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:目的研究上颌尖牙区三维方向上多种因素变化对曲面断层片中牙长轴角度影响.方法用干颅骨标本、模型牙制作模型模拟拔牙矫治后理想牙颌状态,从初始状态开始,依次改变右上尖牙的轴倾度、右上尖牙的转矩、上颌右侧弓形以及曲断选层位置,并在精确定位状态下分别拍摄颅骨模型的曲面断层片,测量右上尖牙牙长轴影像与固定参照平面的夹角.结果尖牙实际轴倾度与曲断片牙长轴角度呈同方向变化;尖牙根颊向转矩使牙根影像趋于后倾,根腭向转矩使牙根影像趋于前倾;弓形尖圆时牙根影像趋于前倾,弓形方圆时牙根影像趋于后倾;选层位置靠后时牙根影像趋于前倾,选层靠前时牙根影像趋于后倾,二者相差1.8°.结论曲面断层片所示的牙齿长轴角度受局部多种三维因素的共同影响,且具有一定的规律性.
简介:目的:为下颌后牙区牙槽嵴增高术提供临床测量方法及定量指标.方法:埘90名50岁以f上中t老年患者的曲面体层片下颌后牙区不同部位颌骨高度进行了测量.结果:颏孔上缘至牙槽嵴顶高度,有牙侧15.91±1.85mm,无牙侧9.07±2.48mm,平均值相差6.84mm;颏孔区下颌体高度,有牙侧33.64±2.69mm,无牙侧23.65±4.28mm,平均值相差9.99mm;下颌后牙区下颌体高度,有牙侧30.68±2.76mm,无牙侧20.96±4.15mm,平均值相差9.72mm.结论:通过曲面体层片测量颏孔和颏孔后1.0cm颌骨高度,了解下颔后牙区骨量丧失情况.为牙槽嵴增高术提供定量数据,方法简单,位置较恒定.下颌后牙区颌骨垂直吸收7~10mm,可供该区牙槽嵴增高术参考.
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.
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
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简介:THEAPPLICATIONOFG ̄1JOINOFRECTANGULARANDTRIANGULARBEZIERPATCHESINSURFACEMODELINGWangTianjun;TangRongxiSMOOTHSURFACEINTERPOLATI...