Computer Aided Geometric Design最新文献

{"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}

{"title":"On G2 approximation of planar algebraic curves under certified error control by quintic Pythagorean-hodograph splines","authors":"Xin-Yu Wang ,&nbsp;Li-Yong Shen ,&nbsp;Chun-Ming Yuan ,&nbsp;Sonia Pérez-Díaz","doi":"10.1016/j.cagd.2024.102374","DOIUrl":"10.1016/j.cagd.2024.102374","url":null,"abstract":"<div><p>The Pythagorean-Hodograph curve (PH curve) is a valuable curve type extensively utilized in computer-aided geometric design and manufacturing. This paper presents an approach to approximate a planar algebraic curve within a bounding box by employing piecewise quintic PH spline curves, while maintaining <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> smoothness of the approximating curve and preserving second-order geometric details at singularities. The bounding box encompasses all <em>x</em>-coordinates of key topological points, ensuring accurate representation. The paper explores the analysis of the <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> interpolation problem for quintic PH curves with invariant convexity, transforming the quest for interpolation solutions into identifying positive roots within a set of algebraic equations. Through infinitesimal order analysis, it is established that a solution necessarily exists following adequate subdivision, laying the groundwork for practical application. Finally, the paper introduces a novel algorithm that integrates prior research to construct the approximating curve while maintaining control over the desired error levels.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"113 ","pages":"Article 102374"},"PeriodicalIF":1.3,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141639021","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":"Calibrating figures","authors":"Niels Lubbes ,&nbsp;Josef Schicho","doi":"10.1016/j.cagd.2024.102365","DOIUrl":"https://doi.org/10.1016/j.cagd.2024.102365","url":null,"abstract":"<div><p>It is known that a camera can be calibrated using three pictures of either squares, or spheres, or surfaces of revolution. We give a new method to calibrate a camera with the picture of a single torus.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"112 ","pages":"Article 102365"},"PeriodicalIF":1.3,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141481969","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":"Shape reconstruction of trapezoidal surfaces from unorganized point clouds","authors":"Arvin Rasoulzadeh,&nbsp;Martin Kilian,&nbsp;Georg Nawratil","doi":"10.1016/j.cagd.2024.102367","DOIUrl":"https://doi.org/10.1016/j.cagd.2024.102367","url":null,"abstract":"<div><p>A smooth T-surface can be thought of as a generalization of a surface of revolution in such a way that the axis of rotation is not fixed at one point but rather traces a smooth path on the base plane. Furthermore, the action, by which the aforementioned surface is obtained does not need to be merely rotation but any “suitable” planar equiform transformation applied to the points of a certain smooth profile curve. In analogy to the smooth setting, if the axis footpoints sweep a polyline on the base plane and if the profile curve is discretely chosen then a T-hedra (discrete T-surface) with trapezoidal faces is obtained.</p><p>The goal of this article is to reconstruct a T-hedron from an already given unorganized point cloud of a T-surface. In doing so, a kinematic approach is taken into account, where the algorithm at first tries to find the aforementioned axis direction associated with the point cloud. Then the algorithm finds a polygonal path through which the axis footpoint moves. Finally, by properly cutting the point cloud with the planes passing through the axis and its footpoints, it reconstructs the surface. The presented method is demonstrated using examples.</p><p>From an applied point of view, the straightforwardness of the generation of these surfaces predestines them for building and design processes. In fact, one can find many built objects belonging to the sub-classes of T-surfaces such as <em>surfaces of revolution</em> and <em>moulding surfaces</em>. Furthermore, the planarity of the faces of the discrete version paves the way for steel/glass construction in industry. Finally, these surfaces are also suitable for transformable designs as they allow an isometric deformation within their class.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"113 ","pages":"Article 102367"},"PeriodicalIF":1.3,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167839624001018/pdfft?md5=a89afc76375e1a62b939020faa4c744d&pid=1-s2.0-S0167839624001018-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141542428","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":"Alzheimer's disease diagnosis by applying Shannon entropy to Ricci flow-based surface indexing and extreme gradient boosting","authors":"Fatemeh Ahmadi,&nbsp;Behroz Bidabad,&nbsp;Mohamad-Ebrahim Shiri,&nbsp;Maral Sedaghat","doi":"10.1016/j.cagd.2024.102364","DOIUrl":"https://doi.org/10.1016/j.cagd.2024.102364","url":null,"abstract":"<div><p>Geometric surface models are extensively utilized in brain imaging to analyze and compare three-dimensional anatomical shapes. Due to the intricate nature of the brain surface, rather than examining the entire cortical surface, we are introducing a new set of signatures focused on characteristics of the hippocampal region, which is linked to aspects of Alzheimer's disease. Our approach focuses on Ricci flow as a conformal parameterization method, permitting us to calculate the conformal factor and mean curvature as conformal surface representations to identify distinct regions within a three-dimensional mesh. For the first time for such settings, we propose a simple while elegant formulation by employing the well-established concept of Shannon entropy on these well-known features. This compact while rich feature formulation turns out to lead to an efficient local surface encoding. We are validating its effectiveness through a series of preliminary experiments on 3D MRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), with the aim of diagnosing Alzheimer's disease. The feature vectors generated and inputted into the XGBoost classifier demonstrate a remarkable level of accuracy, further emphasizing their potential as a valuable additional measure for surface-based cortical morphometry in Alzheimer's disease research.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"113 ","pages":"Article 102364"},"PeriodicalIF":1.3,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141478776","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":"A tour d'horizon of de Casteljau's work","authors":"Andreas Müller","doi":"10.1016/j.cagd.2024.102366","DOIUrl":"https://doi.org/10.1016/j.cagd.2024.102366","url":null,"abstract":"<div><p>Whilst Paul de Casteljau is now famous for his fundamental algorithm of curve and surface approximation, little is known about his other findings. This article offers an insight into his results in geometry, algebra and number theory.</p><p>Related to geometry, his classical algorithm is reviewed as an index reduction of a polar form. This idea is used to show de Casteljau's algebraic way of smoothing, which long went unnoticed. We will also see an analytic polar form and its use in finding the intersection of two curves. The article summarises unpublished material on metric geometry. It includes theoretical advances, e.g., the 14-point strophoid or a way to link Apollonian circles with confocal conics, and also practical applications such as a recurrence for conjugate mirrors in geometric optics. A view on regular polygons leads to an approximation of their diagonals by golden matrices, a generalisation of the golden ratio.</p><p>Relevant algebraic findings include matrix quaternions (and anti-quaternions) and their link with Lorentz' equations. De Casteljau generalised the Euclidean algorithm and developed an automated method for approximating the roots of a class of polynomial equations. His contributions to number theory not only include aspects on the sum of four squares as in quaternions, but also a view on a particular sum of three cubes. After a review of a complete quadrilateral in a heptagon and its angles, the paper concludes with a summary of de Casteljau's key achievements.</p><p>The article contains a comprehensive bibliography of de Casteljau's works, including previously unpublished material.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"113 ","pages":"Article 102366"},"PeriodicalIF":1.3,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167839624001006/pdfft?md5=3258b55a89826636b158851c6197a7cf&pid=1-s2.0-S0167839624001006-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141542419","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":"Reliability-based G1 continuous arc spline approximation","authors":"Jinhwan Jeon ,&nbsp;Yoonjin Hwang ,&nbsp;Seibum B. Choi","doi":"10.1016/j.cagd.2024.102363","DOIUrl":"https://doi.org/10.1016/j.cagd.2024.102363","url":null,"abstract":"<div><p>This paper introduces an algorithm for approximating a set of data points with <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> continuous arcs, leveraging covariance data associated with the points. Prior approaches to arc spline approximation typically assumed equal contribution from all data points, resulting in potential algorithmic instability when outliers are present. To address this challenge, we propose a robust method for arc spline approximation, taking into account the 2D covariance of each data point. Beginning with the definition of models and parameters for <strong>single-arc approximation</strong>, we extend the framework to support <strong>multiple-arc approximation</strong> for broader applicability. Finally, we validate the proposed algorithm using both synthetic noisy data and real-world data collected through vehicle experiments conducted in Sejong City, South Korea.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"112 ","pages":"Article 102363"},"PeriodicalIF":1.5,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141428798","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":"Classification of Dupin cyclidic cubes by their singularities","authors":"Jean Michel Menjanahary ,&nbsp;Eriola Hoxhaj ,&nbsp;Rimvydas Krasauskas","doi":"10.1016/j.cagd.2024.102362","DOIUrl":"https://doi.org/10.1016/j.cagd.2024.102362","url":null,"abstract":"<div><p>Triple orthogonal coordinate systems having coordinate lines as circles or straight lines are considered. Technically, they are represented by trilinear rational quaternionic maps and are called Dupin cyclidic cubes, naturally generalizing the bilinear rational quaternionic parametrizations of principal patches of Dupin cyclides. Dupin cyclidic cubes and their singularities are studied and classified up to Möbius equivalency in Euclidean space.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"112 ","pages":"Article 102362"},"PeriodicalIF":1.5,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141423461","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":"Euler Bézier spirals and Euler B-spline spirals","authors":"Xunnian Yang","doi":"10.1016/j.cagd.2024.102361","DOIUrl":"10.1016/j.cagd.2024.102361","url":null,"abstract":"<div><p>Euler spirals have linear varying curvature with respect to arc length and can be applied in fields such as aesthetics pleasing shape design, curve completion or highway design, etc. However, evaluation and interpolation of Euler spirals to prescribed boundary data is not convenient since Euler spirals are represented by Fresnel integrals but with no closed-form expression of the integrals. We investigate a class of Bézier or B-spline curves called Euler Bézier spirals or Euler B-spline spirals which have specially defined control polygons and approximate linearly varying curvature. This type of spirals can be designed conveniently and evaluated exactly. Simple but efficient algorithms are also given to interpolate <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> boundary data by Euler Bézier spirals or cubic Euler B-spline spirals.</p></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"112 ","pages":"Article 102361"},"PeriodicalIF":1.5,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141402113","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}