简介:给出了n阶带形状参数的三角多项式T-Bézier基函数.由带形状参数的三角多项式T-Bézier基组成的带形状参数的T-Bézier曲线,可通过改变形状参数的取值而调整曲线形状,随着形状参数的增加,带形状参数的T-Bézier曲线将接近于控制多边形,并且可以精确表示圆、螺旋线等曲线.阶数的升高,形状参数的取值范围将扩大.
简介:提出了点集Bézier曲线的概念,给出了点集Bézier曲线的性质及细分算法.按照点集算术的定义,当点集是长方形闭域或圆盘时,点集Bézier曲线就是区间Bézier曲线或圆盘Bézier曲线,因此,点集Bézier曲线是对区间Bézier曲线和圆盘Bézier曲线的推广.
简介:AsolutiontothereparametrizationofBéziercurvesbysinetransformationofBernsteinbasisispresented.Theneweffectivereparametrizationmethodisgiventhroughthefollowingprocedures:educingSineBernstein-BézierClass-SBBCfunction,definingSBBCcurveanddiscussingtherelationbetweenSBBCandBéziercurve.
简介:一个新算法被介绍产生开发通过一条Bézier曲线的表面把一根准线称为的有能力的Bézier。算法基于微分几何学理论在上必要;为是的表面的足够的条件发展能,;在为参数曲线的度评估公式上;为伯恩斯坦基础的线性独立。没有非线性的典型方程不得不被解决。而且为一个锥的顶点;为正切表面的回归的边能容易被获得。Aumann的算法为开发有能力的表面是这篇论文的一种特殊情况。
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简介:对于有界变差函数f的Durrmeyer-Bézier算子Dn,a(f,x)在区间(0,1)上收敛于:1/α+1f(x+)+α/α+1f(x-)的收敛阶进行估计.在Zeng和Chen关于Dn,a(f,x)算子的收敛阶研究的基础上,对其所估计的结果作进一步的改进,得到更精确的系数估计,并且所得到的系数估计关于n和x是一致有界的,改进了原估计非一致有界的不足.
简介:UE-Bézier(unifiedandextendedBézier)basisistheunifiedformofBézier-likebases,includingpolynomialBézierbasis,trigonometricpolynomialandhyperbolicpolynomialBézierbasis.SimilartotheoriginalBézier-likebases,UE-Bézierbasisfunctionsarenotorthogonal.Inthispaper,agroupoforthogonalbasisisconstructedbasedonUE-Bézierbasis.ThetransformationmatricesbetweenUE-Bézierbasisandtheproposedorthogonalbasisarealsosolved.
简介:运用概率型算子的概率性质,研究了局部有界函数厂的Integral型Lupas—Bêzier算子收敛阶,得到更精确的估计。其研究对于Bêzier型算子逼近的研究工作,以及提高运用Bêzier法的计算机辅助设计几何造型的精度的估计有重要意义。
简介:Thispaperpresentsanewbasis,theWSBbasis,whichunifiestheBernsteinbasis,Wang-BallbasisandSaid-Ballbasis,andthereforetheBéziercurve,Wang-BallcurveandSaid-BallcurvearethespecialcasesoftheWSBcurvebasedontheWSBbasis.Inaddition,therelativedegreeelevationformula,recursivealgorithmandconversionformulabetweentheWSBbasisandtheBernsteinbasisaregiven.
简介:ManyworkshaveinvestigatedtheproblemofreparameterizingrationalBéziercurvesorsurfacesviaMbiustransformationtoadjusttheirparametricdistributionaswellasweights,suchthatthemaximalratioofweightsbecomessmallerthatsomealgebraicandcomputationalpropertiesofthecurvesorsurfacescanbeimprovedinaway.However,itisanindicationofveracityandoptimizationofthereparameterizationtodopriortojudgewhetherthemaximalratioofweightsreachesminimum,andverifythenewweightsafterMbiustransformation.What’smoretheusersofcomputeraideddesignsoftwaresmayrequiresomeguidelinesfordesigningrationalBéziercurvesorsurfaceswiththesmallestratioofweights.Inthispaperwepresentthenecessaryandsufficientconditionsthatthemaximalratioofweightsofthecurvesorsurfacesreachesminimumandalsodescribeitbyusingweightssuccinctlyandstraightway.Theweightsbeingsatisfiedtheseconditionsarecalledbeinginthestablestate.Applyingsuchconditions,anygivingrationalBéziercurveorsurfacecanautomaticallybeadjustedtocomeintothestablestatebyCADsystem,thatis,thecurveorsurfacepossessesitsoptimalparametricdistribution.Finally,wegivesomenumericalexamplesfordemonstratingourresultsinimportantapplicationsofjudgingthestablestateofweightsofthecurvesorsurfacesanddesigningrationalBéziersurfaceswithcompactderivativebounds.
简介:在Zeng等人对有界变差函数f的Durrmeyer-Bézier算子在区间(0,1)上收敛于(1/(α+1))f(x+)+(α/(α+1))f(x-)的收敛阶进行研究的基础上,利用基函数的概率性质等方法,对其所给的Durrmeyer-Bézier算子收敛阶估计结果作进一步的改进,得到其收敛阶的精确估计.