简介:传统的建模方法不能精确表示曲面体的弯曲度,针对这些不足,本文采用有理Bezier方法构建曲面模型,给出了椭球体标准型有理二次Bezier控制点和权因子的求解算法;利用非有理Bezier的升阶算法将有理二次Bezier升阶为有理三次Bezier,给出了标准型有理三次Bezier曲线控制点和权因子的求解算法,构建了有理双三次Bezier椭球体曲面模型,通过调整控制点或权因子参数可生成如葫芦、青椒、鸡蛋等光滑的曲面模型.实验表明,该算法具有很好的设计灵活性和交互性,为构建曲面模型提供了新的技术支持.
简介:Inthispaper,theproblemoffindingtheintersectionofatriangularBezierpatchandaplaneisstudied.Forthedegreethatonefrequentlyencountersinpractice,i.e.n=2,3,anefficientandreliablealgorithmisobtained,andcomputationalstepsarepresented.
简介:河北省曲周县位于冀南平原滏阳河畔,历史悠久,物产丰富,土特名产甚多,其中的"曲面"更是风味独特,闻名全国。"曲面"是采用优质吉豆、黄豆和小麦的精粉按比例匹配,以香油、鸡蛋调和而制成的面条。以鸡汁调汤或肉卤相佐,营养丰富,久吃不腻,赞誉不绝,是招待客人和馈赠亲友的美味佳品。历史上的曲周人素以面食为主,常用白面和豆面掺和制作面条,俗称"杂面",是人们的主食之一。明万历年间,由于以制作、出售"杂面"为业的手工作坊和餐馆、饭店的出现,"曲面"在配方比例和制作技术上便更加讲究,并不断改进,在冀南一带及滏阳河流域有较大的名气。清咸丰年间,"曲面"的声誉传进宫中,咸丰皇帝传旨进贡。曲周县城东关祖传经营"杂面"的赵
简介:RationalBéziersurfaceisawidelyusedsurfacefittingtoolinCAD.WhenalltheweightsofarationalBéziersurfacegotoinfinityintheformofpowerfunction,thelimitofsurfaceistheregularcontrolsurfaceinducedbysomeliftingfunction,whichiscalledtoricdegenerationsofrationalBéziersurfaces.Inthispaper,westudyonthedegenerationsoftherationalBéziersurfacewithweightsintheexponentialfunctionandindicatethedifferenceofourresultandtheworkofGarc′?a-Puenteetal.Throughthetransformationofweightsintheformofexponentialfunctionandpowerfunction,theregularcontrolsurfaceofrationalBéziersurfacewithweightsintheexponentialfunctionisdefined,whichisjustthelimitofthesurface.Comparedwiththepowerfunction,theexponentialfunctionapproachesinfinityfaster,whichleadstosurfacewiththeweightsintheformofexponentialfunctiondegeneratesfaster.
简介:Inthispaper,wepresenttwonewunifiedmathematicsmodelsofconicsandpolynomialcurves,calledalgebraichyperbolictrigonometric(AHT)Béziercurvesandnon-uniformalgebraichyperbolictrigonometric(NUAHT)B-splinecurvesofordern,whicharegeneratedoverthespacespan{sint,cost,sinht,cosht,1,t,...,t~(n-5)},n≥5.ThetwokindsofcurvessharemostofthepropertiesasthoseoftheBéziercurvesandB-splinecurvesinpolynomialspace.Inparticular,theycanrepresentexactlysomeremarkabletranscendentalcurvessuchasthehelix,thecycloidandthecatenary.Thesubdivisionformulaeofthesenewkindsofcurvesarealsogiven.Thegenerationsofthetensorproductsurfacesarestraightforward.Usingthenewmathematicsmodels,wepresentthecontrolmeshrepresentationsoftwoclassesofminimalsurfaces.