We propose a new method to accurately approximate the Pompeiu-Hausdorff distance from a triangle soup A to another triangle soup B up to a given tolerance. Based on lower and upper bound computations, we discard triangles from A that do not contain the maximizer of the distance to B and subdivide the others for further processing. In contrast to previous methods, we use four upper bounds instead of only one, three of which newly proposed by us. Many triangles are discarded using the simpler bounds, while the most difficult cases are dealt with by the other bounds. Exhaustive testing determines the best ordering of the four upper bounds. A collection of experiments shows that our method is faster than all previous accurate methods in the literature.
我们提出了一种新方法，可以在给定的容差范围内精确地近似计算从三角形汤 A 到另一个三角形汤 B 的庞培-豪斯多夫距离。根据下界和上界计算，我们从 A 中舍弃不包含到 B 的最大距离的三角形，并细分其他三角形进行进一步处理。与之前的方法不同，我们使用了四个上界，而不是只有一个，其中三个是我们新提出的。使用较简单的上界可以舍弃许多三角形，而使用其他上界则可以处理最困难的情况。详尽的测试确定了四个上限的最佳排序。一系列实验表明，我们的方法比以往文献中的所有精确方法都要快。
{"title":"Cascading upper bounds for triangle soup Pompeiu-Hausdorff distance","authors":"Leonardo Sacht, Alec Jacobson","doi":"10.1111/cgf.15129","DOIUrl":"10.1111/cgf.15129","url":null,"abstract":"<p>We propose a new method to accurately approximate the Pompeiu-Hausdorff distance from a triangle soup A to another triangle soup B up to a given tolerance. Based on lower and upper bound computations, we discard triangles from A that do not contain the maximizer of the distance to B and subdivide the others for further processing. In contrast to previous methods, we use four upper bounds instead of only one, three of which newly proposed by us. Many triangles are discarded using the simpler bounds, while the most difficult cases are dealt with by the other bounds. Exhaustive testing determines the best ordering of the four upper bounds. A collection of experiments shows that our method is faster than all previous accurate methods in the literature.</p>","PeriodicalId":10687,"journal":{"name":"Computer Graphics Forum","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We compute the kernel of a shape embedded in 3D as a polygon mesh, which is defined as the set of all points that have a clear line of sight to every point of the mesh. The KerGen algorithm, short for Kernel Generation, employs efficient plane-plane and line-plane intersections, alongside point classifications based on their positions relative to planes. This approach allows for the incremental addition of kernel vertices and edges to the resulting set in a simple and systematic way. The output is a polygon mesh that represents the surface of the kernel. Extensive comparisons with the existing methods, CGAL and Polyhedron Kernel, demonstrate the remarkable timing performance of our novel additive kernel computation method. Yet another advantage of our additive process is the availability of the partial kernel at any stage, making it useful for specific geometry processing applications such as star decomposition and castable shape reconstruction.
{"title":"KerGen: A Kernel Computation Algorithm for 3D Polygon Meshes","authors":"M. Asiler, Y. Sahillioğlu","doi":"10.1111/cgf.15137","DOIUrl":"10.1111/cgf.15137","url":null,"abstract":"<p>We compute the kernel of a shape embedded in 3D as a polygon mesh, which is defined as the set of all points that have a clear line of sight to every point of the mesh. The KerGen algorithm, short for Kernel Generation, employs efficient plane-plane and line-plane intersections, alongside point classifications based on their positions relative to planes. This approach allows for the incremental addition of kernel vertices and edges to the resulting set in a simple and systematic way. The output is a polygon mesh that represents the surface of the kernel. Extensive comparisons with the existing methods, CGAL and Polyhedron Kernel, demonstrate the remarkable timing performance of our novel additive kernel computation method. Yet another advantage of our additive process is the availability of the partial kernel at any stage, making it useful for specific geometry processing applications such as star decomposition and castable shape reconstruction.</p>","PeriodicalId":10687,"journal":{"name":"Computer Graphics Forum","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Two-scale topology optimization, combined with the design of microstructure families with a broad range of effective material parameters, is widely used in many fabrication applications to achieve a target deformation behavior for a variety of objects. The main idea of this approach is to optimize the distribution of material properties in the object partitioned into relatively coarse cells, and then replace each cell with microstructure geometry that mimics these material properties. In this paper, we focus on adapting this approach to complex shapes in situations when preserving the shape's surface is essential.
Our approach extends any regular (i.e. defined on a regular lattice grid) microstructure family to complex shapes, by enriching it with tiles adapted to the geometry of the cut-cell. We propose a fully automated and robust pipeline based on this approach, and we show that the performance of the regular microstructure family is only minimally affected by our extension while allowing its use on 2D and 3D shapes of high complexity.
{"title":"Cut-Cell Microstructures for Two-scale Structural Optimization","authors":"Davi Colli Tozoni, Zizhou Huang, Daniele Panozzo, Denis Zorin","doi":"10.1111/cgf.15139","DOIUrl":"10.1111/cgf.15139","url":null,"abstract":"<p>Two-scale topology optimization, combined with the design of microstructure families with a broad range of effective material parameters, is widely used in many fabrication applications to achieve a target deformation behavior for a variety of objects. The main idea of this approach is to optimize the distribution of material properties in the object partitioned into relatively coarse cells, and then replace each cell with microstructure geometry that mimics these material properties. In this paper, we focus on adapting this approach to complex shapes in situations when preserving the shape's surface is essential.</p><p>Our approach extends any regular (i.e. defined on a regular lattice grid) microstructure family to complex shapes, by enriching it with tiles adapted to the geometry of the cut-cell. We propose a fully automated and robust pipeline based on this approach, and we show that the performance of the regular microstructure family is only minimally affected by our extension while allowing its use on 2D and 3D shapes of high complexity.</p>","PeriodicalId":10687,"journal":{"name":"Computer Graphics Forum","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Marin, F. Maggioli, S. Melzi, S. Ohrhallinger, M. Wimmer
Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive attention, primarily relying on human assistance, and where not, limited by very strict sampling conditions. In this work, we formally improve on the state-of-the-art requirements and introduce an innovative algorithm capable of reconstructing closed curves directly on surfaces from a given sparse set of sample points. We extend and adapt a state-of-the-art planar curve reconstruction method to the realm of surfaces while dealing with the challenges arising from working on non-Euclidean domains. We demonstrate the robustness of our method by reconstructing multiple curves on various surface meshes. We explore novel potential applications of our approach, allowing for automated reconstruction of curves on Riemannian manifolds.
{"title":"Reconstructing Curves from Sparse Samples on Riemannian Manifolds","authors":"D. Marin, F. Maggioli, S. Melzi, S. Ohrhallinger, M. Wimmer","doi":"10.1111/cgf.15136","DOIUrl":"10.1111/cgf.15136","url":null,"abstract":"<div>\u0000 \u0000 <p>Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive attention, primarily relying on human assistance, and where not, limited by very strict sampling conditions. In this work, we formally improve on the state-of-the-art requirements and introduce an innovative algorithm capable of reconstructing closed curves directly on surfaces from a given sparse set of sample points. We extend and adapt a state-of-the-art planar curve reconstruction method to the realm of surfaces while dealing with the challenges arising from working on non-Euclidean domains. We demonstrate the robustness of our method by reconstructing multiple curves on various surface meshes. We explore novel potential applications of our approach, allowing for automated reconstruction of curves on Riemannian manifolds.</p>\u0000 </div>","PeriodicalId":10687,"journal":{"name":"Computer Graphics Forum","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/cgf.15136","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Constructing well-behaved Laplacian and mass matrices is essential for tetrahedral mesh processing. Unfortunately, the de facto standard linear finite elements exhibit bias on tetrahedralized regular grids, motivating the development of finite-volume methods. In this paper, we place existing methods into a common construction, showing how their differences amount to the choice of simplex centers. These choices lead to satisfaction or breakdown of important properties: continuity with respect to vertex positions, positive semi-definiteness of the implied Dirichlet energy, positivity of the mass matrix, and unbiased-ness on regular grids. Based on this analysis, we propose a new method for constructing dual-volumes which explicitly satisfy all of these properties via convex optimization.
{"title":"Optimized Dual-Volumes for Tetrahedral Meshes","authors":"Alec Jacobson","doi":"10.1111/cgf.15133","DOIUrl":"10.1111/cgf.15133","url":null,"abstract":"<div>\u0000 \u0000 <p>Constructing well-behaved Laplacian and mass matrices is essential for tetrahedral mesh processing. Unfortunately, the <i>de facto</i> standard linear finite elements exhibit bias on tetrahedralized regular grids, motivating the development of finite-volume methods. In this paper, we place existing methods into a common construction, showing how their differences amount to the choice of simplex centers. These choices lead to satisfaction or breakdown of important properties: continuity with respect to vertex positions, positive semi-definiteness of the implied Dirichlet energy, positivity of the mass matrix, and unbiased-ness on regular grids. Based on this analysis, we propose a new method for constructing dual-volumes which explicitly satisfy all of these properties via convex optimization.</p>\u0000 </div>","PeriodicalId":10687,"journal":{"name":"Computer Graphics Forum","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/cgf.15133","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce Coverage Axis++, a novel and efficient approach to 3D shape skeletonization. The current state-of-the-art approaches for this task often rely on the watertightness of the input [LWS*15; PWG*19; PWG*19] or suffer from substantial computational costs [DLX*22; CD23], thereby limiting their practicality. To address this challenge, Coverage Axis++ proposes a heuristic algorithm to select skeletal points, offering a high-accuracy approximation of the Medial Axis Transform (MAT) while significantly mitigating computational intensity for various shape representations. We introduce a simple yet effective strategy that considers shape coverage, uniformity, and centrality to derive skeletal points. The selection procedure enforces consistency with the shape structure while favoring the dominant medial balls, which thus introduces a compact underlying shape representation in terms of MAT. As a result, Coverage Axis++ allows for skeletonization for various shape representations (e.g., water-tight meshes, triangle soups, point clouds), specification of the number of skeletal points, few hyperparameters, and highly efficient computation with improved reconstruction accuracy. Extensive experiments across a wide range of 3D shapes validate the efficiency and effectiveness of Coverage Axis++. Our codes are available at https://github.com/Frank-ZY-Dou/Coverage_Axis.
{"title":"Coverage Axis++: Efficient Inner Point Selection for 3D Shape Skeletonization","authors":"Zimeng Wang, Zhiyang Dou, Rui Xu, Cheng Lin, Yuan Liu, Xiaoxiao Long, Shiqing Xin, Taku Komura, Xiaoming Yuan, Wenping Wang","doi":"10.1111/cgf.15143","DOIUrl":"10.1111/cgf.15143","url":null,"abstract":"<div>\u0000 \u0000 <p>We introduce Coverage Axis++, a novel and efficient approach to 3D shape skeletonization. The current state-of-the-art approaches for this task often rely on the watertightness of the input [LWS*15; PWG*19; PWG*19] or suffer from substantial computational costs [DLX*22; CD23], thereby limiting their practicality. To address this challenge, Coverage Axis++ proposes a heuristic algorithm to select skeletal points, offering a high-accuracy approximation of the Medial Axis Transform (MAT) while significantly mitigating computational intensity for various shape representations. We introduce a simple yet effective strategy that considers shape coverage, uniformity, and centrality to derive skeletal points. The selection procedure enforces consistency with the shape structure while favoring the dominant medial balls, which thus introduces a compact underlying shape representation in terms of MAT. As a result, Coverage Axis++ allows for skeletonization for various shape representations (e.g., water-tight meshes, triangle soups, point clouds), specification of the number of skeletal points, few hyperparameters, and highly efficient computation with improved reconstruction accuracy. Extensive experiments across a wide range of 3D shapes validate the efficiency and effectiveness of Coverage Axis++. Our codes are available at https://github.com/Frank-ZY-Dou/Coverage_Axis.</p>\u0000 </div>","PeriodicalId":10687,"journal":{"name":"Computer Graphics Forum","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/cgf.15143","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Neural implicit surfaces are a promising tool for geometry processing that represent a solid object as the zero level set of a neural network. Usually trained to approximate a signed distance function of the considered object, these methods exhibit great visual fidelity and quality near the surface, yet their properties tend to degrade with distance, making geometrical queries hard to perform without the help of complex range analysis techniques. Based on recent advancements in Lipschitz neural networks, we introduce a new method for approximating the signed distance function of a given object. As our neural function is made 1-Lipschitz by construction, it cannot overestimate the distance, which guarantees robustness even far from the surface. Moreover, the 1-Lipschitz constraint allows us to use a different loss function, called the hinge-Kantorovitch-Rubinstein loss, which pushes the gradient as close to unit-norm as possible, thus reducing computation costs in iterative queries. As this loss function only needs a rough estimate of occupancy to be optimized, this means that the true distance function need not to be known. We are therefore able to compute neural implicit representations of even bad quality geometry such as noisy point clouds or triangle soups. We demonstrate that our methods is able to approximate the distance function of any closed or open surfaces or curves in the plane or in space, while still allowing sphere tracing or closest point projections to be performed robustly.
{"title":"1-Lipschitz Neural Distance Fields","authors":"Guillaume Coiffier, Louis Béthune","doi":"10.1111/cgf.15128","DOIUrl":"10.1111/cgf.15128","url":null,"abstract":"<p>Neural implicit surfaces are a promising tool for geometry processing that represent a solid object as the zero level set of a neural network. Usually trained to approximate a signed distance function of the considered object, these methods exhibit great visual fidelity and quality near the surface, yet their properties tend to degrade with distance, making geometrical queries hard to perform without the help of complex range analysis techniques. Based on recent advancements in Lipschitz neural networks, we introduce a new method for approximating the signed distance function of a given object. As our neural function is made 1-Lipschitz by construction, it cannot overestimate the distance, which guarantees robustness even far from the surface. Moreover, the 1-Lipschitz constraint allows us to use a different loss function, called the <i>hinge-Kantorovitch-Rubinstein</i> loss, which pushes the gradient as close to unit-norm as possible, thus reducing computation costs in iterative queries. As this loss function only needs a rough estimate of occupancy to be optimized, this means that the true distance function need not to be known. We are therefore able to compute neural implicit representations of even bad quality geometry such as noisy point clouds or triangle soups. We demonstrate that our methods is able to approximate the distance function of any closed or open surfaces or curves in the plane or in space, while still allowing sphere tracing or closest point projections to be performed robustly.</p>","PeriodicalId":10687,"journal":{"name":"Computer Graphics Forum","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 field of neural style transfer (NST) has witnessed remarkable progress in the past few years, with approaches being able to synthesize artistic and photorealistic images and videos of exceptional quality. To evaluate such results, a diverse landscape of evaluation methods and metrics is used, including authors' opinions based on side-by-side comparisons, human evaluation studies that quantify the subjective judgements of participants, and a multitude of quantitative computational metrics which objectively assess the different aspects of an algorithm's performance. However, there is no consensus regarding the most suitable and effective evaluation procedure that can guarantee the reliability of the results. In this review, we provide an in-depth analysis of existing evaluation techniques, identify the inconsistencies and limitations of current evaluation methods, and give recommendations for standardized evaluation practices. We believe that the development of a robust evaluation framework will not only enable more meaningful and fairer comparisons among NST methods but will also enhance the comprehension and interpretation of research findings in the field.
{"title":"Evaluation in Neural Style Transfer: A Review","authors":"Eleftherios Ioannou, Steve Maddock","doi":"10.1111/cgf.15165","DOIUrl":"10.1111/cgf.15165","url":null,"abstract":"<p>The field of neural style transfer (NST) has witnessed remarkable progress in the past few years, with approaches being able to synthesize artistic and photorealistic images and videos of exceptional quality. To evaluate such results, a diverse landscape of evaluation methods and metrics is used, including authors' opinions based on side-by-side comparisons, human evaluation studies that quantify the subjective judgements of participants, and a multitude of quantitative computational metrics which objectively assess the different aspects of an algorithm's performance. However, there is no consensus regarding the most suitable and effective evaluation procedure that can guarantee the reliability of the results. In this review, we provide an in-depth analysis of existing evaluation techniques, identify the inconsistencies and limitations of current evaluation methods, and give recommendations for standardized evaluation practices. We believe that the development of a robust evaluation framework will not only enable more meaningful and fairer comparisons among NST methods but will also enhance the comprehension and interpretation of research findings in the field.</p>","PeriodicalId":10687,"journal":{"name":"Computer Graphics Forum","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/cgf.15165","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The realistic rendering of woven and knitted fabrics has posed significant challenges throughout many years. Previously, fiber-based micro-appearance models have achieved considerable success in attaining high levels of realism. However, rendering such models remains complex due to the intricate internal scatterings of hundreds of fibers within a yarn, requiring vast amounts of memory and time to render. In this paper, we introduce a new framework to capture aggregated appearance by tracing many light paths through the underlying fiber geometry. We then employ lightweight neural networks to accurately model the aggregated BSDF, which allows for the precise modeling of a diverse array of materials while offering substantial improvements in speed and reductions in memory. Furthermore, we introduce a novel importance sampling scheme to further speed up the rate of convergence. We validate the efficacy and versatility of our framework through comparisons with preceding fiber-based shading models as well as the most recent yarn-based model.
{"title":"Neural Appearance Model for Cloth Rendering","authors":"G. Y. Soh, Z. Montazeri","doi":"10.1111/cgf.15156","DOIUrl":"10.1111/cgf.15156","url":null,"abstract":"<div>\u0000 <p>The realistic rendering of woven and knitted fabrics has posed significant challenges throughout many years. Previously, fiber-based micro-appearance models have achieved considerable success in attaining high levels of realism. However, rendering such models remains complex due to the intricate internal scatterings of hundreds of fibers within a yarn, requiring vast amounts of memory and time to render. In this paper, we introduce a new framework to capture aggregated appearance by tracing many light paths through the underlying fiber geometry. We then employ lightweight neural networks to accurately model the aggregated BSDF, which allows for the precise modeling of a diverse array of materials while offering substantial improvements in speed and reductions in memory. Furthermore, we introduce a novel importance sampling scheme to further speed up the rate of convergence. We validate the efficacy and versatility of our framework through comparisons with preceding fiber-based shading models as well as the most recent yarn-based model.</p>\u0000 </div>","PeriodicalId":10687,"journal":{"name":"Computer Graphics Forum","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/cgf.15156","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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