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Copyright of Journal of Computer-Aided Design & Computer Graphics / Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener layout by means of B-spline. The other is to build the mapping relationship from the known 3D surface mesh of the thin-walled structure to its parametric domain by means of mesh parameterization. The influence of mesh parameterization upon the stiffener layout is discussed to reveal the matching issue of the combined parameterization. 3D complex surfaces represented by the triangular mesh can be dealt with even though analytical parametric equations are not available. Some numerical examples are solved to demonstrate the direct advantage and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Copyright of Journal of National University of Defense Technology / Guofang Keji Daxue Xuebao is the property of NUDT Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

To address the issues of low efficiencies and serious mapping distortions in current mesh parameterization methods, we present a low distortion mesh parameterization mapping method based on proxy function and combined Newton's method in this paper. First, the proposed method calculates visual blind areas and distortion prone areas of a 3D mesh model, and generates a model slit. Afterwards, the method performs the Tutte mapping on the cut three-dimensional mesh model, measures the mapping distortion of the model, and outputs a distortion metric function and distortion values. Finally, the method sets iteration parameters, establishes a reference mesh, and finds the optimal coordinate points to get a convergent mesh model. When calculating mapping distortions, Dirichlet energy function is used to measure the isometric mapping distortion, and MIPS energy function is used to measure the conformal mapping distortion. To find the minimum value of the mapping distortion metric function, we use an optimal solution method combining proxy functions and combined Newton's method. The experimental data show that the proposed method has high execution efficiency, fast descending speed of mapping distortion energy and stable optimal value convergence quality. When a texture mapping is performed, the texture is evenly colored, close laid and uniformly lined, which meets the standards in practical applications. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Computer-Aided Design & Computer Graphics / Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We present a novel linear solver for interactive parameterization tasks. Our method is based on the observation that quasi-conformal parameterizations of a triangle mesh are largely determined by boundary conditions. These boundary conditions are typically constructed interactively by users, who have to take several artistic and geometric constraints into account while introducing cuts on the geometry. Commonly, the main computational burden in these methods is solving a linear system every time new boundary conditions are imposed. The core of our solver is a novel approach to efficiently update the Cholesky factorization of the linear system to reflect new boundary conditions, thereby enabling a seamless and interactive workflow even for large meshes consisting of several millions of vertices. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Computer-Aided Design & Computer Graphics / Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Mesh data plays a crucial role in a wide range of applications worldwide within the field of 3D computer vision. In contrast to traditional Euclidean space arrangements, meshes encompass spatial information, including edges, faces, angles, and graph structures that embed face information within the mesh data. Nevertheless, conventional deep learning frameworks such as convolutional neural networks (CNNs) have struggled to achieve significant advancements in handling meshes. This paper proposes a simple mesh computation framework called Mesh Decomposition Second-order Sobolev Network (MDSSN) to model triangle meshes and represent their shape. The construction of face-based Riemannian and edge-based Riemannian graphs is motivated by the remarkable representation capabilities of edges and faces in mesh data, achieved through a graph composition mechanism. Furthermore, we design end-to-end operators, including the Sobolev-filter block, pooling, and unpooling blocks, which draw inspiration from traditional deep learning frameworks for modeling the mesh structure. Importantly, the design of the mesh-filter block incorporates the second-order Sobolev metric. To address common challenges in mesh classification and segmentation tasks, we have designed dedicated classification and segmentation modules. We utilize a joint loss function that integrates losses from adjacent faces and categories. We evaluate the performance of the MDSSN in mesh classification and segmentation tasks, focusing on its ability to represent 3D shapes. Experimental results demonstrate that MDSSN achieves superior performance compared to other state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

We present the first, to our knowledge, fully automatic method for the conversion of a general generative design to a watertight B-Rep composed of the exact residual geometry of the input solids and editable T-NURCC surfaces. The design can be synthesized by any combination of both additive and subtractive in-synthesis processes, and constrained by any number of keep-in and -out solids. Our method requires only the input generative setup solids, rudimentary data from the solve, and a boundary mesh of the optimized design. Leveraging the generative solve data, we augment the boundary mesh with "incidence" attributes linking it to the input solids, and partition it into organic and incident regions. The organic regions are parameterized and approximated with T-NURCCs. Then, their boundaries are "pulled" into the adjacent input solids to construct clean intersection curves. Finally, the organic surfaces are combined with the input solids to compose a watertight solid B-Rep of the generative design. Without such an automatic conversion, users seeking to exploit generative designs in downstream workflows (e.g. setting up assembly constraints, simulation analyses, performing parametric edits) have to manually convert the design to a B-Rep, slowing down the path to manufacturing and increasing the product time to market. As a result of our work, engineers can now quickly obtain useful CAD models of any number of generative designs computed by a variety of algorithms, settings and iterations. • High-quality conversion method to obtain editable CAD models from generative designs. • Combines exact residual geometry of the input solids and editable T-NURCC surfaces. • Fully automatic algorithm produces watertight B-Reps. • Any combination of additive and subtractive in-synthesis processes and constraints. [ABSTRACT FROM AUTHOR]

UV mapping is a classical problem in computer graphics aiming at computing a planar parameterization of the input mesh with the lowest possible distortion while minimizing the seams length. Recent works propose optimization methods for solving these two joint problems at the same time with variational models, but they tend to be slower than other cutting methods. We present a new variational approach for this problem inspired by the Ambrosio-Tortorelli functional, which is easier to optimize than already existing methods. This functional has widely been used in image and geometry processing for anisotropic denoising and segmentation applications. The key feature of this functional is to model both regions where smoothing is applied, and the loci of discontinuities corresponding to the cuts. Our approach relies on this principle to model both the low distortion objective of the UV map, and the minimization of the seams length (sequences of mesh edges). Our method significantly reduces the distortion in a faster way than state-of-the art methods, with comparable seam quality. We also demonstrate the versatility of the approach when external constraints on the parameterization are provided (packing constraints, seam visibility). • We provide an Ambrosio-Tortorelli inspired functional to simultaneously optimize distortion and cut length of UV maps. • We propose an efficient projective quasi-newton solver to minimize our Ambrosio-Tortorelli energy. • Our method is faster than state-of-the-arts methods with comparable seam quality. • The method is versatile and can be adapted to handle external constraints such as packing constraints and seam visibility. [ABSTRACT FROM AUTHOR]

Low-distortion mapping of three-dimensional surfaces to the plane is a critical problem in geometry processing. The intrinsic distortion introduced by these UV mappings is highly dependent on the choice of surface cuts that form seamlines which break mapping continuity. Parameterization applications typically require UV maps with an application-specific upper bound on distortion to avoid mapping artifacts; at the same time they seek to reduce cut lengths to minimize discontinuity artifacts. We propose OptCuts, an algorithm that jointly optimizes the parameterization and cutting of a three-dimensional mesh. OptCuts starts from an arbitrary initial embedding and a user-requested distortion bound. It requires no parameter setting and automatically seeks to minimize seam lengths subject to satisfying the distortion bound of the mapping computed using these seams. OptCuts alternates between topology and geometry update steps that consistently decrease distortion and seam length, producing a UV map with compact boundaries that strictly satisfies the distortion bound. OptCuts automatically produces high-quality, globally bijective UV maps without user intervention. While OptCuts can thus be a highly effective tool to create new mappings from scratch, we also show how it can be employed to improve pre-existing embeddings. Additionally, when semantic or other priors on seam placement are desired, OptCuts can be extended to respect these user preferences as constraints during optimization of the parameterization. We demonstrate the scalable performance of OptCuts on a wide range of challenging benchmark parameterization examples, as well as in comparisons with state-of-the-art UV methods and commercial tools. [ABSTRACT FROM AUTHOR]

We proposed a texture mapping technique that comprises mesh partitioning, mesh parameterization and packing, texture transferring, and texture correction and optimization for generating a high-quality texture map of a three-dimensional (3D) model for applications in e-commerce presentations. The main problems in texture mapping are that the texture resolution is generally worse than in the original images and considerable photo inconsistency exists at the transition of different image sources. To improve the texture resolution, we employed an oriented boundary box method for placing mesh islands on the parametric (UV) map. We also provided a texture size that can keep the texture resolution of the 3D textured model similar to that of the object images. To improve the photo inconsistency problem, we employed a method to detect and overcome the missing color that might exist on a texture map. We also proposed a blending process to minimize the transition error caused by different image sources. Thus, a high-quality 3D textured model can be obtained by applying this series of processes for presentations in e-commerce. [ABSTRACT FROM AUTHOR]

Processing signals on surfaces often involves resampling the signal over the vertices of a dense mesh and applying mesh-based filtering operators. We present a framework to process a signal directly in a texture atlas domain. The benefits are twofold: avoiding resampling degradation and exploiting the regularity of the texture image grid. The main challenges are to preserve continuity across atlas chart boundaries and to adapt differential operators to the non-uniform parameterization. We introduce a novel function space and multigrid solver that jointly enable robust, interactive, and geometry-aware signal processing. We demonstrate our approach using several applications including smoothing and sharpening, multiview stitching, geodesic distance computation, and line integral convolution. [ABSTRACT FROM AUTHOR]

Fabrication from developable parts is the basis for arts such as papercraft and needlework, as well as modern architecture and CAD in general, and it has inspired much research. We observe that the assembly of complex 3D shapes created by existing methods often requires first fabricating many small parts and then carefully following instructions to assemble them together. Despite its significance, this error prone and tedious process is generally neglected in the discussion. We present the concept of zippables - single, two dimensional, branching, ribbon-like pieces of fabric that can be quickly zipped up without any instructions to form 3D objects. Our inspiration comes from the so-called zipit bags [zipit 2017], which are made of a single, long ribbon with a zipper around its boundary. In order to "assemble" the bag, one simply needs to zip up the ribbon. Our method operates in the same fashion, but it can be used to approximate a wide variety of shapes. Given a 3D model, our algorithm produces plans for a single 2D shape that can be laser cut in few parts from fabric or paper. A zipper can then be attached along the boundary by sewing, or by gluing using a custom-built fastening rig. We show physical and virtual results that demonstrate the capabilities of our method and the ease with which shapes can be assembled. [ABSTRACT FROM AUTHOR]

Angle-preserving or conformal surface parameterization has proven to be a powerful tool across applications ranging from geometry processing, to digital manufacturing, to machine learning, yet conformal maps can still suffer from severe area distortion. Cone singularities provide a way to mitigate this distortion, but finding the best configuration of cones is notoriously difficult. This paper develops a strategy that is globally optimal in the sense that it minimizes total area distortion among all possible cone configurations (number, placement, and size) that have no more than a fixed total cone angle. A key insight is that, for the purpose of optimization, one should not work directly with curvature measures (which naturally represent cone configurations), but can instead apply Fenchel-Rockafellar duality to obtain a formulation involving only ordinary functions. The result is a convex optimization problem, which can be solved via a sequence of sparse linear systems easily built from the usual cotangent Laplacian. The method supports user-defined notions of importance, constraints on cone angles (e.g., positive, or within a given range), and sophisticated boundary conditions (e.g., convex, or polygonal). We compare our approach to previous techniques on a variety of challenging models, often achieving dramatically lower distortion, and demonstrating that global optimality leads to extreme robustness in the presence of noise or poor discretization. [ABSTRACT FROM AUTHOR]

In this paper, we introduce discrete Calabi flow to the graphics research community and present a novel conformal mesh parameterization algorithm. Calabi energy has a succinct and explicit format. Its corresponding flow is conformal and convergent under certain conditions. Our method is based on the Calabi energy and Calabi flow with solid theoretical and mathematical base. We demonstrate our approach on dozens of models and compare it with other related flow based methods, such as the well-known Ricci flow and conformal equivalence of triangle meshes (CETM). Our experiments show that the performance of our algorithm is comparably the same with other methods. The discrete Calabi flow in our method provides another perspective on conformal flow and conformal parameterization. [ABSTRACT FROM AUTHOR]

Linear mesh parameterization method with a free boundary is an attractive technology and a ubiquitous tool that is widely used in computer graphics and geometry processing. The existing methods always have the shortcoming of element flipping. In this study, a novel linear mesh parameterization method with a free boundary is proposed based on the linear elastic finite element model of a material with negative Poisson's ratio. With appropriate parameter settings, the method can flatten a 3D mesh without element flipping to the most extent. The proposed method is divided into two steps: (1) each element of the 3D mesh is compressed to the origin point; (2) the degenerated mesh is gradually expanded in a plane under the two forces of equal magnitude and opposite directions based on a finite element model of an elastic membrane material with negative Poisson's ratio. Subsequently, the causes of element flipping are analyzed at internal nodes and boundary nodes. The triangle shape transformation (TST) method is proposed to solve the problem of internal element flipping, and the stiffness enhancement method is presented to overcome the boundary element flipping caused by the severe mutual extrusion of the internal elements near the boundary. Finally, typical examples are tested to verify the effectiveness of the proposed mesh parameterization method. • New linear mesh parameterization method to obtain flattened mesh. • A 3D mesh is compressed to origin point, then degenerated mesh expands in a plane. • Finite element method is used in mesh parameterization. • Flattened mesh without element flipping is obtained. [ABSTRACT FROM AUTHOR]

In the context of CAD, CAM, CAE, and reverse engineering, the problem of mesh parameterization is a central process. Mesh parameterization implies the computation of a bijective map ϕ from the original mesh M ∈ R 3 to the planar domain ϕ ( M ) ∈ R 2 . The mapping may preserve angles, areas, or distances. Distance-preserving parameterizations (i.e., isometries) are obviously attractive. However, geodesic-based isometries present limitations when the mesh has concave or disconnected boundary (i.e., holes). Recent advances in computing geodesic maps using the heat equation in 2-manifolds motivate us to revisit mesh parameterization with geodesic maps. We devise a Poisson surface underlying, extending, and filling the holes of the mesh M. We compute a near-isometric mapping for quasi-developable meshes by using geodesic maps based on heat propagation. Our method: (1) Precomputes a set of temperature maps (heat kernels) on the mesh; (2) estimates the geodesic distances along the piecewise linear surface by using the temperature maps; and (3) uses multidimensional scaling (MDS) to acquire the 2D coordinates that minimize the difference between geodesic distances on M and Euclidean distances on R 2 . This novel heat-geodesic parameterization is successfully tested with several concave and/or punctured surfaces, obtaining bijective low-distortion parameterizations. Failures are registered in nonsegmented, highly nondevelopable meshes (such as seam meshes). These cases are the goal of future endeavors.

PolyCubes, or orthogonal polyhedra, are useful as parameterization base-complexes for various operations in computer graphics. However, computing quality PolyCube base-complexes for general shapes, providing a good trade-off between mapping distortion and singularity counts, remains a challenge. Our work improves on the state-of-the-art in PolyCube computation by adopting a graph-cut inspired approach. We observe that, given an arbitrary input mesh, the computation of a suitable PolyCube base-complex can be formulated as associating, or labeling, each input mesh triangle with one of six signed principal axis directions. Most of the criteria for a desirable PolyCube labeling can be satisfied using a multi-label graph-cut optimization with suitable local unary and pairwise terms. However, the highly constrained nature of PolyCubes, imposed by the need to align each chart with one of the principal axes, enforces additional global constraints that the labeling must satisfy. To enforce these constraints, we develop a constrained discrete optimization technique, PolyCut, which embeds a graph-cut multi-label optimization within a hill-climbing local search framework that looks for solutions that minimize the cut energy while satisfying the global constraints. We further optimize our generated PolyCube base-complexes through a combination of distortion-minimizing deformation, followed by a labeling update and a final PolyCube parameterization step. Our PolyCut formulation captures the desired properties of a PolyCube base-complex, balancing parameterization distortion against singularity count, and produces demonstrably better PolyCube base-complexes then previous work. [ABSTRACT FROM AUTHOR]

We proposed a texture mapping technique that comprises mesh partitioning, mesh parameterization and packing, texture transferring, and texture correction and optimization for generating a high-quality texture map of a three-dimensional (3D) model for applications in e-commerce presentations. The main problems in texture mapping are that the texture resolution is generally worse than in the original images and considerable photo inconsistency exists at the transition of different image sources. To improve the texture resolution, we employed an oriented boundary box method for placing mesh islands on the parametric (UV) map. We also provided a texture size that can keep the texture resolution of the 3D textured model similar to that of the object images. To improve the photo inconsistency problem, we employed a method to detect and overcome the missing color that might exist on a texture map. We also proposed a blending process to minimize the transition error caused by different image sources. Thus, a high-quality 3D textured model can be obtained by applying this series of processes for presentations in e-commerce.

In recent years, the photorealistic 3D city models are increasingly important in various geospatial applications related to virtual city tourism, 3D GIS, urban planning, real-estate management. Besides the acquisition of high-precision 3D geometric data, texture reconstruction is also a crucial step for generating high-quality and visually realistic 3D models. However, most of the texture reconstruction approaches are probably leading to texture fragmentation and memory inefficiency. In this paper, we introduce an automatic framework of texture reconstruction to generate textures from oblique images for photorealistic visualization. Our approach include three major steps as follows: mesh parameterization, texture atlas generation and texture blending. Firstly, mesh parameterization procedure referring to mesh segmentation and mesh unfolding is performed to reduce geometric distortion in the process of mapping 2D texture to 3D model. Secondly, in the texture atlas generation step, the texture of each segmented region in texture domain is reconstructed from all visible images with exterior orientation and interior orientation parameters. Thirdly, to avoid color discontinuities at boundaries between texture regions, the final texture map is generated by blending texture maps from several corresponding images. We evaluated our texture reconstruction framework on a dataset of a city. The resulting mesh model can get textured by created texture without resampling. Experiment results show that our method can effectively mitigate the occurrence of texture fragmentation. It is demonstrated that the proposed framework is effective and useful for automatic texture reconstruction of 3D city model. [ABSTRACT FROM AUTHOR]

Objective: Articular cartilage (AC) morphology is an important metric for characterizing degeneration. We propose a novel morphologic analysis using mesh parameterization, enabling the use of surface roughness and thickness metrics to characterize degeneration in a rodent model of post-traumatic osteoarthritis.Methods: Six rats underwent anterior cruciate ligament transection (ACL-T) and six were controls (Control). At 4-weeks, femora and tibiae were harvested and imaged using contrast-enhanced micro-computed tomography (μCT). Cartilage surfaces were manually outlined, and 2-dimensional thickness maps were generated using mesh parameterization and analyzed by thickness and surface roughness (Sa). The parameterization technique was validated against the direct distance transform (DDT) and histologic AC thickness from sagittal Safranin-O/Fast-Green sections. Parameterization and DDT measurements were also validated using known, virtual shapes with zero, one, and two planes of curvature.Results: Parameterization had 0.00-6.26% error and DDT had 5.06-12.02% error in determining thicknesses of known shapes. Parameterization thickness correlated highly to DDT thickness (femur: r = 0.978, P < 0.001; tibia: r = 0.992, P < 0.001) and histologic thickness (femur: r = 0.952, P < 0.001; tibia: r = 0.959, P < 0.001). Thickness maps enabled visualization and quantification of AC degeneration. ACL-T samples displayed general thickening of cartilage, with adjacent regions of thickening and thinning on the medial femoral condyle. Compared to Control, ACL-T thickness was higher in the whole femur, whole tibia, and all compartments and sub-compartments. Sa was higher in the whole femur and medial and lateral condyle, and the whole tibia and medial and lateral plateau. The largest increases in Sa were observed on the medial femoral condyle.Conclusions: Cartilage analysis using parameterization effectively characterized early degeneration in AC, including sub-compartmental thickening/thinning, and is a powerful tool for assessing degeneration in preclinical osteoarthritis. [ABSTRACT FROM AUTHOR]

In recent years, the photorealistic 3D city models are increasingly important in various geospatial applications related to virtual city tourism, 3D GIS, urban planning, real-estate management. Besides the acquisition of high-precision 3D geometric data, texture reconstruction is also a crucial step for generating high-quality and visually realistic 3D models. However, most of the texture reconstruction approaches are probably leading to texture fragmentation and memory inefficiency. In this paper, we introduce an automatic framework of texture reconstruction to generate textures from oblique images for photorealistic visualization. Our approach include three major steps as follows: mesh parameterization, texture atlas generation and texture blending. Firstly, mesh parameterization procedure referring to mesh segmentation and mesh unfolding is performed to reduce geometric distortion in the process of mapping 2D texture to 3D model. Secondly, in the texture atlas generation step, the texture of each segmented region in texture domain is reconstructed from all visible images with exterior orientation and interior orientation parameters. Thirdly, to avoid color discontinuities at boundaries between texture regions, the final texture map is generated by blending texture maps from several corresponding images. We evaluated our texture reconstruction framework on a dataset of a city. The resulting mesh model can get textured by created texture without resampling. Experiment results show that our method can effectively mitigate the occurrence of texture fragmentation. It is demonstrated that the proposed framework is effective and useful for automatic texture reconstruction of 3D city model. [ABSTRACT FROM AUTHOR]