Approximate merging of B-spline curves and surfaces

Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.

Reconstruction of B-spline surface by interpolating boundary curves and approximating inner points

In this paper, we present an algorithm for reconstruction of B-spline surface such that it interpolates the four given bound- ary curves and simultaneously approximates some given inner points. The main idea of our method is： first, we construct an initial surface which interpolates the four given boundary curves; then, while keeping the boundary control points of the initial surface un- changed, we reposition the inner control points of the surface with energy optimization method. Examples show that our algorithm is practicable and effective.

G^0 and G^1 connection between two adjacent B-spline surfaces

In this paper, the smooth connection between two B-spline surfaces is discussed. First, a brief proof of some simple sufficient conditions of Go and G1 continuity is given. On this basis, a novel method for Go or G1 connection between two adjacent B-spline surfaces is presented. A reparameterization step is firstly taken for one of the surfaces such that they have the same parameterization in v direction, then, adjust their boundary control vertices to make them Go or Gl connected. The GI connection parameter is determined by an optimization problem. Compared with the existed methods, our method is simple and easy to be used in practice.

B-Spline Approximation of Ship Waves on the Free Surface

We consider the problem of a ship advancing in waves. In this method, the zone of free surface in the vicinity of body is discretized. On the discretized surface, the first-order and second-order derivatives of ship waves are represented by the B-Spline formulae. Different ship waves are approximated by cubic B-spline and the first and second order derivates of incident waves are calculated and compared with analytical value. It approves that this numerical method has sufficient accuracy and can be also applied to approximate the velocity potential on the free surface.

G^1 Continuity Conditions of B-spline Surfaces

According to the B-spline theory and Boehm algorithm, this paper presents several necessary and sufficient G1 continuity conditions between two adjacent B-spline surfaces. In order to meet the need of application, a kind of sufficient conditions of G1 continuity are developed, and a kind of sufficient conditions of G1 continuity among N(N>2) patch B-spline surfaces meeting at a common corner are given at the end.

RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES

A method to reconstruct symmetric B-spline curves and surfaces is presented. The symmetry property is realized by using symmetric knot vector and symmetric control points. Firstly, data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points. Then the divided data points are parameterized and a symmetric knot vector is selected in order to get symmetric B-spline basis functions. Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be symmetric with respect to the extracted symmetry axis or symmetry plane. Lastly, the constrained least squares fitting problem is solved with the Lagrange multiplier method. Two examples from industry are given to show that the proposed method is efficient, robust and able to meet the general engineering requirements.

Incompressible Surfaces in Almost Alternating Link Exteriors

在这份报纸，我们主要在几乎 altcrnating 连接 complcmcnts.Lct L bc 讨论不可压缩的 pairwise incomprcssiblc surfaccs 的性质几乎连接和坦克登陆艇 F 在 S3 -L.First.we 的不可压缩的表面给表面 F 在 S3 -L.The 交叉与2范围交叉的性质的不可压缩的 paLrwise 由许多圆和塑造僵绳的磁盘正在组成叫了拓扑的 graph.One 能由计算 chara 计算表面的 Euler

Fast B-spline surface extraction algorithm of seismic volume data on GPU

In the process of seismic data interpretation, the extraction of a horizon or a fault is generally needed. In this paper we present a fast extraction method. First select some feature points interactively, then reconstruct the surface according to the selected feature points by using B-spline interpolation curve or surface. In order to solve the error-drawing problem appeared in the process of interactive rendering, which is caused by the change of sampling interval as the view point changes, we combine shear-warp and splatting algorithm to render the surface. The rendering of seismic data and specific surface in our work are achieved on GPU platform using CUDA programming language, which make it able to meet the requirements of real-time rendering.

Modification of B-Spline Surfaces with Optimization

Algorithms of modifying a surface to approximate some scattered points, or pass through some characteristic points/curves are presented. Similar to variational approach, the algorithms are based on optimization. For the deviation between the modified surface and the original one is adopted as the objective functions, the change of the surface shape is as small as possible with the modified surface satisfying the specified requirements.

B-SPLINE SURFACE SMOOTH JOINING

Optimization techniques are being applied to solve the problems of surface interpolation, approximation, smooth joining and fairing, aiming at corresponding objective functions. This paper focuses on the construction of fair surface interpolating the given mesh of curved boundaries with G 2 adjustment at comers and G 1, G 2 smoothness between adjacent patches. Many papers on surface blending have been presented, but almost all of them are restricted to the discussion of Bezier patches, there are no good results for B-spline surface. This paper gives a solution to the B-spline surface, allowing the surface to degenerate at comer in and have different parameterization along the common boundary of two patches.

An Algorithm of B-Spline Surface Interpolation

A surface interpolation algorithm is presented. By using a special kind of knot vector. a B-spline surface can be constructed to interpolate an array of m ×n positions, including parameter u and v tangent vectors and twist vector at each positions. Single surface interpolation approach is easier to ensure the smoothness of the interpolating surface than multi-patches method. This algorithm can be used to solve the approximating problem of B-spline approximation of general parametric surface.

The Existence of a Meridional Curve in Closed Incompressible Surfaces in Fully Alternating Link Complements

Menasco showed that a closed incompressible surface in the complement of a non-split prime alternating link in S^(3) contains a circle isotopic in the link complement to a meridian of the links.Based on this result,he was able to argue the hyperbolicity of non-split prime alternating links in S3.Adams et al.showed that if F■S×I\L is an essential torus,then F contains a circle which is isotopic in S×I\L to a meridian of L.The author generalizes his result as follows:Let S be a closed orientable surface,L be a fully alternating link in S×I\If F ■ S×I\L is a closed essential surface,then F contains a circle which is isotopic in S×I\L to a meridian of L.

INCOMPRESSIBLE PAIRWISE INCOMPRESSIBLE SURFACES IN LINK COMPLEMENTS

The central subject of studying in this paper is incompressible pairwise incompressible surfaces in link complements. Let L be a non-split prime link and let F be an incompressible pairwise incompressible surface in S3 - L. We discuss the properties that the surface F intersects with 2-spheres in S3 - L. The intersection forms a topological graph consisting of a collection of circles and saddle-shaped discs. We introduce topological graphs and their moves （R-move and S2-move）, and define the characteristic number of the topological graph for F∩S2±. The characteristic number is unchanged under the moves. In fact, the number is exactly the Euler Characteristic number of the surface when a graph satisfies some conditions. By these ways, we characterize the properties of incompressible pairwise incompressible surfaces in alternating （or almost alternating） link complements. We prove that the genus of the surface equals zero if the component number of F∩S2＋（or F∩S2-） is less than five and the graph is simple for alternating or almost alternating links. Furthermore, one can prove that the genus of the surface is zero if #（F） ≤8.

Secrecy Rate Analysis for Reconfigurable Intelligent Surface-Assisted MIMO Communications with Statistical CSI

In this paper,a reconfigurable intelligent surface(RIS)-assisted MIMO wireless secure communication system is considered,in which a base station(BS)equipped with multiple antennas exploits statistical channel state information to communicate with a legitimate multi-antenna user,in the presence of an eavesdropper,also equipped with multiple antennas.We firstly obtain an analytical expression of the ergodic secrecy rate based on the results of largedimensional random matrix theory.Then,a jointly alternating optimization algorithm with the method of Taylor series expansion and the projected gradient ascent method is proposed to design the transmit covariance matrix at the BS,as well as the diagonal phaseshifting matrix to maximize the ergodic secrecy rate.Simulations are conducted to demonstrate the accuracy of the derived analytical expressions,as well as the superior performance of our proposed algorithm.

NURBS Parameterization for Medical Surface Reconstruction

InVesalius is an open-source software for reconstruction of computed tomography and magnetic resonance images, which allows the user to make analysis and segmentation of virtual anatomical models. Physical models can be printed with the aid of rapid prototyping, giving the medical community a reliable instrument to help planning surgeries. To offer the user more control over the model, this work describes a methodology and tool developed for NURBS parameterization that provides mechanisms for adjusting the shape or even selecting a particular region of interest of the surface. Furthermore, the tool gives the option to export the final results of the process to a STEP file, which allows further edition in any well-known CAD software.

Novel Evidence Suggests Hepatitis B Virus Surface Proteins Participate in Regulation of HBV Genome Replication

Naturally occurring mutations in surface proteins of Hepatitis B virus(HBV) usually result in altered hepatitis B surface antigen(HBsAg) secretion efficiency.In the present study,we reported two conserved residues,M75 and M103 with respect to HBsAg,mutations of which not only attenuated HBsAg secretion(M75 only),but also suppressed HBV genome replication without compromising the overlapping p-gene product.We also found M75 and M103 can initiate truncated surface protein(TSPs) synthesis upon over-expression of full-length surface proteins,which may possibly contribute to HBV genome replication.However,attempts to rescue replicationdefective HBV mutant by co-expression of TSPs initiated from M75 or M103 were unsuccessful,which indicated surface proteins rather than the putative TSPs were involved in regulation of HBV genome replication.

A Kind of Essential Surfaces in the Complements of Knots

In this paper, by the twist-crossing number of knots, we give an upper bound on the Euler characteristic of a kind of essential surfaces in the complements of alternating knots and almost alternating knots, which improves the estimation of the Euler characteristic of the essential surfaces with boundaries under certain conditions. Furthermore, we give the genus of the essential surfaces.

Reliable approach for bistatic scattering of three-dimensional targets from underlying rough surface based on parabolic equation

A parabolic equation （PE） based method for analyzing composite scattering under an electromagnetic wave incidence at low grazing angle, which composes of three-dimensional （3-D） electrically large targets and rough surface, is presented and discussed. A superior high-order PE version is used to improve the accuracy at wider paraxial angles, and along with the alternating direction implicit （ADI） differential technique, the computational efficiency is further improved. The formula of bistatic normalized radar cross section is derived by definition and near-far field transformation. Numerical examples are given to show the validity and accuracy of the proposed approach, in which the results are compared with those of Kirchhoff approximation （KA） and moment of method （MoM）. Furthermore, the bistatic scattering properties of composite model in which the 3-D PEC targets on or above the two-dimensional Gaussian rough surfaces under the tapered wave incidence are analyzed.

Bounds on partial derivatives of NURBS surfaces

In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline theory and Dir function, some derivative bounds on NURBS curves are provided. Then, the derivative bounds on the magnitudes of NURBS surfaces are proposed by regarding a rational surface as the locus of a rational curve. Finally, some numerical examples are provided to elucidate how tight the bounds are.

Parametric Selection and Continual Combination of Building Surface

A method to reparametrize G retional curve to obtain a C^1 curve is given. A practical G^1 continual connective between adjacent NURUS patches along common guadratic boundary curve is presented in this paper, and a specific algorithm for control points and weights of NURBS patches is discussed.