Computer Aided Geometric Design最新文献_第10页

Efficient computation of moving planes for rational parametric surfaces with base points using Dixon resultants 基于Dixon结果的有理参数曲面运动平面的有效计算

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2023-10-13 DOI: 10.1016/j.cagd.2023.102253

Kai Li , Xiaohong Jia , Falai Chen

引用次数: 0

On the uniqueness of the multirational blossom 论多有理开花的唯一性

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2023-10-12 DOI: 10.1016/j.cagd.2023.102252

O. Oğulcan Tuncer , Plamen Simeonov , Ron Goldman

{"title":"On the uniqueness of the multirational blossom","authors":"O. Oğulcan Tuncer , Plamen Simeonov , Ron Goldman","doi":"10.1016/j.cagd.2023.102252","DOIUrl":"https://doi.org/10.1016/j.cagd.2023.102252","url":null,"abstract":"<div>The multirational blossom of order k and degree −n of a k-times differentiable function <math><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> is defined as a multivariate function <math><mi>f</mi><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>/</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>k</mi><mo>+</mo><mi>n</mi></mrow></msub><mo>)</mo></math> characterized by four axioms: bisymmetry in the u and v parameters, multiaffine in the u parameters, satisfies a cancellation property and reduces to <math><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> along the diagonal. The existence of a multirational blossom was established in Goldman (1999a) by providing an explicit formula for this blossom in terms of divided differences. Here we show that these four axioms uniquely characterize the multirational blossom. We go on to introduce a homogeneous version of the multirational blossom. We then show that for differentiable functions derivatives can be computed in terms of this homogeneous multirational blossom. We also use the homogeneous multirational blossom to convert between the Taylor bases and the negative degree Bernstein bases.</div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"107 ","pages":"Article 102252"},"PeriodicalIF":1.5,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49759702","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

Topological classification of the intersection curves of two quadrics using a set of discriminants 用一组判别式对两个二次曲面的相交曲线进行拓扑分类

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2023-10-10 DOI: 10.1016/j.cagd.2023.102244

Wenbing Shao, Falai Chen

引用次数: 0

On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining 旋转固体包络的C0、C1连续性及其在五轴数控加工中的应用

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2023-10-04 DOI: 10.1016/j.cagd.2023.102245

Felipe Ponce-Vanegas , Michal Bizzarri , Michael Bartoň

{"title":"On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining","authors":"Felipe Ponce-Vanegas , Michal Bizzarri , Michael Bartoň","doi":"10.1016/j.cagd.2023.102245","DOIUrl":"https://doi.org/10.1016/j.cagd.2023.102245","url":null,"abstract":"<div>We study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5-axis Computer Numerically Controlled (CNC) machining. A moving cutting tool, conceptualized as a rotational solid, forms a surface, called envelope, that delimits a part of 3D space where the tool engages the material block. The smoothness of the resulting envelope depends both on the smoothness of the motion and smoothness of the tool. While the motions of the tool are typically required to be at least <math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math>, the tools are frequently only <math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math> continuous, which results in discontinuous envelopes. In this work, we classify a family of instantaneous motions that, in spite of only <math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math> continuous shape of the tool, result in <math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math> continuous envelopes. We show that such motions are flexible enough to follow a free-form surface, preserving tangential contact between the tool and surface along two points, therefore having applications in shape slot milling or in a semi-finishing stage of 5-axis flank machining. We also show that <math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math> tools and motions still can generate smooth envelopes.</div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"107 ","pages":"Article 102245"},"PeriodicalIF":1.5,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49703472","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

An efficient analytical model for the swept volume generation of a flat-end mill in 5-axis CNC milling 五轴数控铣削平面立铣刀扫掠体积生成的有效分析模型

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2023-10-01 DOI: 10.1016/j.cagd.2023.102241

Ahmet Dogrusadik

{"title":"An efficient analytical model for the swept volume generation of a flat-end mill in 5-axis CNC milling","authors":"Ahmet Dogrusadik","doi":"10.1016/j.cagd.2023.102241","DOIUrl":"10.1016/j.cagd.2023.102241","url":null,"abstract":"<div>5-axis CNC (Computer Numerical Control) milling is widely used to create complex part geometries in the industrial area. The cutting tool creates the swept volume as it moves along the defined path. The swept volume is subtracted from the initial stock for the machining simulation. Although a swept volume consists of three parts such as ingress, egress, and swept envelope, the number of faces of the swept volume is higher than three. In this work, parametric equations of the faces of the swept volume were obtained for a flat-end mill in four steps. The model is based on the decomposition of the tool into circles along the tool orientation vector since a flat-end mill can be modeled as a cylinder. The fundamental principle is that each circle is tangent to the swept envelope of the cylinder. Locations of the grazing points with respect to a local coordinate system were determined by applying the Envelope Theory to the parameterized circle of the cylinder. Then, each face of the swept volume was represented based on the equation of the parameterized circle. The model was verified by using an alternative analytical model. As a result, boundaries of the swept volume were represented fully analytically for a flat-end mill in 5-axis CNC milling in an efficient way.</div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"106 ","pages":"Article 102241"},"PeriodicalIF":1.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49041671","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

On the accuracy of de Casteljau-type algorithms and Bernstein representations de casteljau型算法和Bernstein表示的准确性

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2023-10-01 DOI: 10.1016/j.cagd.2023.102243

J. Delgado, E. Mainar, J.M. Peña

引用次数: 0

Partition of the space of planar quintic Pythagorean-hodograph curves 平面五次毕达哥拉斯曲线空间的划分

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2023-10-01 DOI: 10.1016/j.cagd.2023.102242

Rida T. Farouki

{"title":"Partition of the space of planar quintic Pythagorean-hodograph curves","authors":"Rida T. Farouki","doi":"10.1016/j.cagd.2023.102242","DOIUrl":"https://doi.org/10.1016/j.cagd.2023.102242","url":null,"abstract":"<div>The quintics are the lowest–order planar Pythagorean–hodograph (PH) curves suitable for free–form design, since they can exhibit inflections. A quintic PH curve <math><mi>r</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> may be constructed from a complex quadratic pre–image polynomial <math><mi>w</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> by integration of <math><msup><mrow><mi>r</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>w</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo></math>, and it thus incorporates (modulo translations) six real parameters — the real and imaginary parts of the coefficients of <math><mi>w</mi><mo>(</mo><mi>t</mi><mo>)</mo></math>. Within this 6–dimensional space of planar PH quintics, a 5–dimensional hypersurface separates the inflectional and non–inflectional curves. Points of the hypersurface identify exceptional curves that possess a tangent–continuous point of infinite curvature, corresponding to the fact that the parabolic locus specified by the quadratic pre–image polynomial <math><mi>w</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> passes through the origin of the complex plane. Correspondingly, extreme curvatures and tight loops on <math><mi>r</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> are incurred by a close proximity of <math><mi>w</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> to the origin of the complex plane. These observations provide useful insight into the disparate shapes of the four distinct PH quintic solutions to the first–order Hermite interpolation problem.</div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"106 ","pages":"Article 102242"},"PeriodicalIF":1.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49757160","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

Log-aesthetic curves: Similarity geometry, integrable discretization and variational principles 对数美学曲线:相似几何，可积离散化和变分原理

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2023-09-01 DOI: 10.1016/j.cagd.2023.102233

Jun-ichi Inoguchi , Yoshiki Jikumaru , Kenji Kajiwara , Kenjiro T. Miura , Wolfgang K. Schief

{"title":"Log-aesthetic curves: Similarity geometry, integrable discretization and variational principles","authors":"Jun-ichi Inoguchi , Yoshiki Jikumaru , Kenji Kajiwara , Kenjiro T. Miura , Wolfgang K. Schief","doi":"10.1016/j.cagd.2023.102233","DOIUrl":"https://doi.org/10.1016/j.cagd.2023.102233","url":null,"abstract":"<div>In this paper, we consider a class of plane curves called log-aesthetic curves and their generalization which are used in computer aided geometric design. In the framework of similarity geometry, those curves are characterized as invariant curves under the integrable flow on plane curves governed by the Burgers equation. They also admit a variational formulation leading to the stationary Burgers equation as the Euler-Lagrange equation. As an application of the formulation, we propose a discretization of these curves and the associated variational principle which preserves the underlying integrable structure. We finally present algorithms for generating discrete log-aesthetic curves for given <math><msup><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msup></math> data based on similarity geometry. Our method is able to generate S-shaped discrete curves with an inflection as well as C-shaped curves according to the boundary condition. The resulting discrete curves are regarded as self-adaptive discretization and thus high-quality even with the small number of points. Through the continuous representation, those discrete curves provide a flexible tool for the generation of high-quality shapes.</div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"105 ","pages":"Article 102233"},"PeriodicalIF":1.5,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49701708","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: 1

Joint optimization of distortion and cut location for mesh parameterization using an Ambrosio-Tortorelli functional 基于Ambrosio-Tortorelli函数的网格参数化畸变和切割位置联合优化

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2023-09-01 DOI: 10.1016/j.cagd.2023.102231

Colin Weill–Duflos , David Coeurjolly , Fernando de Goes , Jacques-Olivier Lachaud

{"title":"Joint optimization of distortion and cut location for mesh parameterization using an Ambrosio-Tortorelli functional","authors":"Colin Weill–Duflos , David Coeurjolly , Fernando de Goes , Jacques-Olivier Lachaud","doi":"10.1016/j.cagd.2023.102231","DOIUrl":"https://doi.org/10.1016/j.cagd.2023.102231","url":null,"abstract":"<div>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).</div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"105 ","pages":"Article 102231"},"PeriodicalIF":1.5,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49701710","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

Linear interpolation of shape operators for umbilical points through local parametrization 脐点形状算子的局部参数化线性插值

IF 1.5 4区计算机科学

Computer Aided Geometric Design Pub Date : 2023-09-01 DOI: 10.1016/j.cagd.2023.102223

WuJun Che

引用次数: 0