Computer Aided Geometric Design最新文献

{"title":"GeoHi-GNN: Geometry-aware hierarchical graph representation learning for normal estimation","authors":"Nannan Li ,&nbsp;Xinyuan Li ,&nbsp;Jun Zhou ,&nbsp;Dong Jiang ,&nbsp;Jian Liu ,&nbsp;Hong Qin","doi":"10.1016/j.cagd.2024.102390","DOIUrl":"10.1016/j.cagd.2024.102390","url":null,"abstract":"<div><div>Normal estimation has been one of the key tasks in point cloud analysis, while it is challenging when facing with severe noises or complex regions. The challenges mainly come from the selection of supporting points for estimation, that is, improper selections of points and points' scale will lead to insufficient information, loss of details, etc. To this end, this paper proposes one feature-centric fitting scheme, GeoHi-GNN, by learning geometry-aware hierarchical graph representation for fitting weights estimation. The main functional module is the continuously conducted Hierarchically Geometric-aware (HG) module, consisting of two core operations, namely, the graph node construction (GNC) and the geometric-aware dynamic graph convolution (GDGC). GNC aims to aggregate the feature information onto a smaller number of nodes, providing global-to-local information while avoiding the interferences from noises in larger scales. With these nodes distributed in different scales, GDGC dynamically updates the node features regarding to both intrinsic feature and extrinsic geometric information. Finally, the hierarchical graphical features are cascaded to estimate the weights for supporting points in the surface fitting. Through the extensive experiments and comprehensive comparisons with the state-of-the-arts, our scheme has exhibited many attractive advantages such as being geometry-aware and robust, empowering further applications like more accurate surface reconstruction.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"114 ","pages":"Article 102390"},"PeriodicalIF":1.3,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142432316","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}

{"title":"Computing properties of subdivision schemes using small real Fourier indexed matrices","authors":"Cédric Gérot ,&nbsp;Loïc Barthe ,&nbsp;Neil A. Dodgson ,&nbsp;Malcolm A. Sabin","doi":"10.1016/j.cagd.2024.102391","DOIUrl":"10.1016/j.cagd.2024.102391","url":null,"abstract":"<div><div>The quality of a subdivision scheme in the vicinity of a vertex or a face-centre is related to the eigenstructure of the subdivision matrix. When the scheme has the appropriate symmetries, a common technique, based on discrete Fourier transform, builds small complex matrices that ease the numerical analysis of the eigenelements using in particular their Fourier index. But the numerical analysis of the eigenelements remains difficult when matrix entries involve complex numbers and unknowns, for example, in cases where we are tuning a scheme. We present techniques to build similar small matrices, still associated with a Fourier index and whose eigenstructure is simply related to the full matrix, but which are real. They extend the known techniques to schemes which rotate the lattice and with vertices which do not lie topologically on symmetry axes of the studied vicinity of vertex or face centre. Our techniques make it easier to tune these subdivision schemes. We illustrate it with the analysis of the so-called Simplest Scheme at the centre of an <em>n</em>-sided face.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"114 ","pages":"Article 102391"},"PeriodicalIF":1.3,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142426603","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}

{"title":"Computing the cut locus, Voronoi diagram, and signed distance function of polygons","authors":"Csaba Bálint,&nbsp;Róbert Bán,&nbsp;Gábor Valasek","doi":"10.1016/j.cagd.2024.102388","DOIUrl":"10.1016/j.cagd.2024.102388","url":null,"abstract":"<div><p>This paper presents a new method for the computation of the generalized Voronoi diagram of planar polygons. First, we show that the vertices of the cut locus can be computed efficiently. This is achieved by enumerating the tripoints of the polygon, a superset of the cut locus vertices. This is the set of all points that are of equal distance to three distinct topological entities. Then our algorithm identifies and connects the appropriate tripoints to form the cut locus vertex connectivity graph, where edges define linear or parabolic boundary segments between the Voronoi regions, resulting in the generalized Voronoi diagram. Our proposed method is validated on complex polygon soups. We apply the algorithm to represent the exact signed distance function of the polygon by augmenting the Voronoi regions with linear and radial functions, calculating the cut locus both inside and outside.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"114 ","pages":"Article 102388"},"PeriodicalIF":1.3,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167839624001225/pdfft?md5=b31dbc2c8c3b0e635c2e304a68dca304&pid=1-s2.0-S0167839624001225-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142272718","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}

{"title":"Resultants of slice regular polynomials in two quaternionic variables","authors":"Anna Gori ,&nbsp;Giulia Sarfatti ,&nbsp;Fabio Vlacci","doi":"10.1016/j.cagd.2024.102381","DOIUrl":"10.1016/j.cagd.2024.102381","url":null,"abstract":"<div><p>We introduce a non-commutative resultant, for slice regular polynomials in two quaternionic variables, defined in terms of a suitable Dieudonné determinant. We use this tool to investigate the existence of common zeros and common factors of slice regular polynomials and we give a kinematic interpretation of our results.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"114 ","pages":"Article 102381"},"PeriodicalIF":1.3,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142076946","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}

{"title":"Conversion from NURBS to Bézier representation","authors":"Lanlan Yan","doi":"10.1016/j.cagd.2024.102380","DOIUrl":"10.1016/j.cagd.2024.102380","url":null,"abstract":"<div><p>With the help of the Cox-de Boor recursion formula and the recurrence relation of the Bernstein polynomials, two categories of recursive algorithms for calculating the conversion matrix from an arbitrary non-uniform B-spline basis to a Bernstein polynomial basis of the same degree are presented. One is to calculate the elements of the matrix one by one, and the other is to calculate the elements of the matrix in two blocks. Interestingly, the weights in the two most basic recursion formulas are directly related to the weights in the recursion definition of the B-spline basis functions. The conversion matrix is exactly the Bézier extraction operator in isogeometric analysis, and we obtain the local extraction operator directly. With the aid of the conversion matrix, it is very convenient to determine the Bézier representation of NURBS curves and surfaces on any specified domain, that is, the isogeometric Bézier elements of these curves and surfaces.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"113 ","pages":"Article 102380"},"PeriodicalIF":1.3,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141985702","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}

{"title":"1D CNNs and face-based random walks: A powerful combination to enhance mesh understanding and 3D semantic segmentation","authors":"Amine Kassimi ,&nbsp;Jamal Riffi ,&nbsp;Khalid El Fazazy ,&nbsp;Thierry Bertin Gardelle ,&nbsp;Hamza Mouncif ,&nbsp;Mohamed Adnane Mahraz ,&nbsp;Ali Yahyaouy ,&nbsp;Hamid Tairi","doi":"10.1016/j.cagd.2024.102379","DOIUrl":"10.1016/j.cagd.2024.102379","url":null,"abstract":"<div><p>In this paper, we present a novel face-based random walk method aimed at addressing the 3D semantic segmentation issue. Our method utilizes a one-dimensional convolutional neural network for detailed feature extraction from sequences of triangular faces and employs a stacked gated recurrent unit to gather information along the sequence during training. This approach allows us to effectively handle irregular meshes and utilize the inherent feature extraction potential present in mesh geometry. Our study's results show that the proposed method achieves competitive results compared to the state-of-the-art methods in mesh segmentation. Importantly, it requires fewer training iterations and demonstrates versatility by applying to a wide range of objects without the need for the mesh to adhere to manifold or watertight topology requirements.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"113 ","pages":"Article 102379"},"PeriodicalIF":1.3,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941435","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}

{"title":"De Casteljau's geometric approach to geometric design still alive","authors":"Rachid Ait-Haddou ,&nbsp;Marie-Laurence Mazure","doi":"10.1016/j.cagd.2024.102378","DOIUrl":"10.1016/j.cagd.2024.102378","url":null,"abstract":"<div><p>With great enthusiasm and admiration we would like to pay tribute to Paul de Faget de Casteljau for his essential contribution to CAGD. Motivated by the development of automated <em>human-computer collaboration</em> for car industry, not only was he the very first pioneer in this field, but his initial geometric approach to creating <em>shapes from poles</em> was even undeniably the simplest and most remarkably effective. Two crucial points in this approach are to keep in mind: firstly, the idea of splitting one variable into several variables to facilitate the algorithmic construction of curves; secondly, the possibility of controlling shapes by means of osculating flats and corner-cutting algorithms. The present article is a partial survey on Chebyshevian blossoms intended to show that his ideas are still alive.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"113 ","pages":"Article 102378"},"PeriodicalIF":1.3,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141978922","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}

{"title":"Symmetry group detection of point clouds in 3D via a decomposition method","authors":"Michal Bizzarri ,&nbsp;Lukáš Hruda ,&nbsp;Miroslav Lávička ,&nbsp;Jan Vršek","doi":"10.1016/j.cagd.2024.102376","DOIUrl":"10.1016/j.cagd.2024.102376","url":null,"abstract":"<div><p>Analyzing the symmetries present in point clouds, which represent sets of 3D coordinates, is important for understanding their underlying structure and facilitating various applications. In this paper, we propose a novel decomposition-based method for detecting the entire symmetry group of 3D point clouds. Our approach decomposes the point cloud into simpler shapes whose symmetry groups are easier to find. The exact symmetry group of the original point cloud is then derived from the symmetries of these individual components. The method presented in this paper is a direct extension of the approach recently formulated in <span><span>Bizzarri et al. (2022a)</span></span> for discrete curves in plane. The method can be easily modified also for perturbed data. This work contributes to the advancement of symmetry analysis in point clouds, providing a foundation for further research and enhancing applications in computer vision, robotics, and augmented reality.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"113 ","pages":"Article 102376"},"PeriodicalIF":1.3,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141852180","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}

{"title":"Quaternionic Bézier parameterizations of bidegree (2,1)","authors":"R. Krasauskas,&nbsp;S. Zube","doi":"10.1016/j.cagd.2024.102375","DOIUrl":"10.1016/j.cagd.2024.102375","url":null,"abstract":"<div><p>Earlier results on various quaternionic Bézier parametrizations of Darboux cyclides are extended to bidegree <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> parameterizations of a wider class of surfaces containing at least two families of circles. The focus is on one special family of such parametrizations, which depends on 4 control points and defines a pencil of surfaces tangent along the common circle. This construction is used for parametrizing two-oval Darboux cyclides and generating the Gaussian map for rational offsets of ellipsoids and two-sheet hyperboloids.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"113 ","pages":"Article 102375"},"PeriodicalIF":1.3,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141728723","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}

{"title":"Extending the Hough transform to recognize and approximate space curves in 3D models","authors":"Chiara Romanengo,&nbsp;Bianca Falcidieno,&nbsp;Silvia Biasotti","doi":"10.1016/j.cagd.2024.102377","DOIUrl":"10.1016/j.cagd.2024.102377","url":null,"abstract":"<div><p>Feature curves are space curves identified by color or curvature variations in a shape, which are crucial for human perception (<span><span>Biederman, 1995</span></span>). Detecting these characteristic lines in 3D digital models becomes important for recognition and representation processes. For recognizing plane curves in images, the Hough transform (HT) provided a very good solution to the problem. It selects the best-fitting curve in a dictionary of families of curves through a voting procedure that makes it robust to noise and missing parts. Since 3D digital models are often obtained by scanning real objects and may have many defects, the HT has been extended to recognize and approximate space curves in 3D models that correspond to relevant features</p><p>This work overviews three HT-based different approaches for identifying and approximating spatial profiles of points extracted from point clouds or meshes. A first attempt at this extension involved projecting the spatial points onto the regression plane, thus reducing the problem to planar recognition and using families of plane curves. A second approach has been proposed to recognize spatial profiles that cannot be projected onto the regression plane, using two types of space curve families. Unfortunately, the main drawback of methods based on traditional HT is that it requires prior knowledge of which family of curves to look for.</p><p>To overcome this limitation, a third method has been developed that provides a piecewise space curve approximation using specific parametric polynomial curves. Additionally, free-form curves that a parametric or implicit form cannot express can be represented using this technique.</p><p>In the paper, we also analyze the pros and cons of the various approaches and how they managed and reduced the HT's computational cost, given the large number of parameters introduced when families of space curves are considered.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"113 ","pages":"Article 102377"},"PeriodicalIF":1.3,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167839624001110/pdfft?md5=6bb00fd796f369e5995f8832f3474cc5&pid=1-s2.0-S0167839624001110-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141949878","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}