计算机图形学3d变换

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1、4.33DtransformationsTranslate(平移)transformationsRotate(旋转)transformationsScale(缩放)transformationsReflect(反射)transformationsShear(错切)transformationsComposition(复合)of2Dtransformations与二维平移变换类似地使用齐次坐标表示为：记为：其中TranslatetransformationTranslatetransformationRemarked:Whereas:Translate记为：Scalet

2、ransformationAboutoriginCont.AboutarbitrarypointThearbitraryreferencepointis:Consistsof:translate,scaleaboutorigin,inversetranslateCont.则变换矩阵为:Aboutarbitrarypointtranslate,scaleaboutorigin,inversetranslateConsistsof:Thearbitraryreferencepointis:Cont.Aboutarbitrarypointtranslate,scaleabo

3、utorigin,inversetranslateConsistsof:Thearbitraryreferencepointis:Cont.则变换矩阵为:Parameters:rotateaxis,rotateangle二维旋转变换是三维空间中绕Z轴的旋转记为：XYZRotatetransformationRotateaboutXaxisEquallywithchangingthecoordinatesystem[x,y,z]tothecoordinatesystem[y,z,x].YZXXYZRotateaboutYaxisChangingsystem[x,y,z]

4、tosystem[z,x,y]ZXYXYZ?:aboutarbitraryline是关于某直线或平面进行的关于某个轴进行的反射变换等同于关于该轴做180度的旋转变换Forinstance:aboutZaxisReflecttransformation?:aboutarbitrarysymmetryaxisCont.当反射平面是坐标平面时，等同于进行左、右手坐标系的互换，相应变换矩阵是把第三维坐标值取反Forinstance:aboutXOYplane?AboutarbitrarysymmetryplaneCont.关于任意直线(或平面)的反射可以分解为平移、旋转（使得

5、指定的反射直线或平面与某坐标轴或平面重合）和关于坐标直线(或平面)的反射。SheartransformationsDependenceaxis:correspondingcoordinateisremainedDirectionaxis:correspondingcoordinateischangedlinearlyRepresentations:Cont.Representation变换的一般表达式是：Forinstance:rotatingaboutarbitrarylineOverlappingarbitrarylinewithZaxisResolvingase

6、riesofproblemsReflectaboutanarbitrarysymmetrylineReflectaboutanarbitrarysymmetryplaneCompositiontransformations旋转轴不与坐标轴重合时变换的实现：经复合变换使旋转轴与某坐标轴重合绕指定轴进行旋转变换还原坐标系YZXP1P2Rotateaboutarbitraryline（1）translateP1tooverlaporigin不妨设P1P2为方向矢量，P2点为(a,b,c)YZxP1P2Y’Z’x’Cont.XYZOP1P2XYZCont.Cont.P1P2X

7、YZ(2)rotateaboutXaxistoputthelineonXOZXYZCont.(2)rotateaboutXaxistoputthelineonXOZXYZCont.(2)rotateaboutXaxistoputthelineonXOZXYZCont.(2)rotateaboutXaxistoputthelineonXOZXYZCont.(2)rotateaboutXaxistoputthelineonXOZXYZCont.(2)rotateaboutXaxistoputthelineonXOZXYZCont.(2)rot