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S0165168415000067 | Sketch-based human motion retrieval is a hot topic in computer animation in recent years. In this paper, we present a novel sketch-based human motion retrieval method via selected 2-dimensional (2D) Geometric Posture Descriptor (2GPD). Specially, we firstly propose a rich 2D pose feature call 2D Geometric Posture Descr... | Sketch-based human motion retrieval via selected 2D geometric posture descriptor |
S0165168415001073 | In this paper, we address the tasks of audio source counting and separation for a stereo anechoic mixture of audio signals. This will be achieved in two stages. In the first stage, a novel approach is introduced for estimating the number of sources as well as the channel mixing coefficients. For this purpose, a 2-D spe... | Blind audio source counting and separation of anechoic mixtures using the multichannel complex NMF framework |
S0165168415003187 | The fractional Fourier transform (FRFT) is one of the most useful tools for the nonstationary signal processing. In this paper, the randomized nonuniform sampling and approximate reconstruction of the nonstationary random signals in the fractional Fourier domain (FRFD) are developed. The nonuniform samples are treated ... | Randomized nonuniform sampling and reconstruction in fractional Fourier domain |
S0165168416000451 | In signal processing applications, it is often necessary to extract oscillatory components and their properties from time–frequency representations, e.g. the windowed Fourier transform or wavelet transform. The first step in this procedure is to find an appropriate ridge curve: a sequence of amplitude peak positions (r... | Extraction of instantaneous frequencies from ridges in time–frequency representations of signals |
S0167639314000156 | The RSR2015 database, designed to evaluate text-dependent speaker verification systems under different durations and lexical constraints has been collected and released by the Human Language Technology (HLT) department at Institute for Infocomm Research (I2R) in Singapore. English speakers were recorded with a balanced... | Text-dependent speaker verification: Classifiers, databases and RSR2015 |
S0167639314000697 | A spectral envelope estimation algorithm is presented to achieve high-quality speech synthesis. The concept of the algorithm is to obtain an accurate and temporally stable spectral envelope. The algorithm uses fundamental frequency (F0) and consists of F0-adaptive windowing, smoothing of the power spectrum, and spectra... | CheapTrick, a spectral envelope estimator for high-quality speech synthesis |
S0167639314000740 | With teleconferencing becoming more accessible as a communication platform, researchers are working to understand the consequences of the interaction between human perception and this unfamiliar environment. Given the enclosed space of a teleconference room, along with the physical separation between the user, micropho... | Audiovisual temporal integration in reverberant environments |
S0167639315000692 | This paper presents an unsupervised method that allows for gradual interpolation between language varieties in statistical parametric speech synthesis using Hidden Semi-Markov Models (HSMMs). We apply dynamic time warping using Kullback–Leibler divergence on two sequences of HSMM states to find adequate interpolation p... | Unsupervised and phonologically controlled interpolation of Austrian German language varieties for speech synthesis |
S0167642313000452 | The CancerGrid approach to software support for clinical trials is based on two principles: careful curation of semantic metadata about clinical observations, to enable subsequent data integration, and model-driven generation of trial-specific software artefacts from a trial protocol, to streamline the software develop... | The CancerGrid experience: Metadata-based model-driven engineering for clinical trials |
S0167642314000112 | We compare different algorithms for computing eigenvalues and eigenvectors of a symmetric band matrix across a wide range of synthetic test problems. Of particular interest is a comparison of state-of-the-art tridiagonalization-based methods as implemented in Lapack or Plasma on the one hand, and the block divide-and-c... | Comparison of eigensolvers for symmetric band matrices |
S0167642315000659 | A hierarchical approach for modelling the adaptability features of complex systems is introduced. It is based on a structural level S, describing the adaptation dynamics of the system, and a behavioural level B accounting for the description of the admissible dynamics of the system. Moreover, a unified system, called S... | Adaptability checking in complex systems |
S0167642315001288 | In order to provide a rigorous foundation for Software Product Lines (SPLs), several fundamental approaches have been proposed to their formal behavioral modeling. In this paper, we provide a structured overview of those formalisms based on labeled transition systems and compare their expressiveness in terms of the set... | Basic behavioral models for software product lines: Expressiveness and testing pre-orders |
S0167819113001051 | SpiNNaker is a biologically-inspired massively-parallel computer designed to model up to a billion spiking neurons in real-time. A full-fledged implementation of a SpiNNaker system will comprise more than 105 integrated circuits (half of which are SDRAMs and half multi-core systems-on-chip). Given this scale, it is una... | SpiNNaker: Fault tolerance in a power- and area- constrained large-scale neuromimetic architecture |
S0167819114000337 | Linear least squares problems are commonly solved by QR factorization. When multiple solutions need to be computed with only minor changes in the underlying data, knowledge of the difference between the old data set and the new can be used to update an existing factorization at reduced computational cost. We investigat... | Implementing QR factorization updating algorithms on GPUs |
S0167819114000398 | Simulation of in vivo cellular processes with the reaction–diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryo... | Simulation of reaction diffusion processes over biologically relevant size and time scales using multi-GPU workstations |
S0167819114000659 | In this paper, we develop a rank-mapping algorithm for an icosahedral grid system on a massive parallel computer with the 3-D torus network topology, specifically on the K computer. Our aim is to improve the weak scaling performance of the point-to-point communications for exchanging grid-point values between adjacent ... | Scalable rank-mapping algorithm for an icosahedral grid system on the massive parallel computer with a 3-D torus network |
S0167819114000842 | Data scientists have applied various analytic models and techniques to address the oft-cited problems of large volume, high velocity data rates and diversity in semantics. Such approaches have traditionally employed analytic techniques in a streaming or batch processing paradigm. This paper presents CRUCIBLE, a first-i... | Towards unified secure on- and off-line analytics at scale |
S0167819114001148 | We introduce a region template abstraction and framework for the efficient storage, management and processing of common data types in analysis of large datasets of high resolution images on clusters of hybrid computing nodes. The region template abstraction provides a generic container template for common data structur... | Region templates: Data representation and management for high-throughput image analysis |
S0167819115000095 | The human brain is a complex biological neural network characterised by high degrees of connectivity among neurons. Any system designed to simulate large-scale spiking neuronal networks needs to support such connectivity and the associated communication traffic in the form of spike events. This paper investigates how b... | SpiNNaker: Enhanced multicast routing |
S0167819115000472 | Community detection has become a fundamental operation in numerous graph-theoretic applications. It is used to reveal natural divisions that exist within real world networks without imposing prior size or cardinality constraints on the set of communities. Despite its potential for application, there is only limited sup... | Parallel heuristics for scalable community detection |
S0167839613000356 | Motivated by applications in freeform architecture, we study surfaces which are composed of smoothly joined bilinear patches. These surfaces turn out to be discrete versions of negatively curved affine minimal surfaces and share many properties with their classical smooth counterparts. We present computational design a... | Smooth surfaces from bilinear patches: Discrete affine minimal surfaces |
S0167839613000368 | A characterization for spatial Pythagorean-hodograph (PH) curves of degree 7 with rotation-minimizing EulerâRodrigues frames (ERFs) is determined, in terms of one real and two complex constraints on the curve coefficients. These curves can interpolate initial/final positions p i and p f and orientational frames ( t i... | Rotation-minimizing Euler-Rodrigues rigid-body motion interpolants |
S0167839613000502 | We present a fast algorithm for finding a μ-basis for any rational planar curve that has a complex rational parametrization. We begin by identifying two canonical syzygies that can be extracted directly from any complex rational parametrization without performing any additional calculations. For generic complex ration... | μ-Bases for complex rational curves |
S0167839613000514 | This paper is devoted to introducing a new approach for computing the topology of a real algebraic plane curve presented either parametrically or defined by its implicit equation when the corresponding polynomials which describe the curve are known only “by values”. This approach is based on the replacement of the usua... | Computing the topology of a real algebraic plane curve whose defining equations are available only “by values” |
S0167839613000538 | Spiral segments are useful in the design of fair curves. They are important in CAD/CAM applications, the design of highway and railway routes, trajectories of mobile robots and other similar applications. The quintic Pythagorean-hodograph (PH) curve discussed in this article is polynomial; it has the attractive propert... | Curve design with more general planar Pythagorean-hodograph quintic spiral segments |
S0167839613000551 | This paper proposes a generalization of the ordinary de Casteljau algorithm to manifold-valued data including an important special case which uses the exponential map of a symmetric space or Riemannian manifold. We investigate some basic properties of the corresponding Bézier curves and present applications to curve de... | De Casteljauʼs algorithm on manifolds |
S0167839613000575 | Recently a new approach to piecewise polynomial spaces generated by B-spline has been presented by T. Dokken, T. Lyche and H.F. Pettersen, namely Locally Refined splines. In their recent work (Dokken et al., 2013) they define the LR B-spline collection and provide tools to compute the space dimension. Here different pr... | Some properties of LR-splines |
S0167839613000587 | We examine the problem of computing exactly the Voronoi diagram (via the dual Delaunay graph) of a set of, possibly intersecting, smooth convex pseudo-circles in the Euclidean plane, given in parametric form. Pseudo-circles are (convex) sites, every pair of which has at most two intersecting points. The Voronoi diagram... | Exact Voronoi diagram of smooth convex pseudo-circles: General predicates, and implementation for ellipses |
S0167839613000678 | In this paper, a new method for computing intersection between a ray and a parametric surface is proposed, which finds many applications in computer graphics, robotics and geometric modeling. The method uses the second order derivative of the surface, which can handle inherent problems that Newton–Raphson and Halley me... | A second order geometric method for ray/parametric surface intersection |
S0167839613000782 | T-splines are a generalization of NURBS surfaces, the control meshes of which allow T-junctions. T-splines can significantly reduce the number of superfluous control points in NURBS surfaces, and provide valuable operations such as local refinement and merging of several B-splines surfaces in a consistent framework. In... | Modified T-splines |
S0167839613000794 | A method to construct arbitrary order continuous curves, which pass through a given set of data points, is introduced. The method can derive a new family of symmetric interpolating splines with various nice properties, such as partition of unity, interpolation property, local support and second order precision etc. App... | Uniform interpolation curves and surfaces based on a family of symmetric splines |
S0167839613000800 | Smooth freeform skins from simple panels constitute a challenging topic arising in contemporary architecture. We contribute to this problem area by showing how to approximate a negatively curved surface by smoothly joined rational bilinear patches. The approximation problem is solved with help of a new computational ap... | Smooth surfaces from rational bilinear patches |
S0167839613001003 | An orthonormal frame ( f 1 , f 2 , f 3 ) is rotation-minimizing with respect to f i if its angular velocity ω satisfies ω ⋅ f i ≡ 0 — or, equivalently, the derivatives of f j and f k are both parallel to f i . The Frenet frame ( t , p , b ) along a space curve is rotation-minimizing with respect to the principal normal... | Rotation-minimizing osculating frames |
S0167839613001015 | A construction of spline spaces suitable for representing smooth parametric surfaces of arbitrary topological genus and arbitrary order of continuity is proposed. The obtained splines are a direct generalization of bivariate polynomial splines on planar partitions. They are defined as composite functions consisting of ... | RAGS: Rational geometric splines for surfaces of arbitrary topology |
S0167839613001027 | In this paper, the dual representation of spatial parametric curves and its properties are studied. In particular, rational curves have a polynomial dual representation, which turns out to be both theoretically and computationally appropriate to tackle the main goal of the paper: spatial rational Pythagorean-hodograph ... | Dual representation of spatial rational Pythagorean-hodograph curves |
S0167839613001039 | In this work, an extension has been performed on the analysis basis of spline-based meshfree method (SBMFM) to stabilize its solution. The potential weakness of the SBMFM is its numerical instability from using regular grid background mesh. That is, if an extremely small trimmed element is produced by the trimming curv... | Spline-based meshfree method with extended basis |
S0167839613001040 | A new binary four-point subdivision scheme is presented, which keeps the second-order divided difference at the old vertices unchanged when the new vertices are inserted. Using the symbol of the subdivision scheme, we show that the limit curve is at least C 3 continuous. Furthermore, the conditions imposed on the initi... | A new four-point shape-preserving C 3 subdivision scheme |
S0167839613001052 | We develop a method for computing all the generalized asymptotes of a real plane algebraic curve C implicitly defined by an irreducible polynomial f ( x , y ) ∈ R [ x , y ] . The approach is based on the notion of perfect curve introduced from the concepts and results presented in Blasco and Pérez-Díaz (2013). In addit... | Asymptotes and perfect curves |
S0167839613001064 | Geometric partial differential equations for curves and surfaces are used in many fields, such as computational geometry, image processing and computer graphics. In this paper, a few differential operators defined on space curves are introduced. Based on these operators, several second-order and fourth-order geometric ... | Construction of several second- and fourth-order geometric partial differential equations for space curves |
S0167839614000089 | Splines can be constructed by convolving the indicator function of a cell whose shifts tessellate R n . This paper presents simple, geometric criteria that imply that, for regular shift-invariant tessellations, only a small subset of such spline families yield nested spaces: primarily the well-known tensor-product and ... | Refinability of splines derived from regular tessellations |
S0167839614000090 | The problem of designing smoothly rounded right-angle corners with Pythagorean-hodograph (PH) curves is addressed. A G 1 corner can be uniquely specified as a single PH cubic segment, closely approximating a circular arc. Similarly, a G 2 corner can be uniquely constructed with a single PH quintic segment having a unim... | Construction of G 2 rounded corners with Pythagorean-hodograph curves |
S0167839614000107 | We study a particular class of planar four-bar mechanisms FBM ( Q ) which are based on a given quadrilateral (quad) Q = a 0 a 1 a 2 a 3 . The self-motion of FBM ( Q ) consists of two different parts – one is the motion of an anti-parallelogram whilst the other one is a pure translation with circular paths. We will refe... | Overconstrained mechanisms based on planar four-bar-mechanisms |
S0167839614000193 | This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space curves, our method finds the involutions in all cases, and all the rotation sym... | Detecting symmetries of rational plane and space curves |
S0167839614000211 | We provide explicit representations of three moving planes that form a μ-basis for a standard Dupin cyclide. We also show how to compute μ-bases for Dupin cyclides in general position and orientation from their implicit equations. In addition, we describe the role of moving planes and moving spheres in bridging between... | Role of moving planes and moving spheres following Dupin cyclides |
S0167839614000223 | We present an approach to finding the implicit equation of a planar rational parametric cubic curve, by defining a new basis for the representation. The basis, which contains only four cubic bivariate polynomials, is defined in terms of the Bézier control points of the curve. An explicit formula for the coefficients of... | A basis for the implicit representation of planar rational cubic Bézier curves |
S0167839614000247 | This paper describes the application of a structure-preserving matrix method to the deconvolution of two Bernstein basis polynomials. Specifically, the deconvolution h ˆ / f ˆ yields a polynomial g ˆ provided the exact polynomial f ˆ is a divisor of the exact polynomial h ˆ and all computations are performed symbolical... | A structure-preserving matrix method for the deconvolution of two Bernstein basis polynomials |
S0167839614000260 | In Winkel (2001) a generalization of Bernstein polynomials and Bézier curves based on umbral calculus has been introduced. In the present paper we describe new geometric and algorithmic properties of this generalization including: (1) families of polynomials introduced by Stancu (1968) and Goldman (1985), i.e., familie... | On a generalization of Bernstein polynomials and Bézier curves based on umbral calculus |
S0167839614000272 | We present a method for approximating a point sequence of input points by a -continuous (smooth) arc spline with the minimum number of segments while not exceeding a user-specified tolerance. Arc splines are curves composed of circular arcs and line segments (shortly: segments). For controlling the tolerance we follow ... | Optimal arc spline approximation |
S0167839614000296 | We present a simple method for C-shaped G 2 Hermite interpolation by a rational cubic Bézier curve with conic precision. For the interpolating rational cubic Bézier curve, we derive its control points according to two conic Bézier curves, both matching the G 1 Hermite data and one end curvature of the given G 2 Hermite... | C-shaped G 2 Hermite interpolation by rational cubic Bézier curve with conic precision |
S0167839614000302 | New bounds on the magnitudes of the first- and second-order partial derivatives of rational triangular Bézier surfaces are presented. Theoretical analysis shows that the proposed bounds are tighter than the existing ones. The superiority of the proposed new bounds is also illustrated by numerical tests. | An improvement on the upper bounds of the magnitudes of derivatives of rational triangular Bézier surfaces |
S0167839614000491 | Salient features in 3D meshes such as small high-curvature details in the middle of largely flat regions are easily ignored by most mesh simplification methods. Nevertheless, these features can be perceived by human observers as perceptually important in CAD models. Recently, mesh saliency has been introduced to identi... | Reducing complexity in polygonal meshes with view-based saliency |
S0167839614000521 | We introduce a novel basis for multivariate hierarchical tensor-product spline spaces. Our construction combines the truncation mechanism (Giannelli et al., 2012) with the idea of decoupling basis functions (Mokriš et al., 2014). While the first mechanism ensures the partition of unity property, which is essential for ... | TDHB-splines: The truncated decoupled basis of hierarchical tensor-product splines |
S0167839614000533 | By means of bond theory, we study Stewart Gough (SG) platforms with n-dimensional self-motions with n > 2 . It turns out that only architecturally singular manipulators can possess these self-motions. Based on this result, we present a complete list of all SG platforms, which have n-dimensional self-motions. Therefore ... | On Stewart Gough manipulators with multidimensional self-motions |
S0167839614000545 | Ganchev has recently proposed a new approach to minimal surfaces. Introducing canonical principal parameters for these surfaces, he has proved that the normal curvature determines the surface up to its position in the space. Here we prove a theorem that permits to obtain equations of a minimal surface in canonical prin... | Transition to canonical principal parameters on minimal surfaces |
S0167839614000570 | A rational curve on a rational surface such that the unit normal vector field of the surface along this curve is rational will be called a curve providing Pythagorean surface normals (or shortly a PSN curve). These curves represent rational paths on the surface along which the surface possesses rational offset curves. ... | Surfaces with Pythagorean normals along rational curves |
S0167839614000582 | In this work, we propose a structured computational framework for modelling the envelope of the swept volume, that is the boundary of the volume obtained by sweeping an input solid along a trajectory of rigid motions. Our framework is adapted to the well-established industry-standard brep format to enable its implement... | Local and global analysis of parametric solid sweeps |
S0167839614000600 | In this paper, we introduce triangular subdivision operators which are composed of a refinement operator and several averaging operators, where the refinement operator splits each triangle uniformly into four congruent triangles and in each averaging operation, every vertex will be replaced by a convex combination of i... | General triangular midpoint subdivision |
S0167839614000636 | We consider isogeometric functions and their derivatives. Given a geometry mapping, which is defined by an n-dimensional NURBS patch in R d , an isogeometric function is obtained by composing the inverse of the geometry mapping with a NURBS function in the parameter domain. Hence an isogeometric function can be represe... | Derivatives of isogeometric functions on n-dimensional rational patches in R d |
S0167839614000648 | One major issue in CAGD is to model complex objects using free-form surfaces of general topology. A natural approach is curvenet-based design, where designers directly create and modify feature curves. These are interpolated by smoothly connected, multi-sided patches, which can be represented by transfinite surfaces, d... | Ribbon-based transfinite surfaces |
S0167839614000752 | For an arbitrary degree Bézier curve B , we first establish sufficient conditions for its control polygon to become homeomorphic to B via subdivision. This is extended to show a subdivided control polygon that is ambient isotopic to B . We provide closed-form formulas to compute the corresponding number of iterations f... | Isotopic equivalence by Bézier curve subdivision for application to high performance computing |
S0167839614000764 | This paper presents a biarc-based subdivision scheme for space curve interpolation. Given a sequence of space points, or a sequence of space points and tangent vectors, the scheme produces a smooth curve interpolating all input points by iteratively inserting new points and computing new tangent vectors. For each step ... | A biarc based subdivision scheme for space curve interpolation |
S0167839614000806 | In this paper two kinds of bivariate S-λ basis functions, tensor product S-λ basis functions and triangular S-λ basis functions, are constructed by means of the technique of generating functions and transformation factors. These two kinds of bivariate S-λ basis functions have lots of important properties, such as non-n... | Bivariate S-λ bases and S-λ surface patches |
S0167839614000818 | We show how to find four generic interpolants to a C 1 Hermite data-set in the complex representation, using Pythagorean-hodograph curves generated as cuts of degree ( 1 , 3 ) of Laurent series. The developed numerical experiments have shown that two of these interpolants are simple curves and that these (at least) hav... | Planar C 1 Hermite interpolation with PH cuts of degree ( 1 , 3 ) of Laurent series |
S0167839614000983 | The purpose of this paper is to present algorithms for computing all the differential geometry properties of non-transversal intersection curves of three parametric hypersurfaces in Euclidean 4-space. For transversal intersections, the tangential direction at an intersection point can be computed by the extension of th... | Differential geometry of non-transversal intersection curves of three parametric hypersurfaces in Euclidean 4-space |
S0167839614000995 | A swept surface is generated from a profile curve and a sweep curve by employing the latter to define a continuous family of transformations of the former. By using polynomial or rational curves, and specifying the homogeneous coordinates of the swept surface as bilinear forms in the profile and sweep curve homogeneous... | Rational swept surface constructions based on differential and integral sweep curve properties |
S0167839614001009 | Fitting a sparse surface to approximate vast dense data is of interest for many applications: reverse engineering, recognition and compression, etc. The present work provides an approach to fit a Loop subdivision surface to a dense triangular mesh of arbitrary topology, whilst preserving and aligning the original featu... | Subdivision surface fitting to a dense mesh using ridges and umbilics |
S0167839614001010 | A generic planar quadrilateral defines a 2:1 bilinear map. We show that by assigning an appropriate weight to one vertex of any planar quadrilateral, we can create a map whose inverse is rational linear. | Birational quadrilateral maps |
S0167839614001022 | In this work we present a parameter-dependent Refine-and-Smooth (RS) subdivision algorithm where the refine stage R consists in the application of a perturbation of Chaikin's/Doo–Sabin's vertex split, while each smoothing stage S performs averages of adjacent vertices like in the Lane–Riesenfeld algorithm (Lane and Rie... | A Chaikin-based variant of Lane–Riesenfeld algorithm and its non-tensor product extension |
S0167839614001113 | Recently, it was shown that a bi-cubic patch complex with n-sided holes can be completed into a curvature-continuous () surface by n-sided caps of degree bi-5 that offer good and flexible shape (Karciauskas and Peters, 2013). This paper further explores the space of n-sided caps of degree bi-5 but focuses on functional... | Biquintic G 2 surfaces via functionals |
S0167839614001125 | The μ -invariant μ = ( μ 1 , μ 2 , μ 3 ) of a rational space curve gives important information about the curve. In this paper, we describe the structure of all parameterizations that have the same μ -type, what we call a μ-stratum, and as well the closure of strata. Many of our results are based on papers by the second... | Strata of rational space curves |
S0167839615000023 | In this study, we propose a robust algorithm for reconstructing free-form space curves in space using a Non-Uniform Rational B-Spline (NURBS)-snake model. Two perspective images of the required free-form curve are used as the input and a nonlinear optimization process is used to fit a NURBS-snake on the projected data ... | Reconstruction of free-form space curves using NURBS-snakes and a quadratic programming approach |
S0167839615000138 | We present a novel, deterministic, and efficient method to detect whether a given rational space curve is symmetric. By using well-known differential invariants of space curves, namely the curvature and torsion, the method is significantly faster, simpler, and more general than an earlier method addressing a similar pr... | Symmetry detection of rational space curves from their curvature and torsion |
S0167839615000151 | Ck (geometrically continuous surface) constructions were developed to create surfaces that are smooth also at irregular points where, in a quad-mesh, three or more than four elements come together. Isogeometric elements were developed to unify the representation of geometry and of engineering analysis. We show how ma... | Matched G k -constructions always yield C k -continuous isogeometric elements |
S0167839615000163 | We present an efficient adaptive refinement procedure that preserves analysis-suitability of the T-mesh, that is, the linear independence of the T-spline blending functions. We prove analysis-suitability of the overlays and boundedness of their cardinalities, nestedness of the generated T-spline spaces, and linear comp... | Analysis-suitable adaptive T-mesh refinement with linear complexity |
S0167839615000400 | Toric surface patches are a multi-sided generalization of classical rational Bézier surface patches which are widely used in free-form surface modeling. In this paper, we present the first derivatives of toric surface patches along the boundary and study the G 1 continuity between adjacent toric surface patches by the ... | G 1 continuity between toric surface patches |
S0167839615000448 | The purpose of this article is the construction of a normalized basis for a quadratic condensed Powell–Sabin-12 macro-element space introduced by Alfeld et al. (2010). The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction of this basis is adopted from Dierc... | A normalized basis for condensed C 1 Powell–Sabin-12 splines |
S0167839615000540 | The investigation of the umbral calculus based generalization of Bernstein polynomials and Bézier curves is continued in this paper: First a generalization of the de Casteljau algorithm that uses umbral shift operators is described. Then it is shown that the quite involved umbral shifts can be replaced by a surprisingl... | On a generalization of Bernstein polynomials and Bézier curves based on umbral calculus (II): de Casteljau algorithm |
S0167839615000783 | We consider a C 1 cubic spline space defined over a triangulation with Powell–Sabin refinement. The space has some local C 2 super-smoothness and can be seen as a close extension of the classical cubic Clough–Tocher spline space. In addition, we construct a suitable normalized B-spline representation for this spline sp... | A new B-spline representation for cubic splines over Powell–Sabin triangulations |
S0167839615000795 | The boundary representations (B-reps) that are used to represent shape in Computer-Aided Design systems create unavoidable gaps at the face boundaries of a model. Although these inconsistencies can be kept below the scale that is important for visualisation and manufacture, they cause problems for many downstream tasks... | Watertight conversion of trimmed CAD surfaces to Clough–Tocher splines |
S0167839615000801 | We describe a construction of LR-spaces whose bases are composed of locally linearly independent B-splines which also form a partition of unity. The construction conforms to given refinement requirements associated to subdomains. In contrast to the original LR-paper (Dokken et al., 2013) and similarly to the hierarchic... | A hierarchical construction of LR meshes in 2D |
S0167839615000813 | We introduce and analyze univariate, linear, and stationary subdivision schemes for refining noisy data by fitting local least squares polynomials. This is the first attempt to design subdivision schemes for noisy data. We present primal schemes, with refinement rules based on locally fitting linear polynomials to the ... | Univariate subdivision schemes for noisy data with geometric applications |
S0167839615000825 | A new equivalence notion between non-stationary subdivision schemes, termed asymptotic similarity, which is weaker than asymptotic equivalence, is introduced and studied. It is known that asymptotic equivalence between a non-stationary subdivision scheme and a convergent stationary scheme guarantees the convergence of ... | Convergence of univariate non-stationary subdivision schemes via asymptotic similarity |
S0167839615000837 | We introduce the concept of reduced curvature formulae for 3-D space entities (surfaces, curves). A reduced formula entails only derivatives of the functions involved in the entity's representation and admits no further algebraic simplifications. Although not always the most compact, reduced curvature formulae entail o... | Reduced curvature formulae for surfaces, offset surfaces, curves on a surface and surface intersections |
S0167839615000849 | We provide a simple, efficient technique for computing μ-bases for quadric surfaces from their rational quadratic parametrizations. Our major innovation is to simplify the computations by using complex parameters, even though all the surfaces we treat have only real coefficients in both their implicit and parametric re... | Complex μ-bases for real quadric surfaces |
S0167839615000850 | In this article we provide the characterization of analysis suitable T-spline spaces (Beirão da Veiga et al., 2013) as the space of piecewise polynomials with appropriate linear constrains on the subdomain interfaces. We describe AST-meshes for which the linear constrains are equivalent to smoothness conditions and pro... | Characterization of analysis-suitable T-splines |
S0167839615000941 | Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint systems. While the optimal DR-planning problem is NP-hard even for (general) 2D bar–joint constraint systems, we describe an O ( n 3 ) algorithm for a broad class of constraint s... | Optimal decomposition and recombination of isostatic geometric constraint systems for designing layered materials |
S0167839615000953 | In this paper, we discuss the bicubic C 2 spline spaces over hierarchical T-meshes in detail. The topological explanation of the dimension formula is further explored. We provide three necessary conditions for the completeness of the spline spaces. Based on the three conditions, the rule of the refinement of the hierar... | Bicubic hierarchical B-splines: Dimensions, completeness, and bases |
S0167839615000965 | This paper proposes a geometric algorithm for computation of geodesic on surfaces. The geodesics on surfaces are traced in a simple way which is independent of the complex description of the geodesic equations. Through derivation process, the calculation error of this algorithm is obtained. A step size adjustment strat... | A geometric method for computation of geodesic on parametric surfaces |
S0167839615000977 | Many problems in computer aided geometric design and computer graphics can be turned into a root-finding problem of a polynomial equation. Among various solutions, clipping methods based on the Bernstein–Bézier form usually have good numerical stability. A traditional clipping method using polynomials of degree r can a... | A rational cubic clipping method for computing real roots of a polynomial |
S0167839615001004 | The Laplace–Beltrami operator is the foundation of describing geometric partial differential equations, and it also plays an important role in the fields of computational geometry, computer graphics and image processing, such as surface parameterization, shape analysis, matching and interpolation. However, constructing... | Localized discrete Laplace–Beltrami operator over triangular mesh |
S0167839615001016 | This paper presents a novel 3D shape descriptor which explicitly captures the local geometry and encodes it using an efficient representation. Our method consists of multiple evolving fronts which are realized by a set of growing spheres on the surface. At the core of this method is a simple intersection operator betwe... | Sphere intersection 3D shape descriptor (SID) |
S0167839615001028 | In this paper we investigate the problem of interpolating a B-spline curve network, in order to create a surface satisfying such a constraint and defined by blending functions spanning the space of bivariate C 1 quadratic splines on criss–cross triangulations. We prove the existence and uniqueness of the surface, provi... | Curve network interpolation by C 1 quadratic B-spline surfaces |
S0167839615001041 | Extended Chebyshev spaces that also comprise the constants represent large families of functions that can be used in real-life modeling or engineering applications that also involve important (e.g. transcendental) integral or rational curves and surfaces. Concerning CAGD, the unique normalized B-bases of such vector sp... | Control point based exact description of curves and surfaces, in extended Chebyshev spaces |
S0167839615001193 | We propose a general scheme for detecting critical locations (of dimension zero) of piecewise polynomial multivariate equation systems. Our approach generalizes previously known methods for locating tangency events or self-intersections, in contexts such as surfaceâÂÂsurface intersection (SSI) problems and the probl... | Detection of critical points of multivariate piecewise polynomial systems |
S0167839615001211 | In this paper we devise a new algorithm for completing surface with missing geometry and topology founded upon the theory and techniques of sparse signal recovery. The key intuition is that any meaningful 3D shape, represented as a discrete mesh, almost certainly possesses a low-dimensional intrinsic structure, which c... | Surface inpainting with sparsity constraints |
S0167839615001223 | In the paper two new approaches for construction of parametric polynomial approximants of a unit circle are presented. The obtained approximants have better approximation properties than those given by other methods, i.e., smaller radial error, symmetry, and exponential error decay. | Uniform approximation of a circle by a parametric polynomial curve |
S0167839615001351 | We derive explicit formulas for the μ-bases of conic sections and planar rational cubic curves. Using the μ-bases for planar rational cubic curves, we find explicit formulas for their implicit equations and double points. We also extend the explicit formula for the μ-bases of conic sections to μ-bases for rational curv... | Explicit μ-bases for conic sections and planar rational cubic curves |
S0167839615001363 | We consider the adaptive refinement of bivariate quartic C 2 -smooth box spline spaces on the three-directional (type-I) grid G. The polynomial segments of these box splines belong to a certain subspace of the space of quartic polynomials, which will be called the space of special quartics. Given a bounded domain Ω ⊂ R... | Characterization of bivariate hierarchical quartic box splines on a three-directional grid |
S0167839615001375 | Rational curves and surfaces are powerful tools for shape representation and geometric modeling. However, the real weights are generally difficult to choose except for a few special cases such as representing conics. This paper presents an extension of rational curves and surfaces by replacing the real weights with mat... | Matrix weighted rational curves and surfaces |
S0167839615001387 | This survey paper describes the role of splines in geometry and topology, emphasizing both similarities and differences from the classical treatment of splines. The exposition is non-technical and contains many examples, with references to more thorough treatments of the subject. The goal of this survey paper is to des... | Splines in geometry and topology |
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