探析图形渲染中直线扫描转换、线性变换及透视校正研究

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1、西南交通大学博士学位论文图形渲染中直线扫描转换、线性变换及透视校正研究姓名：张华申请学位级别：博士专业：交通信息工程及控制指导教师：诸昌钤20060101第1v页西南交通大学博士研究生学位论文geometric“gebm．Geometricalgebr8ismoreabstracttllaJlvectoralgebraandquatemionalgeb豫，孤disnotpopul盯Iyusedincomputergmphics．By髓alyzingⅡ地derivingmetllodsofma岫x，v

2、ectoraIgcbm觚dquatemionaIgebm，aunifiedderivingfomulaoflinear协msfomationsispresentedbyusinggeometricalalgebra．Themathematicsexpfessio璐ofusingg∞m矧calgebmtosolVetlleunifieddfivingoflineartr蛆sfonnationsareequaItotlIoseOfquatemionalgebm．Simil盯ly'theperpendic

3、Ill盯relationoftwogivenVectorsisnotneededinmeprocessofsolvingtheunifiedd晒vingbyusinggeometricalgebra．Moreover，theexpressionsof∞smtsinrotati∞觚dreflection缸esimplerthantIlosc啦抽gvectOraIgebm蚰dquaterilionalgcbra．4)Theperspectivc—correctfomulausedinGouraudand

4、Phongshadirlgisprovedtobeusedinawidergraphrenderingpipeline，whichisarender．mgpipelinef‰thcstagcofperspectivet啪sfomlation，totllestageofperspectivedivision，tillarriveatViewporttr姐sfo肌ationstage．LowmemodsolvedtheperspectivedistonionofGo啪ud姐dPh∞gshadingonl

5、yintlleperspectivcstagebyusiIlgsiInjl缸tri锄gletlleory-ByanaIyzingtllest姐d盯dgrapmcs托nderirlgpipeline觚dexistedme也odofperspectiVe-correctforITlula，afomlulaOfperspective-co玎ectisObtained☆omthegiVenpipeli∞．Thepmpo∞dfo啪IlIaistlles锄easthatofLowmethod．Resultssh

6、OwthatLowmethodcanbeusednotonlyinmestageofpe船pcctivestage，butal∞intheWhole聊hics陀ndcringpipelinef如mprospectiVetr勰sfomlati∞．Byapplyingtlleproposedfb咖ulatoPhongshading，perspective-correctcurve蛐dexpcrimemsaregiven．5)AperspectiVe—cor弛ctm吼t∞dforequal姐gleinte

7、rp01ationispresented．Linesegmemslerlgthratiois懈edintlleperspective-co玎cctofGour叭d如dPhongshading．Angleratioisuscdintlleequal柚gleintcrl，olationshading．Aperspective-corrcctfb珊ulafbrequal髓glcintelpolati∞shadingisp聆scmed．Theproposedfomltllaalsohastlleadv锄ta

8、geofunitno珊alvector．Finally，acomparisonexperimentofequal锄gleinterpolationshadingispresentedbyllsingtlIepropOsedfbmuIa．1(eyWords：rendcring，geometricalalgebm，uninedderiving’perspectivecorrection，cqual-姐gleintcrpolation第2页西南交通大学博士研究生学位论文点变