Quad-dominant Mesh Research Articles

A Streamline-Guided Dehomogenization Approach for Structural Design

Abstract We present a novel dehomogenization approach for the efficient design of high-resolution load-bearing structures. The proposed approach builds upon a streamline-based parametrization of the design domain, using a set of space-filling and evenly spaced streamlines in the two mutually orthogonal direction fields that are obtained from homogenization-based topology optimization. Streamlines in these fields are converted into a graph, which is then used to construct a quad-dominant mesh whose edges follow the direction fields. In addition, the edge width is adjusted according to the density and anisotropy of the optimized orthotropic cells. In a number of numerical examples, we demonstrate the mechanical performance and regular appearance of the resulting structural designs and compare them with those from classic and contemporary approaches.

Localized remeshing for polyhedral splines

Smooth spline surfaces can now be built with polyhedral control nets rather than just grid-like tensor-product control nets. However, irregularities such as T-junctions, multi-sided facets, and n-valent vertices need to be sufficiently separated. Automatically generated quad-dominant meshes, and meshes created by designers unaware of the requirements for spline surfaces often pack irregularities too tightly.Global refinement, e.g. via two steps of subdivision, can sufficiently separate irregularities. However, each refinement quadruples the number of polynomial pieces. Moreover, first-step artifacts can lead to oscillating and pinched highlight line distributions. We therefore investigate minimal, single edge insertion, re-connection and localized refinement of quad-dominant meshes to make them suitable for polyhedral splines.

Dev2PQ: Planar Quadrilateral Strip Remeshing of Developable Surfaces

We introduce an algorithm to remesh triangle meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips that are aligned to principal curvature directions and closely approximate the curved parts of the input developable, and planar polygons representing the flat parts of the input that connect the PQ strips. Developable PQ-strip meshes are useful in many areas of shape modeling, thanks to the simplicity of fabrication from flat sheet material. Unfortunately, they are difficult to model due to their restrictive combinatorics. Other representations of developable surfaces, such as arbitrary triangle or quad meshes, are more suitable for interactive freeform modeling but generally have non-planar faces or are not aligned to principal curvatures. Our method leverages the modeling flexibility of non-ruling-based representations of developable surfaces while still obtaining developable, curvature-aligned PQ-strip meshes. Our algorithm optimizes for a scalar function on the input mesh, such that its isolines are extrinsically straight and align well to the locally estimated ruling directions. The condition that guarantees straight isolines is non-linear of high order and numerically difficult to enforce in a straightforward manner. We devise an alternating optimization method that makes our problem tractable and practical to compute. Our method works automatically on any developable input, including multiple patches and curved folds, without explicit domain decomposition. We demonstrate the effectiveness of our approach on a variety of developable surfaces and show how our remeshing can be used alongside handle-based interactive freeform modeling of developable shapes.

An Open-Source Processing Pipeline for Quad-Dominant Mesh Generation for Class-Compliant Ship Structural Analysis

We present an algorithm for the fully automatic generation of a class-compliant mesh for ship structural analysis. Our algorithm is implemented as an end-to-end solution. It starts from a description of a geometry and produces a class conforming surface mesh as a result. The algorithm consists of two parts, the automatic geometry refinement and the preconditioned Delaunay frontal quad dominant mesh generator. A geometry is described by a dictionary of elements and it contains points, rods, plates, and openings. A dictionary can contain modeling errors such as unintended overlaps or an unintended loss of connectivity between elements. The main contribution of the paper is the automatic geometry refinement algorithm and the virtual stiffener procedure designed to control the local mesh orientation of a marching front meshing algorithm. The geometry refinement algorithm guarantees that the output dictionary will be such that intersections of the boundary edges of plates are guaranteed to be nodes of any mesh generated by tessellating such geometry. The algorithm is implemented in Python, using the open-source Gmsh system together with the Open CASCADE kernel which is used to implement the automatic geometry refinement. We present several benchmark models from an engineering practice to illustrate our claims as well as to benchmark the efficiency of the various stages of the processing pipeline.

Low degree splines for locally quad-dominant meshes

A mesh is locally quad-dominant (lqd) if all non-4-sided facets are surrounded by quadrilaterals. Lqd meshes allow for irregular nodes where n≠4 quads meet and for multi-sided facets, called T-gons, that end quad-strips and so adjust mesh density.This paper introduces a new class of bi-cubic (bi-3) Geometric T-joint (GT) splines whose control nets are τ-nets, i.e. T-gons surrounded by quads. These GT-splines join smoothly with each other, bi-3 G-splines and regular C1 bi-quadratic splines to form smooth surfaces of degree at most bi-3.

Smooth polar caps for locally quad-dominant meshes

A polar configuration is a node surrounded by m triangles. Polar configurations are common to cap off cylinders and spheres. When the triangles, interpreted as quadrilaterals with one edge collapsed, are surrounded by a quad-strip then the extended polar configuration qualifies as part of a locally quad-dominant (lqd) mesh. Recent constructions, referred to as semi-structured splines, can use lqd meshes as control nets: multi-sided configurations that merge parameter directions are covered by G-spline; and T-junctions that transition from coarse and fine are covered by GT-splines.This paper complements existing semi-structured splines by providing the missing component for polar configurations. A spectrum of constructions of differing degree are introduced, tested and compared. Bi-2 C1 splines are extended to polar configurations covered by C1 surfaces consisting of (macro-)patches of degree as low as bi-2. Bi-3 C2 splines are extended to polar configurations covered by surfaces that are C2 except for a C1 pole and consist of (macro-)patches of degree as low as bi-3.

Refinable smooth surfaces for locally quad-dominant meshes with T-gons

Multi-sided facets in polyhedral models and meshes serve to connect regular sub-meshes (star-configurations) and to start or end quad-strips (T-configurations). Using the polyhedral mesh as control net, recursive subdivision algorithms often yield poor shape for these non-quad configurations. Polynomial surface constructions such as geometrically smooth splines (G-splines) do better, but lack subdivision-like refinability. Such refinability is useful for hierarchical modeling and engineering analysis.This paper introduces a new class of G-splines that generalizes bi-quadratic C1 splines to polyhedral control nets with star- and T-configurations and that is refinable.

Generalized motorcycle graphs for imperfect quad-dominant meshes

We introduce a practical pipeline to create UV T-layouts for real-world quad dominant semi-regular meshes. Our algorithm creates large rectangular patches by relaxing the notion of motorcycle graphs and making it insensitive to local irregularities in the mesh structure such as non-quad elements, redundant irregular vertices, T-junctions, and others. Each surface patch, which can contain multiple singularities and/or polygonal elements, is mapped to an axis-aligned rectangle, leading to a simple and efficient UV layout, which is ideal for texture mapping (allowing for mipmapping and artifact-free bilinear interpolation). We demonstrate that our algorithm is an ideal solution for both recent semi-regular, quad-dominant meshing methods, and for the low-poly meshes typically used in games and movies.

Stitch meshing

We introduce the first fully automatic pipeline to convert arbitrary 3D shapes into knit models. Our pipeline is based on a global parametrization remeshing pipeline to produce an isotropic quad-dominant mesh aligned with a 2-RoSy field. The knitting directions over the surface are determined using a set of custom topological operations and a two-step global optimization that minimizes the number of irregularities. The resulting mesh is converted into a valid stitch mesh that represents the knit model. The yarn curves are generated from the stitch mesh and the final yarn geometry is computed using a yarn-level relaxation process. Thus, we produce topologically valid models that can be used with a yarn-level simulation. We validate our algorithm by automatically generating knit models from complex 3D shapes and processing over a hundred models with various shapes without any user input or parameter tuning. We also demonstrate applications of our approach for custom knit model generation using fabrication via 3D printing.

Automatic Machine Knitting of 3D Meshes

We present the first computational approach that can transform three-dimensional (3D) meshes, created by traditional modeling programs, directly into instructions for a computer-controlled knitting machine. Knitting machines are able to robustly and repeatably form knitted 3D surfaces from yarn but have many constraints on what they can fabricate. Given user-defined starting and ending points on an input mesh, our system incrementally builds a helix-free, quad-dominant mesh with uniform edge lengths, runs a tracing procedure over this mesh to generate a knitting path, and schedules the knitting instructions for this path in a way that is compatible with machine constraints. We demonstrate our approach on a wide range of 3D meshes.

FlowRep

We present FlowRep , an algorithm for extracting descriptive compact 3D curve networks from meshes of free-form man-made shapes. We infer the desired compact curve network from complex 3D geometries by using a series of insights derived from perception, computer graphics, and design literature. These sources suggest that visually descriptive networks are cycle-descriptive , i.e their cycles unambiguously describe the geometry of the surface patches they surround. They also indicate that such networks are designed to be projectable , or easy to envision when observed from a static general viewpoint; in other words, 2D projections of the network should be strongly indicative of its 3D geometry. Research suggests that both properties are best achieved by using networks dominated by flowlines , surface curves aligned with principal curvature directions across anisotropic regions and strategically extended across sharp-features and isotropic areas. Our algorithm leverages these observation in the construction of a compact descriptive curve network. Starting with a curvature aligned quad dominant mesh we first extract sequences of mesh edges that form long, well-shaped and reliable flowlines by leveraging directional similarity between nearby meaningful flowline directions We then use a compact subset of the extracted flowlines and the model's sharp-feature, or trim, curves to form a sparse, projectable network which describes the underlying surface. We validate our method by demonstrating a range of networks computed from diverse inputs, using them for surface reconstruction, and showing extensive comparisons with prior work and artist generated networks.

Robust hex-dominant mesh generation using field-guided polyhedral agglomeration

We propose a robust and efficient field-aligned volumetric meshing algorithm that produces hex-dominant meshes, i.e. meshes that are predominantly composed of hexahedral elements while containing a small number of irregular polyhedra. The latter are placed according to the singularities of two optimized guiding fields, which allow our method to generate meshes with an exceptionally high amount of isotropy. The field design phase of our method relies on a compact quaternionic representation of volumetric octa-fields and a corresponding optimization that explicitly models the discrete matchings between neighboring elements. This optimization naturally supports alignment constraints and scales to very large datasets. We also propose a novel extraction technique that uses field-guided mesh simplification to convert the optimized fields into a hexdominant output mesh. Each simplification operation maintains topological validity as an invariant, ensuring manifold output. These steps easily generalize to other dimensions or representations, and we show how they can be an asset in existing 2D surface meshing techniques. Our method can automatically and robustly convert any tetrahedral mesh into an isotropic hex-dominant mesh and (with minor modifications) can also convert any triangle mesh into a corresponding isotropic quad-dominant mesh, preserving its genus, number of holes, and manifoldness. We demonstrate the benefits of our algorithm on a large collection of shapes provided in the supplemental material along with all generated results.

A robust combinatorial approach to reduce singularities in quadrilateral meshes

There are many automatic quadrilateral mesh generators that can produce a high-quality mesh with low distortion. However, they typically generate a large number of singularities that could be detrimental to downstream applications. This paper introduces Minimum Singularity Templates (MST) to reduce the number of singularities in a pure quad mesh. These templates are easy to encode with high-level grammar rules for complete automation or interactive control. The MST exploits two important properties of quadrilateral meshes: (1) every submesh has even number of quad edges on its boundary, and (2) every submesh with 3, 4 or 5 topological convex corners on its boundary can be transformed into a patch that has at most two interior singularities. The MST (1) does not change the boundary edges of the patch, (2) avoids corner picking on a patch and solving NP-hard interval matching algorithm to select divisions, (3) is extremely fast with time complexity of O(1) in template creation, and (4) has low memory footprint and is robust. To illustrate the concepts, we consider quadrilateral meshes generated using Abaqus, Gmsh, and Cubit, and reduce the singularities within these meshes.Besides improving the topological quality of an existing quad mesh, we describe two additional algorithms that exploit the above MST operations to (1) generate an ab-initio high-quality quadrilateral mesh in a complex domain, and (2) convert a quad-dominant mesh to a pure quadrilateral mesh.

Retiling scheme: a novel approach of direct anisotropic quad-dominant remeshing

Remeshing has been an active research topic in Digital Geometry Processing. In this paper, a novel approach of direct anisotropic quad-dominant remeshing is proposed. We apply the retiling method to the particular problem of quad-dominant remeshing. Compared with other methods, this method can simply partition the surface of an original triangular mesh into connected quads with the mesh edges aligning to the principal directions. The first step in this method is to estimate and smooth the curvature tensor field of the surface at the vertices, and then the quad-dominant mesh is obtained by retiling the quad surface so that quadrilateral edges are parallel to the local principal curvature directions. In addition, to preserve the sharp feature information during remeshing processes, the feature lines can be extracted using mesh segmentation method, and the intersections between the feature lines and the orthogonal planes can be found during the process of retiling. A feature fusion process is presented to join the feature edges and feature points into the quad-dominant mesh. The experiment results show that this new remeshing method is simple and easy to implement. The resolution of the quadrilateral mesh can be controlled during the remeshing. It is applicable to arbitrary genus meshes and can generate high-quality quad-dominant mesh.

Instant field-aligned meshes

We present a novel approach to remesh a surface into an isotropic triangular or quad-dominant mesh using a unified local smoothing operator that optimizes both the edge orientations and vertex positions in the output mesh. Our algorithm produces meshes with high isotropy while naturally aligning and snapping edges to sharp features. The method is simple to implement and parallelize, and it can process a variety of input surface representations, such as point clouds, range scans and triangle meshes. Our full pipeline executes instantly (less than a second) on meshes with hundreds of thousands of faces, enabling new types of interactive workflows. Since our algorithm avoids any global optimization, and its key steps scale linearly with input size, we are able to process extremely large meshes and point clouds, with sizes exceeding several hundred million elements. To demonstrate the robustness and effectiveness of our method, we apply it to hundreds of models of varying complexity and provide our cross-platform reference implementation in the supplemental material.

Using the medial axis to represent flow features for feature-aligned unstructured quad-dominant mesh generation

A method to represent complex flow structures as geometric entities, using the medial axis for the purpose of generating flow feature-aligned meshes, is presented. The medial curves representing the flow features are embedded in the domain to guide mesh alignment and location of background sources, which influence element spacing and orientation when the mesh is regenerated. The resulting meshes possess regions of high-quality anisotropic quadrilateral elements locally aligned with the flow features. To further optimise the mesh based on the solution, a nodal movement adaptation scheme is applied which allows full alignment of the cell interfaces with the flow features, making the mesh more suitable for the one-dimensional approximate Riemann solvers and higher-order reconstruction schemes. The technique and its potential for improving the numerical simulation is presented for a range of test cases for the solution of the Euler and Navier–Stokes equations for compressible flows, which include shock waves, boundary layers and steady trailing wakes as the dominant flow features.

3D models mapping optimization through an integrated parameterization approach: cases studies from Ravenna

Abstract. Image-based modelling tools based on SfM algorithms gained great popularity since several software houses provided applications able to achieve 3D textured models easily and automatically. The aim of this paper is to point out the importance of controlling models parameterization process, considering that automatic solutions included in these modelling tools can produce poor results in terms of texture utilization. In order to achieve a better quality of textured models from image-based modelling applications, this research presents a series of practical strategies aimed at providing a better balance between geometric resolution of models from passive sensors and their corresponding (u,v) map reference systems. This aspect is essential for the achievement of a high-quality 3D representation, since "apparent colour" is a fundamental aspect in the field of Cultural Heritage documentation. Complex meshes without native parameterization have to be "flatten" or "unwrapped" in the (u,v) parameter space, with the main objective to be mapped with a single image. This result can be obtained by using two different strategies: the former automatic and faster, while the latter manual and time-consuming. Reverse modelling applications provide automatic solutions based on splitting the models by means of different algorithms, that produce a sort of "atlas" of the original model in the parameter space, in many instances not adequate and negatively affecting the overall quality of representation. Using in synergy different solutions, ranging from semantic aware modelling techniques to quad-dominant meshes achieved using retopology tools, it is possible to obtain a complete control of the parameterization process.

An effective quad-dominant meshing method for unorganized point clouds

To perform quad meshing on raw point clouds, existing algorithms usually require a time-consuming parameterization or Voronoi space partition process. In this paper, we propose an effective method to generate quad-dominant meshes directly from unorganized point clouds. In the proposed method, we first apply Marinov’s curvature tensor optimization to the input point cloud to reduce the umbilical regions in order to obtain a smooth curvature tensor. We then propose an efficient marching scheme to extract the curvature lines with controllable density from the point cloud. Finally, we apply a specialized K-Dimension (KD) tree structure, which converts the nearest neighbor searching problem into a sorting problem, to efficiently estimate the intersections of curvature lines and recover the topology of the quad-dominant meshes. We have tested the proposed method on different point clouds. Our results show that the proposed method produces good quality meshes with high computational efficiency and low memory requirement.

Surface Parameterization for the Shape Analysis of Tube-Like Objects

In bio-medicine and other fields, shape analysis is very important for diagnosis of diseases and prediction of shape variation. This paper focuses on the surface parameterization of tube-like 3D objects to obtain and analyze shape information from a sample shape, including its size and the shape variation between different samples. It can well represent the global and local shape information for statistical analysis and for the construction of Medial Shape Model. Firstly, we extract the axis curve of the object by a heat conduction model. Secondly, we obtain the latitude circles by using the normal planes to cross the surface. Then we get the final parameterized surface with quad-dominant meshes by registering the points of single latitude circle and between different circles through coordinate transformation and alignment. Subsequently, we apply the approach to parameterization of a rib bone.

Global Anisotropic Quad-Dominant Remeshing

PDF HTML阅读 XML下载 导出引用 引用提醒 全局各向异性四边形主导网格重建方法 DOI: 10.3724/SP.J.1001.2012.03988 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: 国家自然科学基金(U0935004, U1135003, 61100080); 国家重点基础研究发展计划(973)(2011CB302204); 国家科技支撑计划(2011BAH27B01, 2011BHA16B08); 广东省重大科技专项(2011A080401007); 省部产学研结合科技创新平台项目(2011A091000032); 中山大学青年教师培育基金(2009-62000-3161033) Global Anisotropic Quad-Dominant Remeshing Author: Affiliation: Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:四边形网格的结构特点要求网格单元满足全局一致性,难以取得网格质量与表达效率之间的平衡.为此,提出一种基于全局的各向异性四边形主导网格重建方法,可生成网格质量好且冗余程度低的四边形网格.重建过程以主曲率线为基本采样单元,首先计算模型表面的主曲率场并对主曲率场积分,得到密集的主曲率线采样;再根据贪心算法,利用几何形体自身的各向异性找出冗余度最高的主曲率线并予以删除;如此循环,直至达到理想的采样密度.该重建方法适用于任意拓扑网格模型,所得到的各向异性四边形主导网格在网格模型分辨率下降时,由于始终保留重要主曲率线,从而可以更好地保持模型特征.同时,在基于贪心算法的渐进式主曲率线删除过程中,可产生分辨率连续可调的四边形主导网格. Abstract:This paper proposes an anisotropic quad-dominant remeshing algorithm suitable for meshes of arbitrary topology. It takes an approach to the challenging problem of obtaining an anisotropic quad-dominant mesh. The method consists of operations that sample surface geometry by dense principle curvature lines and sort curvature-lines by variations of surface normal and volume related to them. The anisotropic sampling of curvature lines is then obtained by implementing a prioritization scheme of curvature lines elimination. The strategy is simple and straightforward to implement. It is flexible to produce anisotropic quad-dominant meshes ranging from dense to coarse too. The resulting meshes exhibit better anisotropic distribution than comparable methods while maintaining high geometric fidelity. 参考文献 相似文献 引证文献