results show that, as compared to traditional bounding volume hierarchies, our method can provide more than an order of magnitude reduction in energy use and render time, given sufficient computational resources.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"27 7","pages":"1 - 15"},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138602621","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 estimate the three Herschel-Bulkley parameters (yield stress σY, power-law index n, and consistency parameter η) for shear-dependent fluid-like materials possibly with large-scale inclusions, for which rheometers may fail to provide a useful measurement. We perform experiments using the unknown material for dam-break (or column collapse) setups and capture video footage. We then use simulations to optimize for the material parameters. For better match up with the simple shear flow encountered in a rheometer, we modify the flow rule for the elasto-viscoplastic Herschel-Bulkley model. Analyzing the loss landscape for optimization, we realize a similarity relation; material parameters far away within this relation would result in matched simulations, making it hard to distinguish the parameters. We found that by exploiting the setup dependency of the similarity relation, we can improve on the estimation using multiple setups, which we propose by analyzing the Hessian of the similarity relation. We validate the efficacy of our method by comparing the estimations to the measurements from a rheometer (for materials without large-scale inclusions) and show applications to materials with large-scale inclusions, including various salad or pasta sauces, and congee.
{"title":"Non-Newtonian ViRheometry via Similarity Analysis","authors":"Mitsuki Hamamichi, Kentaro Nagasawa, Masato Okada, Ryohei Seto, Yonghao Yue","doi":"10.1145/3618310","DOIUrl":"https://doi.org/10.1145/3618310","url":null,"abstract":"We estimate the three Herschel-Bulkley parameters (yield stress σY, power-law index n, and consistency parameter η) for shear-dependent fluid-like materials possibly with large-scale inclusions, for which rheometers may fail to provide a useful measurement. We perform experiments using the unknown material for dam-break (or column collapse) setups and capture video footage. We then use simulations to optimize for the material parameters. For better match up with the simple shear flow encountered in a rheometer, we modify the flow rule for the elasto-viscoplastic Herschel-Bulkley model. Analyzing the loss landscape for optimization, we realize a similarity relation; material parameters far away within this relation would result in matched simulations, making it hard to distinguish the parameters. We found that by exploiting the setup dependency of the similarity relation, we can improve on the estimation using multiple setups, which we propose by analyzing the Hessian of the similarity relation. We validate the efficacy of our method by comparing the estimations to the measurements from a rheometer (for materials without large-scale inclusions) and show applications to materials with large-scale inclusions, including various salad or pasta sauces, and congee.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"4 5","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":"138603489","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}
Kirchhoff-Love shells are commonly used in many branches of engineering, including in computer graphics, but have so far been simulated only under limited nonlinear material options. We derive the Kirchhoff-Love thin-shell mechanical energy for an arbitrary 3D volumetric hyperelastic material, including isotropic materials, anisotropic materials, and materials whereby the energy includes both even and odd powers of the principal stretches. We do this by starting with any 3D hyperelastic material, and then analytically computing the corresponding thin-shell energy limit. This explicitly identifies and separates in-plane stretching and bending terms, and avoids numerical quadrature. Thus, in-plane stretching and bending are shown to originate from one and the same process (volumetric elasticity of thin objects), as opposed to from two separate processes as done traditionally in cloth simulation. Because we can simulate materials that include both even and odd powers of stretches, we can accommodate standard mesh distortion energies previously employed for 3D solid simulations, such as Symmetric ARAP and Co-rotational materials. We relate the terms of our energy to those of prior work on Kirchhoff-Love thin-shells in computer graphics that assumed small in-plane stretches, and demonstrate the visual difference due to the presence of our exact stretching and bending terms. Furthermore, our formulation allows us to categorize all distinct hyperelastic Kirchhoff-Love thin-shell energies. Specifically, we prove that for Kirchhoff-Love thin-shells, the space of all hyperelastic materials collapses to two-dimensional hyperelastic materials. This observation enables us to create an interface for the design of thin-shell Kirchhoff-Love mechanical energies, which in turn enables us to create thin-shell materials that exhibit arbitrary stiffness profiles under large deformations.
{"title":"Kirchhoff-Love Shells with Arbitrary Hyperelastic Materials","authors":"Jiahao Wen, J. Barbič","doi":"10.1145/3618405","DOIUrl":"https://doi.org/10.1145/3618405","url":null,"abstract":"Kirchhoff-Love shells are commonly used in many branches of engineering, including in computer graphics, but have so far been simulated only under limited nonlinear material options. We derive the Kirchhoff-Love thin-shell mechanical energy for an arbitrary 3D volumetric hyperelastic material, including isotropic materials, anisotropic materials, and materials whereby the energy includes both even and odd powers of the principal stretches. We do this by starting with any 3D hyperelastic material, and then analytically computing the corresponding thin-shell energy limit. This explicitly identifies and separates in-plane stretching and bending terms, and avoids numerical quadrature. Thus, in-plane stretching and bending are shown to originate from one and the same process (volumetric elasticity of thin objects), as opposed to from two separate processes as done traditionally in cloth simulation. Because we can simulate materials that include both even and odd powers of stretches, we can accommodate standard mesh distortion energies previously employed for 3D solid simulations, such as Symmetric ARAP and Co-rotational materials. We relate the terms of our energy to those of prior work on Kirchhoff-Love thin-shells in computer graphics that assumed small in-plane stretches, and demonstrate the visual difference due to the presence of our exact stretching and bending terms. Furthermore, our formulation allows us to categorize all distinct hyperelastic Kirchhoff-Love thin-shell energies. Specifically, we prove that for Kirchhoff-Love thin-shells, the space of all hyperelastic materials collapses to two-dimensional hyperelastic materials. This observation enables us to create an interface for the design of thin-shell Kirchhoff-Love mechanical energies, which in turn enables us to create thin-shell materials that exhibit arbitrary stiffness profiles under large deformations.","PeriodicalId":7077,"journal":{"name":"ACM Transactions on Graphics (TOG)","volume":"3 5","pages":"1 - 15"},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138603888","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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