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.

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.

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.

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 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.

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.

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

本文提出了在Ｔｒａｎｓｐｕｔｅｒ网络上计算均匀双３次Ｂ样条曲面的一种并行实现．

基于重新参数化的Bézier曲面求交算法

现有的参数曲面求交算法在求得一系列交点之后,需要再次用B样条插值才能表示出交线,且求得的交线无法保证精确落在任一给定曲面上。针对这一问题,提出一种基于重新参数化的求交算法。首先,通过曲面升阶加密曲面的控制网格,并求2个曲面控制网格的交线;然后,将交线映射到参数域,通过分段B样条曲线拟合,将拟合结果作为牛顿迭代的初值;最后,运用牛顿迭代求得更精确的参数域交线。相比于传统跟踪算法,该算法可直接得到交线的有理多项式表示形式,且求得的交线严格落在其中一个曲面上,在计算的交点个数更少的同时获得更高的逼近精度,并通过仿真实验验证了算法的精确性和有效性。

Hepatitis B surface antigen clearance in inactive hepatitis B surface antigen carriers treated with peginterferon alfa-2a

AIM: To examine the association between interferon(IFN) therapy and loss of hepatitis B surface antigen(HBs Ag) in inactive HBs Ag carriers. METHODS: This was a retrospective cohort study in inactive HBs Ag carriers, who were treatment-naive, with a serum HBs Ag level < 100 IU/m L and an undetectable hepatitis B virus(HBV) DNA level(< 100 IU/m L). All the 20 treated patients received subcutaneous PEG-IFN alfa-2a 180 μg/wk for 72 wk and were then followed for 24 wk. There were 40 untreated controls matched with 96 wk of observation. Serum HBs Ag, HBV DNA, and alanine aminotransferases were monitored every 3 mo in the treatment group and every 3-6 mo in the control group. RESULTS: Thirteen(65.0%) of 20 treated patients achieved HBs Ag loss, 12 of whom achieved HBs Ag seroconversion. Mean HBs Ag level in treated patients decreased to 6.69 ± 13.04 IU/m L after 24 wk of treatment from a baseline level of 26.22 ± 33.00 IU/m L. Serum HBV DNA level remained undetectable(< 100 IU/m L) in all treated patients during the study. HBs Ag level of the control group decreased from 25.72 ± 25.58 IU/m L at baseline to 17.11 ± 21.62 IU/m L at week 96(P = 0.108). In the control group, no patient experienced HBs Ag loss/seroconversion, and two(5.0%) developed HBV reactivation.CONCLUSION: IFN treatment results in HBs Ag loss and seroconversion in a considerable proportion of inactive HBs Ag carriers with low HBs Ag concentrations.

Hepatitis B virus infection:defective surface antigen expression and pathogenesis

Hepatitis B virus(HBV) infection is a global public health concern. HBV causes chronic infection in patients and can lead to liver cirrhosis, hepatocellular carcinoma, and other severe liver diseases. Thus, understanding HBV-related pathogenesis is of particular importance for prevention and clinical intervention. HBV surface antigens are indispensable for HBV virion formation and are useful viral markers for diagnosis and clinical assessment. During chronic HBV infection, HBV genomes may acquire and accumulate mutations and deletions, leading to the expression of defective HBV surface antigens. These defective HBV surface antigens have been found to play important roles in the progression of HBV-associated liver diseases. In this review, we focus our discussion on the nature of defective HBV surface antigen mutations and their contribution to the pathogenesis of fulminant hepatitis B. The relationship between defective surface antigens and occult HBV infection are also discussed.

Clinical utility of hepatitis B surface antigen kinetics in treatment-na?ve chronic hepatitis B patients during longterm entecavir therapy

AIM To investigate the utility of hepatitis B surface antigen(HBsAg) kinetics in chronic hepatitis B patients during long-term entecavir treatment.METHODS This retrospective study included treatment-na?ve chronic hepatitis B patients who received at least 2 years of consecutive entecavir treatment. Patients were followed up at three to six month intervals with liver biochemistry, hepatitis B virus DNA, and abdominal sonography. In hepatitis B e antigen(HBeAg)-positive patients, HBeAg levels were assessed every three to six month until results became negative. Serum HBsAg levels were determined at the baseline, oneyear and five-year time points. Liver cirrhosis was diagnosed through liver biopsy, imaging examinations, or clinical findings of portal hypertension. Hepatocellular carcinoma was diagnosed by histological examination or dynamic image studies.RESULTS A total of 211 patients were enrolled. The median treatment time was 5.24(2.00-9.62) years. Multivariate analysis showed that lower baseline HBsAg levels were associated with an earlier virological response, earlier hepatitis B e antigen(HBeAg) seroconversion, and earlier biochemical response in HBeAg-positive patients(cut-off value: 4 log IU/mL) and an earlier virological response in HBeAg-negative non-cirrhotic patients(cut-off value: 2.4 log IU/mL). Although HBsAg levels decreased slowly during long-term entecavir treatment, higher HBsAg decrease rates were found in the first year for HBeAg-positive non-cirrhotic patients, and patients with higher baseline HBsAg levels. More favorable clinical outcomes were not observed by a rapid HBsAg decline per se, but depended on lower baseline HBsAg levels.CONCLUSION Baseline HBsAg can be used to predict treatment responses. HBsAg levels and decrease rates should be considered together according to disease status while interpreting HBsAg changes.

Hepatitis B surface antigen levels during natural history of chronic hepatitis B: A Chinese perspective study

AIM: To determine the baseline hepatitis B surface antigen(HBsAg) levels during the different phases of chronic hepatitis B(CHB) patients in China.METHODS: Six hundred and twenty-three hepatitis B virus or un-infected patients not receiving antiviral therapy were analyzed in a cross-sectional study. The CHB patients were classified into five phases: immunetolerant(IT, n = 108), immune-clearance(IC, n = 161), hepatitis B e antigen negative hepatitis(ENH, n = 149), low-replicative(LR, n = 135), and liver cirrhosis(LC, n = 70). HBsAg was quantified(Abbott ARCHITECT assay) and correlated with hepatitis B virus(HBV) DNA, and serum alanine aminotransferase/aspartate aminotransferase(ALT/AST) in each phase of CHB was also determined.RESULTS: Median HBsAg titers were different in each phase of CHB(P < 0.001): IT(4.85 log10 IU/mL), IC(4.36 log10 IU/mL), ENH(2.95 log10 IU/mL), LR(3.18 log10 IU/mL) and LC(2.69 log10 IU/mL). HBsAg titers were highest in the IT phase and lowest in the LC phase. Serum HBsAg titers showed a strong correlation with HBV viral load in the IC phase(r = 0.683, P < 0.001). No correlation between serum HBsAg level and ALT/AST was observed.CONCLUSION: The mean baseline HBsAg levels differ significantly during the five phases of CHB, providing evidence on the natural history of HBV infection. HBsAg quantification may predict the effects of immunemodulator or oral nucleos(t)ide analogue therapy.