A new algorithm for designing developable Bézier surfaces

A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm is based on differential geometry theory on necessary and sufficient conditions for a surface which is developable, and on degree evaluation formula for parameter curves and linear independence for Bernstein basis. No nonlinear characteristic equations have to be solved. Moreover the vertex for a cone and the edge of regression for a tangent surface can be obtained easily. Aumann’s algorithm for developable surfaces is a special case of this paper.

Computation of lower derivatives of rational triangular Bézier surfaces and their bounds estimation

By introducing the homogenous coordinates, degree elevation formulas and combinatorial identities, also by using multiplication of Bernstein polynomials and identity transformation on equations, this paper presents some explicit formulas of the first and second derivatives of rational triangular Bézier surface with respect to each variable (including the mixed derivative) and derives some estimations of bound both on the direction and magnitude of the corresponding derivatives. All the results above have value not only in surface theory but also in practice.

Visible region extraction from a sequence of rational Bézier surfaces

A method for computing the visible regions of free-form surfaces is proposed in this paper. Our work is focused on accurately calculating the visible regions of the sequenced rational Bézier surfaces forming a solid model and having coincident edges but no inner-intersection among them. The proposed method calculates the silhouettes of the surfaces without tessellating them into triangle meshes commonly used in previous methods so that arbitrary precision can be obtained. The computed sil- houettes of visible surfaces are projected onto a plane orthogonal to the parallel light. Then their spatial relationship is applied to calculate the boundaries of mutual-occlusion regions. As the connectivity of the surfaces on the solid model is taken into account, a surface clustering technique is also employed and the mutual-occlusion calculation is accelerated. Experimental results showed that our method is efficient and robust, and can also handle complex shapes with arbitrary precision.

Real-time accurate Free-Form Deformation in terms of triangular Bézier surfaces

We implemented accurate FFD in terms of triangular Bezier surfaces as matrix multiplications in CUDA and rendered them via OpenGL. Experimental results show that the proposed algorithm is more efficient than the previous GPU acceleration algorithm and tessel- lation shader algorithms.

Mixed tensor product negative Bernstein-Bézier surfaces

A kind of mixed tensor product negative Bemstein-B6zier basis function is presented in this paper. Some important prop- erties of this kind of basis function are discussed and mixed tensor product negative Bemstein-B6zier is defined based on it. The ba- sic properties of the such surface are discussed. Via de Casteljan algorithm, the evaluation algorithm and subdivision algorithm for mixed tensor product negative Bernstein-B6zier surfaces are derived as extensions of the algorithms of B6zier curves and negative Bernstein curves.

Recurrence and influencing factors of hepatitis B surface antigen seroclearance induced by peginterferon alpha-based regimens

BACKGROUND The long-term stability of hepatitis B surface antigen(HBsAg)seroclearance following peginterferon alpha(peg-IFN-α)-based therapy has not been extensively studied,leaving the full potential and limitations of this strategy unclear.AIM To assess HBsAg recurrence after seroclearance achieved by peg-IFN-αregimens.METHODS This prospective,multicenter,observational study was conducted from November 2015 to June 2021 at three Chinese hospitals:The Second Affiliated Hospital of Xi’an Jiaotong University,Ankang Central Hospital,and The Affiliated Hospital of Yan’an University.Participants who achieved HBsAg seroclearance following peg-IFN-α-based treatments were monitored every 4-12 weeks post-treatment for hepatitis B virus(HBV)markers,HBV DNA,and liver function.The primary outcome was HBV recurrence,defined as the reemergence of HBsAg,HBV DNA,or both,at least twice within 4-8 weeks of follow-up.RESULTS In total,121 patients who achieved HBsAg seroclearance were enrolled.After a median follow-up of 84.0(48.0,132.0)weeks,four subjects were lost to follow-up.HBsAg recurrence was detected in 16 patients.The cumulative HBsAg recurrence rate in the intention-to-treat population was 15.2%.Multivariate logistic regression analysis demonstrated that consolidation time<12 weeks[odds ratio(OR)=28.044,95%CI:4.525-173.791]and hepatitis B surface antibody disappearance during follow-up(OR=46.445,95%CI:2.571-838.957)were strong predictors of HBsAg recurrence.HBV DNA positivity and decompensation of liver cirrhosis and hepatocellular carcinoma were not observed.CONCLUSION HBsAg seroclearance following peg-IFN-αtreatment was durable over 84 weeks of follow-up with a cumulative recurrence rate of 15.2%.

Hepatitis B surface antigen-negative but hepatitis B envelope antigen-positive false occult hepatitis B virus infection:A case report

BACKGROUND Occult hepatitis B infection(OBI)is characterized by the detection of hepatitis B virus(HBV)DNA in serum(usually HBV DNA<200 IU/mL)or the liver but negativity for hepatitis B surface antigen(HBsAg).The diagnosis of OBI relies on the sensitivity of assays used in the detection of HBV DNA and HBsAg.HBsAg assays with inadequate sensitivity or inability to detect HBV S variants may lead to misdiagnosis of OBI in people with overt HBV infection.CASE SUMMARY We report a HBsAg-negative but hepatitis B envelope antigen-positive patient who had a significant HBV DNA level.The patient was initially diagnosed as having OBI.However,sequence analysis revealed a unique insertion of amino acid residues at positions 120-124 in the S protein,which affects the formation of a disulfide bond that is associated with the formation of a loop.It is well known that there is an overlap between the S protein and Pol protein.We found that this new insertion site occurred in polymerase/reverse transcriptase domain,indi-cating that this insertion might be involved in HBV pathogenicity.The patient was finally diagnosed with a false OBI.CONCLUSION An insertion of amino acid residues at positions 120-124 of the S protein affects the formation of immunodominant epitopes and results in negative HBsAg levels.

Quantitative hepatitis B core antibody and quantitative hepatitis B surface antigen:Novel viral biomarkers for chronic hepatitis B management

The management of hepatitis B virus(HBV)infection now involves regular and appropriate monitoring of viral activity,disease progression,and treatment response.Traditional HBV infection biomarkers are limited in their ability to predict clinical outcomes or therapeutic effectiveness.Quantitation of HBV core antibodies(qAnti-HBc)is a novel non-invasive biomarker that may help with a variety of diagnostic issues.It was shown to correlate strongly with infection stages,hepatic inflammation and fibrosis,chronic infection exacerbations,and the presence of occult infection.Furthermore,qAnti-HBc levels were shown to be predictive of spontaneous or treatment-induced HBeAg and HBsAg seroclearance,relapse after medication termination,re-infection following liver transplantation,and viral reactivation in the presence of immunosuppression.qAnti-HBc,on the other hand,cannot be relied on as a single diagnostic test to address all problems,and its diagnostic and prognostic potential may be greatly increased when paired with qHBsAg.Commercial qAnti-HBc diagnostic kits are currently not widely available.Because many methodologies are only semi-quantitative,comparing data from various studies and defining universal cut-off values remains difficult.This review focuses on the clinical utility of qAnti-HBc and qHBsAg in chronic hepatitis B management.

Reconstruction from contour lines based on bi-cubic Bézier spline surface

A novel reconstruction method from contours lines is provided. First, we use a simple method to get rid of redundant points on every contour, then we interpolate them by using cubic Bézier spline curve. For corresponding points of different con- tours, we interpolate them by the cubic Bézier spline curve too, so the whole surface can be reconstructed by the bi-cubic Bézier spline surface. The reconstructed surface is smooth because every Bézier surface is patched with G2 continuity, the reconstruction speed is fast because we can use the forward elimination and backward substitution method to solve the system of tridiagonal equations. We give some reconstruction examples at the end of this paper. Experiments showed that our method is applicable and effective.

基于4阶Bézier曲线的路径平滑方法研究

路径平滑技术旨在采用以曲代直的方法解决路径规划中存在的尖角问题,实现路径的平滑化,以满足外形设计和运动规划等工程应用需求。文中在深入探讨了Bézier曲线在路径平滑领域的应用优势及其在路径拟合中产生的较大偏差后,提出了一种基于内外比例因子的4阶Bézier曲线路径平滑新方法。通过严谨的理论分析,证明了该方法能够有效控制平滑误差,在不考虑路径节点坐标的情况下,误差上限为4.25,从而实现对原始路径的高精度平滑近似。在无人机路径平滑的仿真实验中,该方法耗时0.0061 s,证明了其在平滑处理速度方面的优越性。综合理论分析与实验结果,该方法不仅在平滑效果上表现出色,而且在处理速度上也具有明显优势。同时由于仅涉及内外比例因子两个自由参数,因此,操作简单,易于实现,具有较强的适用性和灵活性。

A Subdivision Scheme for Rational Triangular Bézier Surfaces

An explicit formula is developed to decompose a rational triangular Bezierpatch into three non-degenerate rational rectangular B6zier patches of the samedegree. This formula yields a stable algorithm to compute the control verticesof those three rectallgular subpatches. Some properties of the subdivision arediscussed and the formula is illustrated with an example.

Convexity and Positivity of Bivariate Quadratic Bézier Surfaces over a Rectangle

With the help of several discriminants about the zero points of a quartic polynomial, the sufficient and necessary conditions for the positivity and nonnegativity of the quartic polynomial over an interval I(-∞,+∞) was derived. Based on these conclusions, the sufficient and necessary conditions for the positivity and convexity of the 2×2 Bézier surface over a rectangle were obtained. A simple sufficient condition was deduced also and finally several examples were given.

A Sufficient Convexity Condition for Parametric Bézier Surface over Rectangle

Surface convexity is a key issue in computer aided geometric design, which is widely applied in geometric modeling field, such as physical models, industrial design, automatic manufacturing, etc. In this paper, a sufficient convexity condition of the parametric Bézier surface over rectangles is proposed, which is firstly considered as a sufficient convexity condition for the Bézier control grid. The condition is proved by De Casteljau surface subdivision arithmetic, in which the recursive expressions elaborate that the control grid eventually converges to the surface. At last, two examples for the modeling of interpolation-type surface are discussed, one of which is a general surface and the other is a degenerate surface.

带形状参数的三角λ-Bézier曲线

为了克服传统Bézier曲线缺乏局部调整性并且不能精确表达圆锥曲线的缺点,构造了一个带形状参数的n(n≥2)次三角λ-Bézier曲线,为了降低工作难度,各阶曲线的形状参数取值范围保持不变。首先将基函数设置在三角多项式空间中,利用递推性构造了λ-Bernstein基函数,进而讨论了该基函数的端点性和对称性等重要性质,并由该基函数定义了n(n≥2)次λ-Bézier曲线。另外,讨论了形状参数取不同值时对曲线形状的影响以及曲线的拼接条件:在一定的条件下,该曲线可达到G2拼接;最后,给出了张量积形式的λ-Bézier曲面以及性质。实例表明,该曲线克服了传统Bézier曲线缺乏局部调整性的缺点且能近似表达圆弧和抛物线等圆锥曲线。

Assimilation of Ocean Surface Wind Data by the HY-2B Satellite in GRAPES: Impacts on Analyses and Forecasts

The ocean surface wind(OSW)data retrieved from microwave scatterometers have high spatial accuracy and represent the only wind data assimilated by global numerical models on the ocean surface,thus playing an important role in improving the forecast skills of global medium-range weather prediction models.To improve the forecast skills of the Global/Regional Assimilation and Prediction System Global Forecast System(GRAPES_GFS),the HY-2B OSW data is assimilated into the GRAPES_GFS four-dimensional variational assimilation(4DVAR)system.Then,the impacts of the HY-2B OSW data assimilation on the analyses and forecasts of GRAPES_GFS are analyzed based on one-month assimilation cycle experiments.The results show that after assimilating the HY-2B OSW data,the analysis errors of the wind fields in the lower-middle troposphere(1000-600 hPa)of the tropics and the southern hemisphere(SH)are significantly reduced by an average rate of about 5%.The impacts of the HY-2B OSW data assimilation on the analysis fields of wind,geopotential height,and temperature are not solely limited to the boundary layer but also extend throughout the entire troposphere after about two days of cycling assimilation.Furthermore,assimilating the HY-2B OSW data can significantly improve the forecast skill of wind,geopotential height,and temperature in the troposphere of the tropics and SH.

A synthetic aperture radar sea surface distribution estimation by n-order Bézier curve and its application in ship detection

To dates,most ship detection approaches for single-pol synthetic aperture radar（SAR） imagery try to ensure a constant false-alarm rate（CFAR）.A high performance ship detector relies on two key components：an accurate estimation to a sea surface distribution and a fine designed CFAR algorithm.First,a novel nonparametric sea surface distribution estimation method is developed based on n-order Bézier curve.To estimate the sea surface distribution using n-order Bézier curve,an explicit analytical solution is derived based on a least square optimization,and the optimal selection also is presented to two essential parameters,the order n of Bézier curve and the number m of sample points.Next,to validate the ship detection performance of the estimated sea surface distribution,the estimated sea surface distribution by n-order Bézier curve is combined with a cell averaging CFAR（CA-CFAR）.To eliminate the possible interfering ship targets in background window,an improved automatic censoring method is applied.Comprehensive experiments prove that in terms of sea surface estimation performance,the proposed method is as good as a traditional nonparametric Parzen window kernel method,and in most cases,outperforms two widely used parametric methods,K and G0 models.In terms of computation speed,a major advantage of the proposed estimation method is the time consuming only depended on the number m of sample points while independent of imagery size,which makes it can achieve a significant speed improvement to the Parzen window kernel method,and in some cases,it is even faster than two parametric methods.In terms of ship detection performance,the experiments show that the ship detector which constructed by the proposed sea surface distribution model and the given CA-CFAR algorithm has wide adaptability to different SAR sensors,resolutions and sea surface homogeneities and obtains a leading performance on the test dataset.

Surface plasmon resonance-induced visible-light photocatalytic performance of silver/silver molybdate composites

Novel silver/silver molybdate（Ag/Ag2MoO4） composites with surface plasmon resonance（SPR）-enhanced photocatalytic performance were successfully fabricated via a facile one-pot hydrothermal route with the presence of sodium dodecyl sulfate（SDS） in this study.The as prepared silver/silver molybdate（Ag/Ag2MoO4） composites were systematically characterized by X-ray diffraction（XRD）,scanning electron microscopy（SEM） and ultraviolet-visible diffuse reflectance absorption spectroscopy（DRS） in order to investigate their crystal structure,morphology and optical property as well.The photocatalytic activities of the composites were subsequently evaluated by their ability to degrade rhodamine B（RhB） under visible-light irradiation.Varies of controlled experiments were then carefully operated to gain a deep insight into the assembling of Ag/Ag2MoO4composites.It was found that preparation conditions such as pH,reaction time,and the amount of surfactant played important roles in the formation of composites with octahedral microstructures.And the composite obtained at 160 ℃ using 0.5 g of sodium dodecyl sulfate exhibited the highest photocatalytic performance under visible-light irradiation.Capture experiments were also conducted to clarify the function of different active species generated on the surface of Ag/Ag2MoO4during the photocatalytic process,in which both holes and ·OH radicals were found to play crucial role in photocatalytic removal of RhB under visible light irradiation.A possible photocatalytic mechanism of Ag/Ag2MoO4 was finally proposed on the basis of all the results to explain the higher photocatalytic activity of the octahedral Ag/Ag2MoO4 composites.It was inferred that the photoinduced ＂hot＂ electrons can quickly transfer from the Ag NPs to the conduction band of Ag2MoO4 and react with oxygen and H2O to generate a large quality of active radicals such as ·OH and ·O2^- because of the SPR effects.Besides,this SPR effects of Ag nanoparticles deposited on the surface of Ag2MoO4 can not only dramatically amplify its light absorption,especially in the visible region,but also promote the separation of photoexcited electron-hole pairs and effectively decrease electron-hole recombination.

基于四元数和Bézier方法的五次空间PH曲线

为保证空间Pythagorean-hodograph(PH)曲线的光顺性并使曲线最小旋转,提出了五次空间PH曲线构造。给定空间4个控制点,在给定的端点属性下,运用四元数方法构造四次Bézier曲线。对该曲线积分得到插值端点的五次PH曲线。此PH曲线的控制顶点是在原控制点的中间插入2个新节点,并且这些顶点可以用四元数运算表示。构造的五次PH曲线包含多个自由度,利用这些自由度可以对曲线进行优化调节。一方面,可以利用自由参数,根据曲线几何意义对曲线的光顺性及最小旋转进行优化;另一方面,可以通过自由参数约束曲线合理的弧长。此PH曲线本身就是Bézier曲线,且带有自由参数,能实现分段曲线的光滑拼接。

HBV C基因型有关的HBsAg阴性HBV DNA阳性患者S区突变对HBsAg的影响

目的通过构建HBV C基因型突变质粒研究HBsAg阴性HBV DNA阳性患者HBV S区突变对HBsAg水平的影响。方法收集2022年8月至2023年4月首都医科大学附属北京佑安医院107例HBsAg-/HBV DNA+患者血液样本,对成功提取扩增的HBV DNA S区进行测序,通过构建HBV C基因型突变质粒对HBV S区突变位点进行细胞功能验证,探讨OBI可能发生的分子机制。结果对成功提取扩增的68例患者进行测序,发现HBV S区存在大量突变,包括免疫逃逸突变(如sG145R、sK122R、sS114T、sT131P等)和跨膜结构域(transmembrane domain,TMD)突变(如sT5A、sG10D、sF20S等)。通过构建HBV C基因型突变质粒,进行细胞转染和细胞免疫荧光实验发现sG145R突变会明显降低HBsAg的表达,但是sK122R、sI26N、sQ29N、sR169H、sS114T、sT131P这6个突变位点并未影响细胞内外HBsAg的表达。结论通过测序发现HBsAg-/HBV DNA+患者HBV S区存在大量突变位点,通过构建sG145R、sK122R、sI26N、sQ29N、sS114T和ST131P等突变质粒发现sG145R突变会明显降低细胞内外HBsAg的表达,但是sK122R、sI26N、sQ29N、sR169H、sS114T、sT131P并未明显降低细胞内外HBsAg的表达。

Computing B-Spline Surfaces on Transputer Networks

This paper presents a parallel implementation of computing uniform bicubic B spline surfaces on Transputer networks. The work is essential for building Transputer based CAD and graphics systems.