Computer Aided Geometric Design最新文献_第7页

Maximally smooth cubic spline quasi-interpolants on arbitrary triangulations 任意三角形上的最大平滑三次样条准内插法

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-05-21 DOI: 10.1016/j.cagd.2024.102348

Michelangelo Marsala , Carla Manni , Hendrik Speleers

{"title":"Maximally smooth cubic spline quasi-interpolants on arbitrary triangulations","authors":"Michelangelo Marsala , Carla Manni , Hendrik Speleers","doi":"10.1016/j.cagd.2024.102348","DOIUrl":"10.1016/j.cagd.2024.102348","url":null,"abstract":"<div><p>We investigate the construction of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> cubic spline quasi-interpolants on a given arbitrary triangulation <span><math><mi>T</mi></math></span> to approximate a sufficiently smooth function <em>f</em>. The proposed quasi-interpolants are locally represented in terms of a simplex spline basis defined on the cubic Wang–Shi refinement of the triangulation. This basis behaves like a B-spline basis within each triangle of <span><math><mi>T</mi></math></span> and like a Bernstein basis for imposing smoothness across the edges of <span><math><mi>T</mi></math></span>. Any element of the cubic Wang–Shi spline space can be uniquely identified by considering a local Hermite interpolation problem on every triangle of <span><math><mi>T</mi></math></span>. Different <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> cubic spline quasi-interpolants are then obtained by feeding different sets of Hermite data to this Hermite interpolation problem, possibly reconstructed via local polynomial approximation. All the proposed quasi-interpolants reproduce cubic polynomials and their performance is illustrated with various numerical examples.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"112 ","pages":"Article 102348"},"PeriodicalIF":1.5,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167839624000827/pdfft?md5=3323aa8370f60e90cbc4a16e5bad56ff&pid=1-s2.0-S0167839624000827-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141133010","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}

引用次数: 0

Interactive reverse engineering of CAD models 交互式 CAD 模型逆向工程

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-05-13 DOI: 10.1016/j.cagd.2024.102339

Zhenyu Zhang , Mingyang Zhao , Zeyu Shen , Yuqing Wang , Xiaohong Jia , Dong-Ming Yan

{"title":"Interactive reverse engineering of CAD models","authors":"Zhenyu Zhang , Mingyang Zhao , Zeyu Shen , Yuqing Wang , Xiaohong Jia , Dong-Ming Yan","doi":"10.1016/j.cagd.2024.102339","DOIUrl":"https://doi.org/10.1016/j.cagd.2024.102339","url":null,"abstract":"<div><p>Reverse engineering <em>Computer-Aided Design</em> (CAD) models based on the original geometry is a valuable and challenging research problem that has numerous applications across various tasks. However, previous approaches have often relied on excessive manual interaction, leading to limitations in reconstruction speed. To mitigate this issue, in this study, we approach the reconstruction of a CAD model by sequentially constructing geometric primitives (such as vertices, edges, loops, and faces) and performing Boolean operations on the generated CAD modules. We address the complex reconstruction problem in four main steps. Firstly, we use a plane to cut the input mesh model and attain a loop cutting line, ensuring accurate normals. Secondly, the cutting line is automatically fitted to edges using primitive information and connected to form a primitive loop. This eliminates the need for time-consuming manual selection of each endpoint and significantly accelerates the reconstruction process. Subsequently, we construct the loop of primitives as a chunked CAD model through a series of CAD procedural operations, including <em>extruding, lofting, revolving, and sweeping</em>. Our approach incorporates an automatic height detection mechanism to minimize errors that may arise from manual designation of the extrusion height. Finally, by merging Boolean operations, these CAD models are assembled together to closely approximate the target geometry. We conduct a comprehensive evaluation of our algorithm using a diverse range of CAD models from both the Thingi10K dataset and real-world scans. The results validate that our method consistently delivers accurate, efficient, and robust reconstruction outcomes while minimizing the need for manual interactions. Furthermore, our approach demonstrates superior performance compared to competing methods, especially when applied to intricate geometries.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"111 ","pages":"Article 102339"},"PeriodicalIF":1.5,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140951770","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}

引用次数: 0

Investigations of a functional version of a blending surface scheme for regular data interpolation 对用于常规数据插值的混合曲面方案功能版本的研究

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-05-13 DOI: 10.1016/j.cagd.2024.102345

Stephen Mann

引用次数: 0

Hermite subdivision schemes for manifold-valued Hermite data 流形值 Hermite 数据的 Hermite 细分方案

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-05-13 DOI: 10.1016/j.cagd.2024.102342

Hofit Ben-Zion Vardi, Nira Dyn, Nir Sharon

引用次数: 0

pκ-Curves: Interpolatory curves with curvature approximating a parabola pκ 曲线曲率近似抛物线的插值曲线

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-05-10 DOI: 10.1016/j.cagd.2024.102330

Zhihao Wang , Juan Cao , Tuan Guan , Zhonggui Chen , Yongjie Jessica Zhang

引用次数: 0

Real-time volume rendering with octree-based implicit surface representation 使用基于八度的隐式表面表示法进行实时体绘制

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-05-08 DOI: 10.1016/j.cagd.2024.102322

Jiaze Li , Luo Zhang , Jiangbei Hu , Zhebin Zhang , Hongyu Sun , Gaochao Song , Ying He

{"title":"Real-time volume rendering with octree-based implicit surface representation","authors":"Jiaze Li , Luo Zhang , Jiangbei Hu , Zhebin Zhang , Hongyu Sun , Gaochao Song , Ying He","doi":"10.1016/j.cagd.2024.102322","DOIUrl":"https://doi.org/10.1016/j.cagd.2024.102322","url":null,"abstract":"<div><p>Recent breakthroughs in neural radiance fields have significantly advanced the field of novel view synthesis and 3D reconstruction from multi-view images. However, the prevalent neural volume rendering techniques often suffer from long rendering time and require extensive network training. To address these limitations, recent initiatives have explored explicit voxel representations of scenes to expedite training. Yet, they often fall short in delivering accurate geometric reconstructions due to a lack of effective 3D representation. In this paper, we propose an octree-based approach for the reconstruction of implicit surfaces from multi-view images. Leveraging an explicit, network-free data structure, our method substantially increases rendering speed, achieving real-time performance. Moreover, our reconstruction technique yields surfaces with quality comparable to state-of-the-art network-based learning methods. The source code and data can be downloaded from <span>https://github.com/LaoChui999/Octree-VolSDF</span><svg><path></path></svg>.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"111 ","pages":"Article 102322"},"PeriodicalIF":1.5,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140913891","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}

引用次数: 0

Planar quartic G2 Hermite interpolation for curve modeling 用于曲线建模的平面四次 G2 赫米特插值法

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-05-07 DOI: 10.1016/j.cagd.2024.102303

Angyan Li, Lizheng Lu, Kesheng Wang

{"title":"Planar quartic G2 Hermite interpolation for curve modeling","authors":"Angyan Li, Lizheng Lu, Kesheng Wang","doi":"10.1016/j.cagd.2024.102303","DOIUrl":"https://doi.org/10.1016/j.cagd.2024.102303","url":null,"abstract":"<div><p>We study planar quartic <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> Hermite interpolation, that is, a quartic polynomial curve interpolating two planar data points along with the associated tangent directions and curvatures. When the two specified tangent directions are non-parallel, a quartic Bézier curve interpolating such <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> data is constructed using two geometrically meaningful shape parameters which denote the magnitudes of end tangent vectors. We then determine the two parameters by minimizing a quadratic energy functional or curvature variation energy. When the two specified tangent directions are parallel, a quartic <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> interpolating curve exists only when an additional condition on <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> data is satisfied, and we propose a modified optimization approach. Finally, we demonstrate the achievable quality with a range of examples and the application to curve modeling, and it allows to locally create <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> smooth complex shapes. Compared with the existing quartic interpolation scheme, our method can generate more satisfactory results in terms of approximation accuracy and curvature profiles.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"111 ","pages":"Article 102303"},"PeriodicalIF":1.5,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140947280","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}

引用次数: 0

Construction of the ellipse with maximum area inscribed in an arbitrary convex quadrilateral 构建任意凸四边形中面积最大的椭圆

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-05-07 DOI: 10.1016/j.cagd.2024.102323

Long Ma, Yuanfeng Zhou

{"title":"Construction of the ellipse with maximum area inscribed in an arbitrary convex quadrilateral","authors":"Long Ma, Yuanfeng Zhou","doi":"10.1016/j.cagd.2024.102323","DOIUrl":"https://doi.org/10.1016/j.cagd.2024.102323","url":null,"abstract":"<div><p>An ellipse can be uniquely determined by five tangents. Given a convex quadrilateral, there are infinitely many ellipses inscribed in it, but the one with maximum area is unique. In this paper, we give a concise and effective solution of this problem. Our solution is composed of three steps: First, we transform the problem from the maximal ellipse construction problem into the minimal quadrilateral construction problem by an affine transformation. And then, we convert the construction problem into a conditional extremum problem by analyzing the key angles. At last, we derive the solution of the conditional extremum problem with Lagrangian multiplier. Based on the conclusion, we designed an algorithm to achieve the construction. The numerical experiment shows that the ellipse constructed by our algorithm has the maximum area. It is interesting and surprising that our constructions only need to solve quadratic equations, which means the geometric information of the ellipse can even be derived with ruler and compass constructions. The solution of this problem means all the construction problems of conic with extremum area from given pure tangents are solved, which is a necessary step to solve more problems of constructing ellipses with extremum areas. Our work also provides a useful conclusion to solve the maximal inscribed ellipse problem for an arbitrary polygon in Computational Geometry.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"111 ","pages":"Article 102323"},"PeriodicalIF":1.5,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140951789","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}

引用次数: 0

The architectural application of shells whose boundaries subtend a constant solid angle 边界包含恒定实体角的壳体在建筑上的应用

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-05-03 DOI: 10.1016/j.cagd.2024.102331

Emil Adiels, Mats Ander, Chris J.K. Williams

{"title":"The architectural application of shells whose boundaries subtend a constant solid angle","authors":"Emil Adiels, Mats Ander, Chris J.K. Williams","doi":"10.1016/j.cagd.2024.102331","DOIUrl":"https://doi.org/10.1016/j.cagd.2024.102331","url":null,"abstract":"<div><p>Surface geometry plays a central role in the design of bridges, vaults and shells, using various techniques for generating a geometry which aims to balance structural, spatial, aesthetic and construction requirements.</p><p>In this paper we propose the use of surfaces defined such that given closed curves subtend a constant solid angle at all points on the surface and form its boundary. Constant solid angle surfaces enable one to control the boundary slope and hence achieve an approximately constant span-to-height ratio as the span varies, making them structurally viable for shell structures. In addition, when the entire surface boundary is in the same plane, the slope of the surface around the boundary is constant and thus follows a principal curvature direction. Such surfaces are suitable for surface grids where planar quadrilaterals meet the surface boundaries. They can also be used as the Airy stress function in the form finding of shells having forces concentrated at the corners.</p><p>Our technique employs the Gauss-Bonnet theorem to calculate the solid angle of a point in space and Newton's method to move the point onto the constant solid angle surface. We use the Biot-Savart law to find the gradient of the solid angle. The technique can be applied in parallel to each surface point without an initial mesh, opening up for future studies and other applications when boundary curves are known but the initial topology is unknown.</p><p>We show the geometrical properties, possibilities and limitations of surfaces of constant solid angle using examples in three dimensions.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"111 ","pages":"Article 102331"},"PeriodicalIF":1.5,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140879527","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}

引用次数: 0

Alternating size field optimizing and parameterization domain CAD model remeshing 交替尺寸场优化和参数化域 CAD 模型重塑

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-05-03 DOI: 10.1016/j.cagd.2024.102294

Shiyi Wang , Bochun Yang , Hujun Bao , Jin Huang

{"title":"Alternating size field optimizing and parameterization domain CAD model remeshing","authors":"Shiyi Wang , Bochun Yang , Hujun Bao , Jin Huang","doi":"10.1016/j.cagd.2024.102294","DOIUrl":"https://doi.org/10.1016/j.cagd.2024.102294","url":null,"abstract":"<div><p>Tessellating CAD models into triangular meshes is a long-lasting problem. Size field is widely used to accommodate varieties of requirements in remeshing, and it is usually discretized and optimized on a prescribed background mesh and kept constant in the subsequent remeshing procedure. Instead, we propose optimizing the size field on the current mesh, then using it as guidance to generate the next mesh. This simple strategy eliminates the need of building a proper background mesh and greatly simplifies the size field query. For better quality and convergence, we also propose a geodesic distance based initialization and adaptive re-weighting strategy in size field optimization. Similar to existing methods, we also view the remeshing of a CAD model as the remeshing of its parameterization domain, which guarantees that all the vertices lie exactly on the CAD surfaces and eliminates the need for costly and error-prone projection operations. However, for vertex smoothing which is important for mesh quality, we carefully optimize the vertex's location in the parameterization domain for the optimal Delaunay triangulation condition, along with a high-order cubature scheme for better accuracy. Experiments show that our method is fast, accurate and controllable. Compared with state-of-the-art methods, our approach is fast and usually generates meshes with smaller Hausdorff error, larger minimal angle with a comparable number of triangles.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"111 ","pages":"Article 102294"},"PeriodicalIF":1.5,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140879312","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}

引用次数: 0