Shlomi Steinberg, R. Ramamoorthi, Benedikt Bitterli, Arshiya Mollazainali, Eugene d'Eon, Matt Pharr
Free-space diffractions are an optical phenomenon where light appears to "bend" around the geometric edges and corners of scene objects. In this paper we present an efficient method to simulate such effects. We derive an edge-based formulation of Fraunhofer diffraction, which is well suited to the common (triangular) geometric meshes used in computer graphics. Our method dynamically constructs a free-space diffraction BSDF by considering the geometry around the intersection point of a ray of light with an object, and we present an importance sampling strategy for these BSDFs. Our method is unique in requiring only ray tracing to produce free-space diffractions, works with general meshes, requires no geometry preprocessing, and is designed to work with path tracers with a linear rendering equation. We show that we are able to reproduce accurate diffraction lobes, and, in contrast to any existing method, are able to handle complex, real-world geometry. This work serves to connect free-space diffractions to the efficient path tracing tools from computer graphics.
{"title":"A Free-Space Diffraction BSDF","authors":"Shlomi Steinberg, R. Ramamoorthi, Benedikt Bitterli, Arshiya Mollazainali, Eugene d'Eon, Matt Pharr","doi":"10.1145/3658166","DOIUrl":"https://doi.org/10.1145/3658166","url":null,"abstract":"Free-space diffractions are an optical phenomenon where light appears to \"bend\" around the geometric edges and corners of scene objects. In this paper we present an efficient method to simulate such effects. We derive an edge-based formulation of Fraunhofer diffraction, which is well suited to the common (triangular) geometric meshes used in computer graphics. Our method dynamically constructs a free-space diffraction BSDF by considering the geometry around the intersection point of a ray of light with an object, and we present an importance sampling strategy for these BSDFs. Our method is unique in requiring only ray tracing to produce free-space diffractions, works with general meshes, requires no geometry preprocessing, and is designed to work with path tracers with a linear rendering equation. We show that we are able to reproduce accurate diffraction lobes, and, in contrast to any existing method, are able to handle complex, real-world geometry. This work serves to connect free-space diffractions to the efficient path tracing tools from computer graphics.","PeriodicalId":50913,"journal":{"name":"ACM Transactions on Graphics","volume":null,"pages":null},"PeriodicalIF":7.8,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141821095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
As a natural extension to the harmonic coordinates, the biharmonic coordinates have been found superior for planar shape and image manipulation with an enriched deformation space. However, the 3D biharmonic coordinates and their derivatives have remained unexplored. In this work, we derive closed-form expressions for biharmonic coordinates and their derivatives for 3D triangular cages. The core of our derivation lies in computing the closed-form expressions for the integral of the Euclidean distance over a triangle and its derivatives. The derived 3D biharmonic coordinates not only fill a missing component in methods of generalized barycentric coordinates but also pave the way for various interesting applications in practice, including producing a family of biharmonic deformations, solving variational shape deformations, and even unlocking the closed-form expressions for recently-introduced Somigliana coordinates for both fast and accurate evaluations.
{"title":"Biharmonic Coordinates and their Derivatives for Triangular 3D Cages","authors":"J. Thiery, Élie Michel, Jiong Chen","doi":"10.1145/3658208","DOIUrl":"https://doi.org/10.1145/3658208","url":null,"abstract":"\u0000 As a natural extension to the harmonic coordinates, the biharmonic coordinates have been found superior for planar shape and image manipulation with an enriched deformation space. However, the 3D biharmonic coordinates and their derivatives have remained unexplored. In this work, we derive closed-form expressions for biharmonic coordinates and their derivatives for 3D triangular cages. The core of our derivation lies in computing the closed-form expressions for the integral of the Euclidean distance over a triangle\u0000 and\u0000 its derivatives. The derived 3D biharmonic coordinates not only fill a missing component in methods of generalized barycentric coordinates but also pave the way for various interesting applications in practice, including producing a family of biharmonic deformations, solving variational shape deformations, and even unlocking the closed-form expressions for recently-introduced Somigliana coordinates for both fast and accurate evaluations.\u0000","PeriodicalId":50913,"journal":{"name":"ACM Transactions on Graphics","volume":null,"pages":null},"PeriodicalIF":7.8,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141821747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The method of fundamental solutions (MFS) and its associated boundary element method (BEM) have gained popularity in computer graphics due to the reduced dimensionality they offer: for three-dimensional linear problems, they only require variables on the domain boundary to solve and evaluate the solution throughout space, making them a valuable tool in a wide variety of applications. However, MFS and BEM have poor computational scalability and huge memory requirements for large-scale problems, limiting their applicability and efficiency in practice. By leveraging connections with Gaussian Processes and exploiting the sparse structure of the inverses of boundary integral matrices, we introduce a variational preconditioner that can be computed via a sparse inverse-Cholesky factorization in a massively parallel manner. We show that applying our preconditioner to the Preconditioned Conjugate Gradient algorithm greatly improves the efficiency of MFS or BEM solves, up to four orders of magnitude in our series of tests.
基本解法（MFS）及其相关的边界元法（BEM）在计算机图形学领域广受欢迎，这是因为它们可以降低维度：对于三维线性问题，它们只需要域边界上的变量就可以求解并评估整个空间的解，这使它们成为各种应用中的重要工具。然而，MFS 和 BEM 的计算可扩展性较差，而且在处理大规模问题时需要占用大量内存，这限制了它们在实际应用中的适用性和效率。通过利用与高斯过程（Gaussian Processes）的联系和边界积分矩阵逆的稀疏结构，我们引入了一种变分预处理器，它可以通过稀疏的逆-Cholesky 因式分解以大规模并行的方式进行计算。我们的研究表明，将我们的预处理器应用于预处理共轭梯度算法，可大大提高 MFS 或 BEM 的求解效率，在我们的一系列测试中，效率最高可达四个数量级。
{"title":"Lightning-fast Method of Fundamental Solutions","authors":"Jiong Chen, Florian Schaefer, Mathieu Desbrun","doi":"10.1145/3658199","DOIUrl":"https://doi.org/10.1145/3658199","url":null,"abstract":"The method of fundamental solutions (MFS) and its associated boundary element method (BEM) have gained popularity in computer graphics due to the reduced dimensionality they offer: for three-dimensional linear problems, they only require variables on the domain boundary to solve and evaluate the solution throughout space, making them a valuable tool in a wide variety of applications. However, MFS and BEM have poor computational scalability and huge memory requirements for large-scale problems, limiting their applicability and efficiency in practice. By leveraging connections with Gaussian Processes and exploiting the sparse structure of the inverses of boundary integral matrices, we introduce a variational preconditioner that can be computed via a sparse inverse-Cholesky factorization in a massively parallel manner. We show that applying our preconditioner to the Preconditioned Conjugate Gradient algorithm greatly improves the efficiency of MFS or BEM solves, up to four orders of magnitude in our series of tests.","PeriodicalId":50913,"journal":{"name":"ACM Transactions on Graphics","volume":null,"pages":null},"PeriodicalIF":7.8,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141822451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yiwen Ju, Xingyi Du, Qingnan Zhou, Nathan Carr, Tao Ju
We present a method for generating a simplicial (e.g., triangular or tetrahedral) grid to enable adaptive discretization of implicit shapes defined by a vector function. Such shapes, which we call implicit complexes, are generalizations of implicit surfaces and useful for representing non-smooth and non-manifold structures. While adaptive grid generation has been extensively studied for polygonizing implicit surfaces, few methods are designed for implicit complexes. Our method can generate adaptive grids for several implicit complexes, including arrangements of implicit surfaces, CSG shapes, material interfaces, and curve networks. Importantly, our method adapts the grid to the geometry of not only the implicit surfaces but also their lower-dimensional intersections. We demonstrate how our method enables efficient and detail-preserving discretization of non-trivial implicit shapes.
{"title":"Adaptive grid generation for discretizing implicit complexes","authors":"Yiwen Ju, Xingyi Du, Qingnan Zhou, Nathan Carr, Tao Ju","doi":"10.1145/3658215","DOIUrl":"https://doi.org/10.1145/3658215","url":null,"abstract":"We present a method for generating a simplicial (e.g., triangular or tetrahedral) grid to enable adaptive discretization of implicit shapes defined by a vector function. Such shapes, which we call implicit complexes, are generalizations of implicit surfaces and useful for representing non-smooth and non-manifold structures. While adaptive grid generation has been extensively studied for polygonizing implicit surfaces, few methods are designed for implicit complexes. Our method can generate adaptive grids for several implicit complexes, including arrangements of implicit surfaces, CSG shapes, material interfaces, and curve networks. Importantly, our method adapts the grid to the geometry of not only the implicit surfaces but also their lower-dimensional intersections. We demonstrate how our method enables efficient and detail-preserving discretization of non-trivial implicit shapes.","PeriodicalId":50913,"journal":{"name":"ACM Transactions on Graphics","volume":null,"pages":null},"PeriodicalIF":7.8,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141823356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ningxiao Tao, Liangwang Ruan, Yitong Deng, Bo Zhu, Bin Wang, Bao Chen
This paper introduces a novel physically-based vortex fluid model for films, aimed at accurately simulating cascading vortical structures on deforming thin films. Central to our approach is a novel mechanism decomposing the film's tangential velocity into circulation and dilatation components. These components are then evolved using a hybrid particle-mesh method, enabling the effective reconstruction of three-dimensional tangential velocities and seamlessly integrating surfactant and thickness dynamics into a unified framework. By coupling with its normal component and surface-tension model, our method is particularly adept at depicting complex interactions between in-plane vortices and out-of-plane physical phenomena, such as gravity, surfactant dynamics, and solid boundary, leading to highly realistic simulations of complex thin-film dynamics, achieving an unprecedented level of vortical details and physical realism.
{"title":"A Vortex Particle-on-Mesh Method for Soap Film Simulation","authors":"Ningxiao Tao, Liangwang Ruan, Yitong Deng, Bo Zhu, Bin Wang, Bao Chen","doi":"10.1145/3658165","DOIUrl":"https://doi.org/10.1145/3658165","url":null,"abstract":"This paper introduces a novel physically-based vortex fluid model for films, aimed at accurately simulating cascading vortical structures on deforming thin films. Central to our approach is a novel mechanism decomposing the film's tangential velocity into circulation and dilatation components. These components are then evolved using a hybrid particle-mesh method, enabling the effective reconstruction of three-dimensional tangential velocities and seamlessly integrating surfactant and thickness dynamics into a unified framework. By coupling with its normal component and surface-tension model, our method is particularly adept at depicting complex interactions between in-plane vortices and out-of-plane physical phenomena, such as gravity, surfactant dynamics, and solid boundary, leading to highly realistic simulations of complex thin-film dynamics, achieving an unprecedented level of vortical details and physical realism.","PeriodicalId":50913,"journal":{"name":"ACM Transactions on Graphics","volume":null,"pages":null},"PeriodicalIF":7.8,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141823400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The behavior of a rigid body primarily depends on its mass moments, which consist of the mass, center of mass, and moments of inertia. It is possible to manipulate these quantities without altering the geometric appearance of an object by introducing cavities in its interior. Algorithms that find cavities of suitable shapes and sizes have enabled the computational design of spinning tops, yo-yos, wheels, buoys, and statically balanced objects. Previous work is based, for example, on topology optimization on voxel grids, which introduces a large number of optimization variables and box constraints, or offset surface computation, which cannot guarantee that solutions to a feasible problem will always be found. In this work, we provide a mathematical analysis of constrained topology optimization problems that depend only on mass moments. This class of problems covers, among others, all applications mentioned above. Our main result is to show that no matter the outer shape of the rigid body to be optimized or the optimization objective and constraints considered, the optimal solution always features a quadric-shaped interface between material and cavities. This proves that optimal interfaces are always ellipsoids, hyperboloids, paraboloids, or one of a few degenerate cases, such as planes. This insight lets us replace a difficult topology optimization problem with a provably equivalent non-linear equation system in a small number (<10) of variables, which represent the coefficients of the quadric. This system can be solved in a few seconds for most examples, provides insights into the geometric structure of many specific applications, and lets us describe their solution properties. Finally, our method integrates seamlessly into modern fabrication workflows because our solutions are analytical surfaces that are native to the CAD domain.
{"title":"Spin-It Faster: Quadrics Solve All Topology Optimization Problems That Depend Only On Mass Moments","authors":"Christian Hafner, Mickaël Ly, Christopher Wojtan","doi":"10.1145/3658194","DOIUrl":"https://doi.org/10.1145/3658194","url":null,"abstract":"The behavior of a rigid body primarily depends on its mass moments, which consist of the mass, center of mass, and moments of inertia. It is possible to manipulate these quantities without altering the geometric appearance of an object by introducing cavities in its interior. Algorithms that find cavities of suitable shapes and sizes have enabled the computational design of spinning tops, yo-yos, wheels, buoys, and statically balanced objects. Previous work is based, for example, on topology optimization on voxel grids, which introduces a large number of optimization variables and box constraints, or offset surface computation, which cannot guarantee that solutions to a feasible problem will always be found.\u0000 In this work, we provide a mathematical analysis of constrained topology optimization problems that depend only on mass moments. This class of problems covers, among others, all applications mentioned above. Our main result is to show that no matter the outer shape of the rigid body to be optimized or the optimization objective and constraints considered, the optimal solution always features a quadric-shaped interface between material and cavities. This proves that optimal interfaces are always ellipsoids, hyperboloids, paraboloids, or one of a few degenerate cases, such as planes.\u0000 This insight lets us replace a difficult topology optimization problem with a provably equivalent non-linear equation system in a small number (<10) of variables, which represent the coefficients of the quadric. This system can be solved in a few seconds for most examples, provides insights into the geometric structure of many specific applications, and lets us describe their solution properties. Finally, our method integrates seamlessly into modern fabrication workflows because our solutions are analytical surfaces that are native to the CAD domain.","PeriodicalId":50913,"journal":{"name":"ACM Transactions on Graphics","volume":null,"pages":null},"PeriodicalIF":7.8,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141823595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hugo Schott, Eric Galin, É. Guérin, A. Paris, A. Peytavie
Modeling high-resolution terrains is a perennial challenge in the creation of virtual worlds. In this paper, we focus on the amplification of a low-resolution input terrain into a high-resolution, hydrologically consistent terrain featuring complex patterns by a multi-scale approach. Our framework combines the best of both worlds, relying on physics-inspired erosion models producing consistent erosion landmarks and introducing control at different scales, thus bridging the gap between physics-based erosion simulations and multi-scale procedural modeling. The method uses a fast and accurate approximation of different simulations, including thermal, stream power erosion and deposition performed at different scales to obtain a range of effects. Our approach provides landscape designers with tools for amplifying mountain ranges and valleys with consistent details.
{"title":"Terrain Amplification using Multi Scale Erosion","authors":"Hugo Schott, Eric Galin, É. Guérin, A. Paris, A. Peytavie","doi":"10.1145/3658200","DOIUrl":"https://doi.org/10.1145/3658200","url":null,"abstract":"Modeling high-resolution terrains is a perennial challenge in the creation of virtual worlds. In this paper, we focus on the amplification of a low-resolution input terrain into a high-resolution, hydrologically consistent terrain featuring complex patterns by a multi-scale approach. Our framework combines the best of both worlds, relying on physics-inspired erosion models producing consistent erosion landmarks and introducing control at different scales, thus bridging the gap between physics-based erosion simulations and multi-scale procedural modeling. The method uses a fast and accurate approximation of different simulations, including thermal, stream power erosion and deposition performed at different scales to obtain a range of effects. Our approach provides landscape designers with tools for amplifying mountain ranges and valleys with consistent details.","PeriodicalId":50913,"journal":{"name":"ACM Transactions on Graphics","volume":null,"pages":null},"PeriodicalIF":7.8,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141820878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces a novel Induce-on-Boundary (IoB) solver designed to address the magnetostatic governing equations of ferrofluids. The IoB solver is based on a single-layer potential and utilizes only the surface point cloud of the object, offering a lightweight, fast, and accurate solution for calculating magnetic fields. Compared to existing methods, it eliminates the need for complex linear system solvers and maintains minimal computational complexities. Moreover, it can be seamlessly integrated into conventional fluid simulators without compromising boundary conditions. Through extensive theoretical analysis and experiments, we validate both the convergence and scalability of the IoB solver, achieving state-of-the-art performance. Additionally, a straightforward coupling approach is proposed and executed to showcase the solver's effectiveness when integrated into a grid-based fluid simulation pipeline, allowing for realistic simulations of representative ferrofluid instabilities.
{"title":"An Induce-on-Boundary Magnetostatic Solver for Grid-Based Ferrofluids","authors":"Xingyu Ni, Ruicheng Wang, Bin Wang, Bao Chen","doi":"10.1145/3658124","DOIUrl":"https://doi.org/10.1145/3658124","url":null,"abstract":"This paper introduces a novel Induce-on-Boundary (IoB) solver designed to address the magnetostatic governing equations of ferrofluids. The IoB solver is based on a single-layer potential and utilizes only the surface point cloud of the object, offering a lightweight, fast, and accurate solution for calculating magnetic fields. Compared to existing methods, it eliminates the need for complex linear system solvers and maintains minimal computational complexities. Moreover, it can be seamlessly integrated into conventional fluid simulators without compromising boundary conditions. Through extensive theoretical analysis and experiments, we validate both the convergence and scalability of the IoB solver, achieving state-of-the-art performance. Additionally, a straightforward coupling approach is proposed and executed to showcase the solver's effectiveness when integrated into a grid-based fluid simulation pipeline, allowing for realistic simulations of representative ferrofluid instabilities.","PeriodicalId":50913,"journal":{"name":"ACM Transactions on Graphics","volume":null,"pages":null},"PeriodicalIF":7.8,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141821074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yuta Noma, Silvia Sellán, Nicholas Sharp, Karan Singh, Alec Jacobson
We introduce a fast, robust, and user-controllable algorithm to generate surface-filling curves. We compute these curves through the gradient flow of a simple sparse energy, making our method several orders of magnitude faster than previous works. Our algorithm makes minimal assumptions on the topology and resolution of the input surface, achieving improved robustness. Our framework provides tuneable parameters that guide the shape of the output curve, making it ideal for interactive design applications.
{"title":"Surface-Filling Curve Flows via Implicit Medial Axes","authors":"Yuta Noma, Silvia Sellán, Nicholas Sharp, Karan Singh, Alec Jacobson","doi":"10.1145/3658158","DOIUrl":"https://doi.org/10.1145/3658158","url":null,"abstract":"We introduce a fast, robust, and user-controllable algorithm to generate surface-filling curves. We compute these curves through the gradient flow of a simple sparse energy, making our method several orders of magnitude faster than previous works. Our algorithm makes minimal assumptions on the topology and resolution of the input surface, achieving improved robustness. Our framework provides tuneable parameters that guide the shape of the output curve, making it ideal for interactive design applications.","PeriodicalId":50913,"journal":{"name":"ACM Transactions on Graphics","volume":null,"pages":null},"PeriodicalIF":7.8,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141822271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Octave Crespel, Émile Hohnadel, T. Metivet, Florence Bertails-Descoubes
Computer Graphics has a long history in the design of effective algorithms for handling contact and friction between solid objects. For the sake of simplicity and versatility, most methods rely on low-order primitives such as line segments or triangles, both for the detection and the response stages. In this paper we carefully analyse, in the case of fibre systems, the impact of such choices on the retrieved contact forces. We highlight the presence of artifacts in the force response that are tightly related to the low-order geometry used for contact detection. Our analysis draws upon thorough comparisons between the high-order super-helix model and the low-order discrete elastic rod model. These reveal that when coupled to a low-order, segment-based detection scheme, both models yield spurious jumps in the contact force profile. Moreover, these artifacts are shown to be all the more visible as the geometry of fibres at contact is curved. In order to remove such artifacts we develop an accurate high-order detection scheme between two smooth curves, which relies on an efficient adaptive pruning strategy. We use this algorithm to detect contact between super-helices at high precision, allowing us to recover, in the range of wavy to highly curly fibres, much smoother force profiles during sliding motion than with a classical segment-based strategy. Furthermore, we show that our approach offers better scaling properties in terms of efficiency vs. precision compared to segment-based approaches, making it attractive for applications where accurate and reliable forces are desired. Finally, we demonstrate the robustness and accuracy of our fully high-order approach on a challenging hair combing scenario.
{"title":"Contact detection between curved fibres: high order makes a difference","authors":"Octave Crespel, Émile Hohnadel, T. Metivet, Florence Bertails-Descoubes","doi":"10.1145/3658191","DOIUrl":"https://doi.org/10.1145/3658191","url":null,"abstract":"Computer Graphics has a long history in the design of effective algorithms for handling contact and friction between solid objects. For the sake of simplicity and versatility, most methods rely on low-order primitives such as line segments or triangles, both for the detection and the response stages. In this paper we carefully analyse, in the case of fibre systems, the impact of such choices on the retrieved contact forces. We highlight the presence of artifacts in the force response that are tightly related to the low-order geometry used for contact detection. Our analysis draws upon thorough comparisons between the high-order super-helix model and the low-order discrete elastic rod model. These reveal that when coupled to a low-order, segment-based detection scheme, both models yield spurious jumps in the contact force profile. Moreover, these artifacts are shown to be all the more visible as the geometry of fibres at contact is curved. In order to remove such artifacts we develop an accurate high-order detection scheme between two smooth curves, which relies on an efficient adaptive pruning strategy. We use this algorithm to detect contact between super-helices at high precision, allowing us to recover, in the range of wavy to highly curly fibres, much smoother force profiles during sliding motion than with a classical segment-based strategy. Furthermore, we show that our approach offers better scaling properties in terms of efficiency vs. precision compared to segment-based approaches, making it attractive for applications where accurate and reliable forces are desired. Finally, we demonstrate the robustness and accuracy of our fully high-order approach on a challenging hair combing scenario.","PeriodicalId":50913,"journal":{"name":"ACM Transactions on Graphics","volume":null,"pages":null},"PeriodicalIF":7.8,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141822353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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