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2D Bézier curves with monotone curvature based on Class A matrices Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2024-03-11 Aizeng Wang, Chuan He, Yang Song, Gang Zhao
In this paper, we construct 2D Bézier curves with monotone curvature using Class A matrices. A new sufficient condition for Class A matrices based on its singular values, is provided and proved, generalizing the 2D typical curves proposed by Mineur et al. (1998). An algorithm is provided utilizing the condition for easier Class A curve creation. Several 2D aesthetic curve examples are constructed to
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Paul de Casteljau: The story of my adventure: From an autobiographical letter Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2024-03-05 Andreas Müller
Paul de Faget de Casteljau (19.11.1930 - 24.3.2022) has left us an extensive autobiography, written in 1997. In 19 sections, he takes us through his eventful life which he describes with wit and humor. We read about his youth in occupied France and his education at the . He describes in detail various episodes from his time at Citroën, the situation during and after the discovery of his now famous
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Fast evaluation of derivatives of Bézier curves Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2024-02-28 Filip Chudy, Paweł Woźny
New geometric methods for fast evaluation of derivatives of polynomial and rational Bézier curves are proposed. They apply an algorithm for evaluating polynomial or rational Bézier curves, which was recently given by the authors. Numerical tests show that the new approach is more efficient than the methods which use the famous de Casteljau algorithm. The algorithms work well even for high-order derivatives
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Shape-preserving interpolation on surfaces via variable-degree splines Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2024-02-28 P.D. Kaklis, S. Stamatelopoulos, A.-A.I. Ginnis
This paper proposes two, geodesic-curvature based, criteria for shape-preserving interpolation on smooth surfaces, the first criterion being of non-local nature, while the second criterion is a local (weaker) version of the first one. These criteria are tested against a family of on-surface splines obtained by composing the parametric representation of the supporting surface with variable-degree (≥3)
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Computing the intersection between a rational parametric curve and a rational parametric surface Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2024-02-08 Bingwei Zhang, Xi Wu, Jin-San Cheng, Kexin Ding
In this paper, we present an algorithm to compute the intersection between a rational curve and a rational surface. Evaluating the parametric curve into the matrix representation of the parametric surface for implicitization, we get a matrix with one variable. We find the intersection from the matrix with the theory of real root isolation of univariate functions without computing its determinant as
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Subdivision algorithms with modular arithmetic Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2024-01-09 Ron Goldman
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Conics in rational cubic Bézier form made simple Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-12-12 Javier Sánchez-Reyes
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New algebraic and geometric characterizations of planar quintic Pythagorean-hodograph curves Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-12-06 Kai Hormann, Lucia Romani, Alberto Viscardi
The aim of this work is to provide new characterizations of planar quintic Pythagorean-hodograph curves. The first two are algebraic and consist of two and three equations, respectively, in terms of the edges of the Bézier control polygon as complex numbers. These equations are symmetric with respect to the edge indices and cover curves with generic as well as degenerate control polygons. The last
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Detecting and parametrizing polynomial surfaces without base points Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-11-15 Sonia Pérez-Díaz, Marian Fernández de Sevilla, Rafael Magdalena Benedicto, Li-Yong Shen
Given an algebraic surface implicitly defined by an irreducible polynomial, we present a method that decides whether or not this surface can be parametrized by a polynomial parametrization without base points and, in the affirmative case, we show how to compute this parametrization.
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Apollonian de Casteljau–type algorithms for complex rational Bézier curves Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-10-17 Bert Jüttler, Josef Schicho, Zbyněk Šír
We describe a new de Casteljau–type algorithm for complex rational Bézier curves. After proving that these curves exhibit the maximal possible circularity, we construct their points via a de Casteljau–type algorithm over complex numbers. Consequently, the line segments that correspond to convex linear combinations in affine spaces are replaced by circular arcs. In difference to the algorithm of Sánchez-Reyes
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Efficient computation of moving planes for rational parametric surfaces with base points using Dixon resultants Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-10-13 Kai Li, Xiaohong Jia, Falai Chen
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On the uniqueness of the multirational blossom Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-10-12 O. Oğulcan Tuncer, Plamen Simeonov, Ron Goldman
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Topological classification of the intersection curves of two quadrics using a set of discriminants Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-10-10 Wenbing Shao, Falai Chen
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On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-10-04 Felipe Ponce-Vanegas, Michal Bizzarri, Michael Bartoň
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On the accuracy of de Casteljau-type algorithms and Bernstein representations Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-09-19 J. Delgado, E. Mainar, J.M. Peña
This paper summarizes interesting results on systematic backward and forward error analyses performed for corner cutting algorithms providing evaluation of univariate and multivariate functions defined in terms of Bernstein and Bernstein related bases. Relevant results on the conditioning of the bases are also recalled. Finally, the paper surveys important advances, lately obtained, for the design
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Partition of the space of planar quintic Pythagorean-hodograph curves Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-09-17 Rida T. Farouki
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An efficient analytical model for the swept volume generation of a flat-end mill in 5-axis CNC milling Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-09-04 Ahmet Dogrusadik
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Log-aesthetic curves: Similarity geometry, integrable discretization and variational principles Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-07-25 Jun-ichi Inoguchi, Yoshiki Jikumaru, Kenji Kajiwara, Kenjiro T. Miura, Wolfgang K. Schief
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A new method for researching and constructing spherical bicentric polygons based on geometric mapping Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-07-20 Junhao Cheng, Long Ma, Yuanfeng Zhou
A bicentric polygon is a special planar polygon that has both a circumcircle and an incircle. Many interesting properties of a planar bicentric polygon have been discovered. However, searching the geometric properties of a spherical bicentric polygon with elementary geometric method is very difficult. In this paper, we propose a special mapping for a pair of circles between a plane and a sphere. This
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Joint optimization of distortion and cut location for mesh parameterization using an Ambrosio-Tortorelli functional Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-07-05 Colin Weill–Duflos, David Coeurjolly, Fernando de Goes, Jacques-Olivier Lachaud
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
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Linear interpolation of shape operators for umbilical points through local parametrization Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-06-19 WuJun Che
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Blending Bézier patch for multi-sided surface modeling Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-06-16 Kaikai Qin, Yajuan Li, Chongyang Deng
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Computing symmetries of implicit algebraic surfaces Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-06-07 Juan Gerardo Alcázar, Miroslav Lávička, Jan Vršek
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Sasaki metric for spline models of manifold-valued trajectories Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-06-05 Esfandiar Nava-Yazdani, Felix Ambellan, Martin Hanik, Christoph von Tycowicz
We propose a generic spatiotemporal framework to analyze manifold-valued measurements, which allows for employing an intrinsic and computationally efficient Riemannian hierarchical model. Particularly, utilizing regression, we represent discrete trajectories in a Riemannian manifold by composite Bézier splines, propose a natural metric induced by the Sasaki metric to compare the trajectories, and estimate
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TPNet: A novel mesh analysis method via topology preservation and perception enhancement Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-05-29 Peifang Li, Fazhi He, Bo Fan, Yupeng Song
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PSPDNet: Part-aware shape and pose disentanglement neural network for 3D human animating meshes Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-05-19 Guiqing Li, Juncheng Zeng, Fanzhong Zeng, Chenhao Yao, Bixia Kuang, Yongwei Nie
Disentangled representations of shape and pose are essential for animating human body meshes in computer animation, computer games, and virtual reality applications. While recent deep neural networks have achieved impressive effectiveness, their performance in terms of interpretability, reconstruction precision, and fine-grained control is not satisfactory. To address these issues, we propose the Part-aware
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CasViGE: Learning robust point cloud registration with cascaded visual-geometric encoding Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-05-19 Zheng Qin, Changjian Wang, Yuxing Peng, Kai Xu
In this work, we present Cascaded Visual-Geometric Encoding (CasViGE), a novel inter-modality feature learning method to improve point cloud registration via the visual information from RGB images. Registering point clouds based on solely the 3D geometric structure suffers from severe matching ambiguity caused by repeated geometric patterns and geometrically less discriminative regions. For this reason
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Accelerating surface remeshing through GPU-based computation of the restricted tangent face Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-05-18 Yuyou Yao, Jingjing Liu, Wenming Wu, Gaofeng Zhang, Benzhu Xu, Liping Zheng
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D-Net: Learning for distinctive point clouds by self-attentive point searching and learnable feature fusion Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-05-10 Xinhai Liu, Zhizhong Han, Sanghuk Lee, Yan-Pei Cao, Yu-Shen Liu
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Point-normal subdivision curves and surfaces Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-05-09 Xunnian Yang
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Kernel-based construction operators for Boolean sum and ruled geometry Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-05-03 Haitham Fadila, Q Youn Hong, Gershon Elber
Boolean sum and ruling are two well-known construction operators for both parametric surfaces and trivariates. In many cases, the input freeform curves in or surfaces in are complex, and as a result, these construction operators might fail to build the parametric geometry so that it has a positive Jacobian throughout the domain. In this work, we focus on cases in which those constructors fail to build
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Computing the Riemannian center of mass on meshes Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-04-24 Claudio Mancinelli, Enrico Puppo
The Riemannian center of mass (a.k.a. Karcher mean or Fréchet mean) provides the equivalent to the Euclidean affine average on manifolds. In spite of its many potential applications in computer graphics and geometric modeling, there exist surprisingly few algorithms to compute it. We present a direct method for computing the Riemannian center of mass on a triangle mesh. Our method works in the polyhedral
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Sharp feature consolidation from raw 3D point clouds via displacement learning Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-04-26 Tong Zhao, Mulin Yu, Pierre Alliez, Florent Lafarge
Detecting sharp features in raw 3D point clouds is an essential step for designing efficient priors in several 3D Vision applications. This paper presents a deep learning-based approach that learns to detect and consolidate sharp feature points on raw 3D point clouds. We devise a multi-task neural network architecture that identifies points near sharp features and predicts displacement vectors toward
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Generalized plane offsets and rational parameterizations Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-04-21 David Rochera
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Point normal orientation and surface reconstruction by incorporating isovalue constraints to Poisson equation Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-04-23 Dong Xiao, Zuoqiang Shi, Siyu Li, Bailin Deng, Bin Wang
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Extraction and application of super-smooth cubic B-splines over triangulations Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-04-20 Jan Grošelj, Hendrik Speleers
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Shape control tools for periodic Bézier curves Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-04-20 Andriamahenina Ramanantoanina, Kai Hormann
Bézier curves are an essential tool for curve design. Due to their properties, common operations such as translation, rotation, or scaling can be applied to the curve by simply modifying the control polygon of the curve. More flexibility, and thus more diverse types of curves, can be achieved by associating a weight with each control point, that is, by considering rational Bézier curves. As shown by
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Construction of planar quintic Pythagorean-hodograph curves by control-polygon constraints Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-04-20 Rida T. Farouki, Francesca Pelosi, Maria Lucia Sampoli
In the construction and analysis of a planar Pythagorean–hodograph (PH) quintic curve r(t), t∈[0,1] using the complex representation, it is convenient to invoke a translation/rotation/scaling transformation so r(t) is in canonical form with r(0)=0, r(1)=1 and possesses just two complex degrees of freedom. By choosing two of the five control–polygon legs of a quintic PH curve as these free complex parameters
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Local linear independence of bilinear (and higher degree) B-splines on hierarchical T-meshes Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-04-18 Lisa Groiss, Bert Jüttler, Maodong Pan
We generate hierarchical T-meshes by repeatedly inserting new line segments, in order to adapt both the size and the shape of the cells to the specific requirements of the underlying application. The associated spaces of bilinear spline functions are spanned by the locally refined (LR) B-splines of Dokken et al. (2013), which are products of univariate B-splines defined over local knot vectors. Our
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On an improved PDE-based elliptic parameterization method for isogeometric analysis using preconditioned Anderson acceleration Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-04-18 Ye Ji, Kewang Chen, Matthias Möller, Cornelis Vuik
Constructing an analysis-suitable parameterization for the computational domain from its boundary representation plays a crucial role in the isogeometric design-through-analysis pipeline. PDE-based elliptic grid generation is an effective method for generating high-quality parameterizations with rapid convergence properties for the planar case. However, it may generate non-uniform grid lines, especially
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Computing the topology of the image of a parametric planar curve under a birational transformation Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-03-28 Juan Gerardo Alcázar, Gema M. Diaz-Toca
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G1 interpolation of v-asymmetric data with arc-length constraints by Pythagorean-hodograph cubic splines Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-03-24 Yong-Xia Hao, Wen-Qing Fei
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Shear-reduced seamless parametrization Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-03-01 Zohar Levi
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A Chebyshev metamodel based BnB approach to efficiently search global optimum for 3D ICP point set registration Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-02-21 Yuesheng Liu, Xindu Chen, Kefeng Wang, Shipu Diao, Yunbao Huang, Haiyan Li, Lei Wu
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Mean curvature flow for generating discrete surfaces with piecewise constant mean curvatures Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-01-24 Kazuki Hayashi, Yoshiki Jikumaru, Makoto Ohsaki, Takashi Kagaya, Yohei Yokosuka
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Discrete exterior calculus for meshes with concyclic polygons Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2023-01-24 Alexander Schier, Reinhard Klein
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Screw rotor manufacturing via 5-axis flank CNC machining using conical tools Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2022-12-01 Michal Bizzarri, Pengbo Bo, Michael Bartoň
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Generalized Savitzky–Golay filter for smoothing triangular meshes Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2022-11-23 Gábor Fábián
In this paper, the well-known Savitzky–Golay filter is generalized for three-dimensional triangular meshes. Savitzky–Golay filter is designed for smoothing noisy measurement signals, initially, a locally polynomial model is fitted to approximate the discrete measurement values. We will show, that the original idea can be naturally adapted for smoothing functions defined on an irregular two-dimensional
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Rational framing motions and spatial rational Pythagorean hodograph curves Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2022-11-07 Bahar Kalkan, Daniel F. Scharler, Hans-Peter Schröcker, Zbyněk Šír
We propose a new method for constructing rational spatial Pythagorean Hodograph (PH) curves based on determining a suitable rational framing motion. While the spherical component of the framing motion is arbitrary, the translation part is determined be a modestly sized and nicely structured system of linear equations. Rather surprisingly, generic input data will only result in polynomial PH curves
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Polynomial curves with projections to PH curves Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2022-10-25 Miroslav Lávička, Jan Vršek
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G1 – Smooth biquintic approximation of Catmull-Clark subdivision surfaces Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2022-10-13 Michelangelo Marsala, Angelos Mantzaflaris, Bernard Mourrain
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An unrefinement algorithm for planar THB-spline parameterizations Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2022-10-06 Teymur Heydarov, Annalisa Buffa, Bert Jüttler
Unrefinement is a tool that allows to perform faster numerical simulations by controlling the level of precision in the specified area. We introduce an algorithm that creates a coarser geometry from an initial regular geometry, which is represented with respect to THB-splines, so that the coarser geometry approximates the initial geometry with a given level of the precision and is regular. The algorithm
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Topology of the singularities of 3-RPR planar parallel robots Comput. Aided Geom. Des. (IF 1.5) Pub Date : 2022-09-24 Christoforos Spartalis, Jose Capco
Given a general 3-RPR planar parallel robot with linear platforms, it is proven that there are no singularity-free paths between non-symmetrical direct kinematics solutions. We provide an alternative proof of this. We also provide a proof that shows that there is a singularity-free path between two symmetrical solutions if an appropriate condition is satisfied. This condition will be automatically