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Curvature computations for the intersection curves of hypersurfaces in Euclidean n-space Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-12-29 B. Merih Özçetin; Mustafa Düldül
The aim of this paper is to derive the curvatures and Frenet vectors of the intersection curve of (n−1) transversally intersecting hypersurfaces represented either in implicit or in parametric form in Euclidean n-space. Since the intersection of (n−1) implicit hypersurfaces defines an implicit curve in n-dimensions, the method derived for the implicit case can be considered as a partial answer to the
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A sampling type discernment approach towards reconstruction of a point set in R2 Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-12-15 Safeer Babu Thayyil; Jiju Peethambaran; Ramanathan Muthuganapathy
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Kinematic interpretation of Darboux cyclides Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-10-26 R. Krasauskas; S. Zube
Kinematic interpretation of quaternionic–Bézier curves and surfaces is revealed. This combination of kinematic and geometric modeling methods is used to characterize orbits of quadratic surfaces in the Study quadric under the kinematic map as certain Darboux cyclides. In particular, earlier unknown rational parametrizations of one-oval Darboux cyclides are found.
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Characterizing envelopes of moving rotational cones and applications in CNC machining Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-10-16 Mikhail Skopenkov; Pengbo Bo; Michael Bartoň; Helmut Pottmann
Motivated by applications in CNC machining, we provide a characterization of surfaces which are enveloped by a one-parametric family of congruent rotational cones. As limit cases, we also address ruled surfaces and their offsets. The characterizations are higher order nonlinear PDEs generalizing the ones by Gauss and Monge for developable surfaces and ruled surfaces, respectively. The derivation includes
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Handling heterogeneous structures and materials using blending schemes in V-reps Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-10-10 Emiliano Cirillo; Gershon Elber
Additive manufacturing has recently enabled the creation of heterogeneous objects in which different materials can be specified at different locations. This creates new exciting perspectives in additive crafting but also presents several challenges, including the problem of specifying rules for varying materials at particular locations as well as encoding user specified properties (such as stress tensors)
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Real-World Textured Things: A repository of textured models generated with modern photo-reconstruction tools Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-10-09 Andrea Maggiordomo; Federico Ponchio; Paolo Cignoni; Marco Tarini
We are witnessing a proliferation of textured 3D models captured from the real world with automatic photo-reconstruction tools by people and professionals without a proper technical background in computer graphics. Digital 3D models of this class come with a unique set of characteristics and defects – especially concerning their parametrization – setting them starkly apart from 3D models originating
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Low degree splines for locally quad-dominant meshes Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-09-25 Kȩstutis Karčiauskas; Jörg Peters
A mesh is locally quad-dominant (lqd) if all non-4-sided facets are surrounded by quadrilaterals. Lqd meshes allow for irregular nodes where n≠4 quads meet and for multi-sided facets, called T-gons, that end quad-strips and so adjust mesh density. This paper introduces a new class of bi-cubic (bi-3) Geometric T-joint (GT) splines whose control nets are τ-nets, i.e. T-gons surrounded by quads. These
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Singular cases of planar and spatial C1 Hermite interpolation problems based on quintic Pythagorean-hodograph curves Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-09-21 Rida T. Farouki; Kai Hormann; Federico Nudo
A well–known feature of the Pythagorean–hodograph (PH) curves is the multiplicity of solutions arising from their construction through the interpolation of Hermite data. In general, there are four distinct planar quintic PH curves that match first–order Hermite data, and a two–parameter family of spatial quintic PH curves compatible with such data. Under certain special circumstances, however, the
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Inflection points on 3D curves Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-09-23 Nikolaos C. Gabrielides; Nickolas S. Sapidis
Existing definitions for inflection point on 3D curves lack the direct relation to local shape-characteristics of the 3D curve that the corresponding definition for planar curves has. This paper presents a new generalization of the definition of planar-curve inflection to the case of a 3D curve that is directly related to the local convexity of the 3D curve and to that of orthogonal projections of
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On a progressive and iterative approximation method with memory for least square fitting Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-09-23 Zheng-Da Huang; Hui-Di Wang
In this paper, we present a progressive and iterative approximation method with memory for least square fitting (MLSPIA). It adjusts the control points and the weighted sums iteratively to construct a series of fitting curves (surfaces) with three weights. For any normalized totally positive basis, even when the collocation matrix is of deficient column rank, we obtain a condition to guarantee that
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A few conjectures on a four-point interpolatory subdivision scheme Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-09-22 Ren-Jiang Zhang
Dubuc pioneered a method of interpolation iterative scheme, which is called four-point interpolatory subdivision scheme. Since then, the method has been developed extensively and deeply. However some precise problems proposed by Dubuc are still unsolved after thirty years. In this paper, we will partially solve these problems.
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Visibility-driven skeleton extraction from unstructured points Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-09-12 Lifeng Zhu, Wen Xing, Aiguo Song, Yongjie Jessica Zhang
We present an algorithm for curve skeleton extraction from unstructured points using visibility as a guide. We introduce visible cells inside the point samples. By locating a viewpoint in the space, visible points from the viewpoint are connected to indicate the visible region, which locally captures the interior structure of the points and is called a visible cell. We then analyze and clean the visible
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SP-Flow: Self-supervised optical flow correspondence point prediction for real-time SLAM Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-08-31 Zixuan Qin, Mengxiao Yin, Guiqing Li, Feng Yang
This paper presents a self-supervised learning network called SP-Flow to generate keypoints in real-time for SLAM systems. Optical flows are employed to match the keypoints between two successive frames in the training process of SP-Flow. This approach enables the network to use datasets without manual annotations. To show the efficacy of our SP-Flow, we built an SP-Flow SLAM system by replacing ORB
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The distance function from a real algebraic variety Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-08-27 Giorgio Ottaviani, Luca Sodomaco
For any (real) algebraic variety X in a Euclidean space V endowed with a nondegenerate quadratic form q, we introduce a polynomial EDpolyX,u(t2) which, for any u∈V, has among its roots the distance from u to X. The degree of EDpolyX,u is the Euclidean Distance degree of X. We prove a duality property when X is a projective variety, namely EDpolyX,u(t2)=EDpolyX∨,u(q(u)−t2) where X∨ is the dual variety
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Extending Ball B-spline by B-spline Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-08-25 Xinyue Liu, Xingce Wang, Zhongke Wu, Dan Zhang, Xiangyuan Liu
Extending a Ball B-spline Curve (BBSC) is a useful function in the shape modelling of freeform tubular objects. In this paper, we aim to obtain a cubic BBSC B‾(t‾) that can smoothly and fairly extend a given cubic BBSC B(t) to a target ball R. BBSCs with one endpoint satisfying G2 continuity with B(t) and the other endpoint passing through R are optional extending results. We choose the fairest of
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Multi-stage point completion network with critical set supervision Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-08-21 Wenxiao Zhang, Chengjiang Long, Qingan Yan, Alix L.H. Chow, Chunxia Xiao
Point cloud based shape completion has great significant application values and refers to reconstructing a complete point cloud from a partial input. In this paper, we propose a multi-stage point completion network (MSPCN) with critical set supervision. In our network, a cascade of upsampling units is used to progressively recover the high-resolution results with several stages. Different from the
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Shape analysis of planar PH curves with the Gauss–Legendre control polygons Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-08-17 Hwan Pyo Moon, Soo Hyun Kim, Song-Hwa Kwon
Kim and Moon (2017) have recently proposed rectifying control polygons as an alternative to Bézier control polygons and a way of controlling planar PH curves by the rectifying control polygons. While a Bézier control polygon determines a unique polynomial curve, a rectifying control polygon gives a multitude of PH curves. This multiplicity of PH curves naturally raises the selection problem of the
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An efficient method to integrate polynomials over polytopes and curved solids Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-07-21 Eric B. Chin, N. Sukumar
In this paper, we present an efficient approach to compute the integral of monomials and polynomials over polyhedra and regions defined by parametric curved boundary surfaces. We use Euler's theorem for homogeneous functions in combination with Stokes's theorem to reduce the integration of a monomial over a three-dimensional solid to its boundary. If the solid is a polytope, through a recursive application
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Dynamic spline bas-relief modeling with isogeometric collocation method Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-07-15 Jinlan Xu, Chengnan Ling, Gang Xu, Zhongping Ji, Xiangyang Wu, Timon Rabczuk
In this paper, we propose a novel framework for dynamic spline bas-relief modeling based on isogeometric collocation method. In the proposed method, the bas-relief model is separated into two parts: the base surface and the relief surface; and both of them are represented in spline form. To simplify the construction, the spline bases for representing the base surface and relief surface are in the same
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Fitting a planar quadratic slerp motion Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-07-03 Glen Mullineux, Robert J. Cripps, Ben Cross
This paper presents a geometric construction for fitting planar motions to three control poses within a particular geometric algebra. The immediate impact of the geometric construction along with the control pose representation is the provision of simple, usable tools for the design and manipulation of motions in a similar way to the highly successful B-spline approach for curves and surfaces in CAD
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From theoretical to applied geometry - recent developments. Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-07-02 Marjeta Knez,Martin Peternell,Juan Gerardo Alcázar
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3D grasp saliency analysis via deep shape correspondence Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-06-30 Li-na Zhang, Shi-yao Wang, Jun Zhou, Jian Liu, Chun-gang Zhu
Grasp saliency map is an important analysis tool to explore human grasping skills and has many potential applications in visual and robotic fields. Currently, few works concentrate on the 3D grasp saliency detection for novel challenging instances, since the calculation of the grasp saliency map depends on the insufficient human grasping data and geometry of the 3D shapes. To address the above problem
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Non-rigid 3D shape retrieval based on multi-scale graphical image and joint Bayesian Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-06-18 Haohao Li, Zhixun Su, Nannan Li, Ximin Liu, Shengfa Wang, Zhongxuan Luo
Feature analysis plays a crucial role in various applications in both computer vision and computer graphics. The semantic gap between 2D images and 3D graphical models is the major obstacle to improve the universality of existing valuable technologies. To bridge the gap, we propose an effective and robust representation of 3D models, named multi-scale Graphical Image (GI), which is constructed by introducing
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Tetrahedral mesh deformation with positional constraints Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-06-16 Wenjing Zhang, Yuewen Ma, Jianmin Zheng, William J. Allen
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Recognizing algebraic affine rotation surfaces Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-06-12 Juan G. Alcázar, Ron Goldman
We investigate the problem of recognizing a generalization of surfaces of revolution appearing in the field of affine differential geometry, namely affine rotation surfaces. By using some notions from affine differential geometry, we determine how to detect whether or not a given implicit algebraic surface is an affine rotation surface. These results generalize some previous results of the authors
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Adaptive IGAFEM with optimal convergence rates: T-splines Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-06-09 Gregor Gantner, Dirk Praetorius
We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations. We employ analysis-suitable T-splines of arbitrary odd degree on T-meshes generated by the refinement strategy of Morgenstern and Peterseim (2015) in 2D and Morgenstern (2016) in 3D. Adaptivity is driven by some weighted
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Consistent dynamic map labeling with fairness and importance Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-06-08 Xiao Zhang, Sheung-Hung Poon, Shengxin Liu, Minming Li, Victor C.S. Lee
Geographical visualization systems, such as online maps, provide interactive operations of continuous zooming and panning. With consistent dynamic map labeling, users can navigate continuously in the map areas such that labels are not allowed to exhibit abrupt change in terms of their positions or sizes, and labels should not suddenly disappear or reappear when zooming in or pop up when zooming out
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Smooth polar caps for locally quad-dominant meshes. Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-06-08 Kȩstutis Karčiauskas,Jörg Peters
A polar configuration is a node surrounded by m triangles. Polar configurations are common to cap off cylinders and spheres. When the triangles, interpreted as quadrilaterals with one edge collapsed, are surrounded by a quad-strip then the extended polar configuration qualifies as part of a locally quad-dominant (lqd) mesh. Recent constructions, referred to as semi-structured splines, can use lqd meshes
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Local computation of homology variations over a construction process Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-06-05 Wassim Rharbaoui, Sylvie Alayrangues, Pascal Lienhardt, Samuel Peltier
This paper deals with the homology computation of a subdivided object during its construction. In this paper, we focus on the construction operation consisting of merging cells. For each step of the construction, a homological equivalence is maintained. This algebraic structure connects the chain complex associated with the object to a smaller object (i.e. containing less cells) having the same homology
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Osculating conic biarcs Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-06-04 A. Gfrerrer, G. Weiss
A circular biarc can be defined by using two points K and L with their (oriented) tangents gK and gL as input. It is well-known that one can determine a one parametric set of circular arc pairs k,ℓ such that k starts at K with tangent gK, ℓ ends at L with tangent gL and k and ℓ meet with a common tangent in an intermediate point P. In this paper we investigate a similar construction where we replace
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Evaluation and subdivision algorithms for general classes of totally positive rational bases Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-06-03 E. Mainar, J.M. Peña, B. Rubio
Weighted φ-transformed systems include many systems of functions useful in C.A.G.D. It is proved that these systems inherit some geometric properties of a given initial system, such as shape preservation or optimal shape preservation. A general class of important rational bases can be obtained as a particular example of weighted φ-transformed systems. For these bases, evaluation and subdivision algorithms
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Quasi-elastic cubic splines in Rd Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-06-02 Hakim S. Johnson, Michael J. Johnson
Given points P1,P2,…,Pn in Rd (d≥2), we consider the problem of constructing a fair interpolating curve. For d=2, we proposed and analyzed, in Johnson and Johnson (2016), a method which first generates a family of G1 interpolating curves, where each piece is a parametric cubic. An energy functional, that loosely approximates bending energy, is defined on this family and then one seeks a curve with
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Optimal parametric interpolants of circular arcs Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-05-28 Aleš Vavpetič
The aim of this paper is a construction of quartic parametric polynomial interpolants of a circular arc, where two boundary points of a circular arc are interpolated. For every unit circular arc of an inner angle not greater than 2π we find the best interpolant, where the optimality is measured by the simplified radial error.
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A trivariate T-spline based framework for modeling heterogeneous solids Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-05-25 Bin Li, Jianzhong Fu, Yongjie Jessica Zhang, Aishwarya Pawar
We present a robust framework to conduct material modeling suitable for continuously varying materials with a local material composition control. The geometry and attribute representations are defined using two trivariate T-splines based on the same parametric domain. The optimization process decreases the mismatch of geometry and attribute between the input tetrahedral mesh and the trivariate T-splines
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An optimized yarn-level geometric model for Finite Element Analysis of weft-knitted fabrics Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-05-18 Paras Wadekar, Vignesh Perumal, Genevieve Dion, Antonios Kontsos, David Breen
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Reverse engineering of CAD models via clustering and approximate implicitization Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-05-15 Andrea Raffo, Oliver J.D. Barrowclough, Georg Muntingh
In applications like computer aided design, geometric models are often represented numerically as polynomial splines or NURBS, even when they originate from primitive geometry. For purposes such as redesign and isogeometric analysis, it is of interest to extract information about the underlying geometry through reverse engineering. In this work we develop a novel method to determine these primitive
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Variational shape approximation of point set surfaces Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-05-13 Martin Skrodzki, Eric Zimmermann, Konrad Polthier
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Dimension of polynomial splines of mixed smoothness on T-meshes Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-05-13 Deepesh Toshniwal, Nelly Villamizar
In this paper we study the dimension of splines of mixed smoothness on axis-aligned T-meshes. This is the setting when different orders of smoothness are required across the edges of the mesh. Given a spline space whose dimension is independent of its T-mesh's geometric embedding, we present constructive and sufficient conditions that ensure that the smoothness across a subset of the mesh edges can
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Spherical interpolatory geometric subdivision schemes Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-05-13 Mohamed Bellaihou, Aziz Ikemakhen
We define general geometric subdivision schemes generating curves on the 2-dimensional unit sphere by using geodesic polygons and the spherical distance. We show that a spherical interpolatory geometric subdivision scheme is convergent if the sequence of maximum edge lengths is summable and the limit curve is G1-continuous if in addition the sequence of maximum angular defects is summable. In particular
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Isogeometric shape optimization of an acoustic horn using the teaching-learning-based optimization (TLBO) algorithm Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-05-13 Vinay K. Ummidivarapu, Hari K. Voruganti, Tahsin Khajah, Stéphane Pierre Alain Bordas
Isogeometric shape optimization has been receiving great attention due to its advantages of exact geometry representation and smooth representation of the boundaries. In the present study, the optimum shape of a horn speaker was found to minimize the back reflection and improve impedance matching. The acoustic field was estimated by isogeometric analysis (IGA). Horn reflections are sensitive to the
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An input-independent single pass algorithm for reconstruction from dot patterns and boundary samples Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-05-12 Safeer Babu Thayyil, Amal Dev Parakkat, Ramanathan Muthuganapathy
Given a set of points S∈R2, reconstruction is a process of identifying the boundary edges that best approximates the set of points. In general, the set of points can either be derived from only the boundaries of the curves (called as boundary sample) or can be derived from both boundary and interior of the curves (called as dot pattern). Most of the existing algorithms focus towards reconstruction
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Refinable tri-variate C 1 splines for box-complexes including irregular points and irregular edges. Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-05-12 Jörg Peters
C1 splines over box-complexes generalize C1 degree 3 (cubic) tensor-product splines. A box-complex is a collection of 3-dimensional boxes forming an unstructured hexahedral mesh that can include irregular points and irregular edges where the layout deviates from the tensor-product grid layout. For example, an edge shared and enclosed by five boxes is irregular. Where the mesh is locally regular, the
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Construction of Minkowski Pythagorean hodograph B-spline curves Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-05-11 Michal Bizzarri, Miroslav Lávička
Following and extending the recent results of Albrecht et al. (2017) for planar Pythagorean hodograph (PH) B-spline curves to the Minkowski 3-space, we introduce a class of Minkowski Pythagorean hodograph (MPH) B-spline curves. The distinguished property of these curves is that the Minkowski norm of their hodograph is a B-spline function. We focus mainly on the clamped case and using Clifford algebra
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P2MAT-NET: Learning medial axis transform from sparse point clouds Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-05-11 Baorong Yang, Junfeng Yao, Bin Wang, Jianwei Hu, Yiling Pan, Tianxiang Pan, Wenping Wang, Xiaohu Guo
The medial axis transform (MAT) of a 3D shape includes the set of centers and radii of the maximally inscribed spheres, and is a complete shape descriptor that can be used to reconstruct the original shape. It is a compact representation that jointly describes geometry, topology, and symmetry properties of a given shape. In this work, we present P2MAT-NET, a neural network which learns the pattern
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Algebraic and geometric characterizations of a class of planar quartic curves with rational offsets Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-05-06 Kai Hormann, Jianmin Zheng
Planar polynomial curves have rational offset curves, if they are either Pythagorean-hodograph (PH) or indirect Pythagorean-hodograph (iPH) curves. In this paper, we derive an algebraic and two geometric characterizations for planar quartic iPH curves. The characterizations are given in terms of quantities related to the Bézier control polygon of the curve, and naturally extend to quartic and cubic
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Persistent manifolds of the special Euclidean group SE(3): A review Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-05-05 Yuanqing Wu, Marco Carricato
Mechanisms and robots often share the following fundamental property: the instantaneous twist space generated by the end-effector at a generic pose is a rigidly-displaced copy of the one generated at the home configuration, i.e., the tangent spaces at all points of its motion manifold (a manifold of the Lie group of rigid displacements SE(3)) are mutually congruent. A manifold of this kind, hereafter
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EasyMesh: An efficient method to reconstruct 3D mesh from a single image Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-04-28 Xiao Sun, Zhouhui Lian
How to reconstruct the complete 3D mesh model from a single natural image is now still considered as a challenging problem. Most existing methods describe 3D shapes in the form of voxel or point cloud, and it is not always trivial to convert them into meshes with high quality. In this paper, we present a novel method to effectively address this problem by using a specially-designed GAN model to map
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Four-bar linkages, elliptic functions, and flexible polyhedra Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-04-27 Ivan Izmestiev
We revisit Darboux' parametrization of the configuration space of a quadrilateral with fixed side lengths by elliptic functions, remind how it implies Darboux' folding porism, and relate it to Bottema's zigzag porism. Further, we review some mechanical applications of this parametrization giving rise to overconstrained linkages and polyhedra.
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NLIGA: A MATLAB framework for nonlinear isogeometric analysis Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-04-24 Xiaoxiao Du, Gang Zhao, Wei Wang, Mayi Guo, Ran Zhang, Jiaming Yang
Nonlinear behaviors are commonplace in many engineering applications, e.g., metal forming and vehicle crash tests. Different from linear systems, nonlinear problems cannot be solved by using a system of linear equations and there is no guarantee that a unique solution can be found. In this work, we develop a unified framework, NLIGA (Non-Linear Isogeometric Analysis), for mainly solving two and three-dimensional
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Spatial Pythagorean-Hodograph B–Spline curves and 3D point data interpolation Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-04-23 Gudrun Albrecht, Carolina Vittoria Beccari, Lucia Romani
This article deals with the spatial counterpart of the recently introduced class of planar Pythagorean-Hodograph (PH) B–Spline curves. Spatial Pythagorean-Hodograph B–Spline curves are odd-degree, non-uniform, parametric spatial B–Spline curves whose arc length is a B–Spline function of the curve parameter and can thus be computed explicitly without numerical quadrature. After giving a general definition
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Isogeometric analysis for trimmed CAD surfaces using multi-sided toric surface patches Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-04-23 Xuefeng Zhu, Ye Ji, Chungang Zhu, Ping Hu, Zheng-Dong Ma
We propose a new isogeometric method using Toric surface patches for trimmed CAD planar surfaces. This method converts each trimmed spline element into a Toric surface patch with conforming boundary representation and converts each non-trimmed spline element into a Bézier element. Because the Toric surface patches are a multi-sided generalization of classical Bézier surface patches, all trimmed and
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h-Bernstein basis functions over a triangular domain Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-04-22 P. Lamberti, M. Lamnii, S. Remogna, D. Sbibih
In this paper, we introduce and study new h-Bernstein basis functions over a triangular domain. In particular, after defining the h-Bernstein polynomial functions of degree n, we prove their algebraic and geometric properties, such as partition of unity and degree elevation and we show that they form a basis for the space of polynomials of total degree less than or equal to n on a triangle. Then, we
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Pose to Seat: Automated design of body-supporting surfaces Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-04-22 Kurt Leimer, Andreas Winkler, Stefan Ohrhallinger, Przemyslaw Musialski
The design of functional seating furniture is a complicated process which often requires extensive manual design effort and empirical evaluation. We propose a computational design framework for pose-driven automated generation of body-supports which are optimized for comfort of sitting. Given a human body in a specified pose as input, our method computes an approximate pressure distribution that also
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Interpolatory Catmull-Clark volumetric subdivision over unstructured hexahedral meshes for modeling and simulation applications Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-04-22 Jin Xie, Jinlan Xu, Zhenyu Dong, Gang Xu, Chongyang Deng, Bernard Mourrain, Yongjie Jessica Zhang
Volumetric modeling is an important topic for material modeling and isogeometric simulation. In this paper, two kinds of interpolatory Catmull-Clark volumetric subdivision approaches over unstructured hexahedral meshes are proposed based on the limit point formula of Catmull-Clark subdivision volume. The basic idea of the first method is to construct a new control lattice, whose limit volume by the
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LRC-Net: Learning discriminative features on point clouds by encoding local region contexts Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-04-21 Xinhai Liu, Zhizhong Han, Fangzhou Hong, Yu-Shen Liu, Matthias Zwicker
Learning discriminative feature directly on point clouds is still challenging in the understanding of 3D shapes. Recent methods usually partition point clouds into local region sets, and then extract the local region features with fixed-size CNN or MLP, and finally aggregate all individual local features into a global feature using simple max pooling. However, due to the irregularity and sparsity in
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As-developable-as-possible B-spline surface interpolation to B-spline curves Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-04-21 Pengbo Bo, Yujian Zheng, Dianhui Chu, Caiming Zhang
A method is proposed to computing a B-spline surface bounded by two fixed B-spline curves such that the surface achieves as large developability as possible. Existing methods generate discrete developable surfaces from line sequences connecting prespecified points sampled on input curves and need a highly dense sampling to achieve a high degree of developability which largely increases the problem
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Controlling extremal Pythagorean hodograph curves by Gauss–Legendre polygons Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-04-21 Hwan Pyo Moon, Soo Hyun Kim, Song-Hwa Kwon
The problem of constructing spatial Pythagorean hodograph (PH) curves with a given Gauss–Legendre polygon is addressed. For planar/spatial PH curves of degree 2n+1, the Gauss–Legendre polygon, which consists of n+1 edges, obtained by evaluating the hodograph at the nodes of the Gauss–Legendre quadrature, is the rectifying polygon, which has the same length as the PH curve. On the other hand, if a planar
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Local (T)HB-spline projectors via restricted hierarchical spline fitting Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-04-21 Alessandro Giust, Bert Jüttler, Angelos Mantzaflaris
This paper is devoted to techniques for adaptive spline projection via quasi-interpolation, enabling the efficient approximation of given functions. We employ local least-squares fitting in restricted hierarchical spline spaces to establish novel projection operators for hierarchical splines of degree p. This leads to efficient spline projectors that require O(pd) floating point operations and O(1)
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Classification of planar Pythagorean hodograph curves Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-04-21 Zbyněk Šír
We classify planar polynomial Pythagorean-hodograph curves of any degree with respect to Euclidean similarities. We also analyze possible global shapes of the Pythagorean-hodograph curves of degree four and five and describe all possible configurations of their singular points. This description results in a classification of Pythagorean-hodograph quartics and quintics with respect to the homeomorphisms
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Robust atlas generation via angle-based segmentation Comput. Aided Geom. Des. (IF 1.23) Pub Date : 2020-04-20 Chi Zhang, Mao-Feng Xu, Shuangming Chai, Xiao-Ming Fu
We present a robust method to generate atlases with low isometric distortion and high packing efficiency. Given a surface that has been cut to disk topology, the algorithm contains four steps: (1) computing a bijective parameterization with low isometric distortion; (2) partitioning the input parameterized charts into a set of rectangle-like patches; (3) mapping rectangle-like patches onto rectangles
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