计算机图形学基于任意点的旋转变换ppt课件.ppt

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1、RotatetransformationaboutarbitrarypointSupposethepointisthenthetransformationcanbecomposedbysomefundamentaltransformations•Translation(T)•Rotation(R)••InversetranslationT=T-1·R·TCont.ScalingaboutarbitrarypointReferencepoint:,fixuppointbeforeandafterscalingCompositionof

2、translate,scaleaboutorigin,andinversetranslatetransformationsCont.Namely:SymmetryaboutarbitrarylineTRS4.2window-to-viewporttransformationWorldDomain(用户域WD)指程序员用来定义草图的整个自然空间.Window(窗口区W)在用户坐标系(世界坐标系WC）中预先选定的将产生图形显示的区域称为窗口.World-coordinatesystem(用户坐标系WC)世界坐标系右手直角坐标系Relatedc

3、onceptsCont.ScreenDomain(屏幕域SD)设备输图形的最大区域,是有限的整数域.Viewport(视图区V)在显示器坐标系中规定的显示图形的区域称为视(图)区.Screencoordinates(normalized)devicecoordinatesdevicecoordinates:addressingbypixelsNDC:[-1，1][-a，a]窗口的取景器作用Windowasaviewfinder利用窗口尺寸变化改变显示图形的大小选窗口的视见变换选窗口的视见变换Cont.视见变换将用户坐标系中窗口内

4、的图形变换到显示器中的视见区中产生显示.Window-to-ViewporttransformationwindowWxlWxrWybWyt•P(x,y)VxlVxrviewportVybVyt•P(x’,y’)Cont.windowWxlWxrWybWyt•P(x,y)VxlVxrviewportVybVyt•P(x’,y’)Cont.transformmatrix窗口WxlWxrWybWytWxlWxrWybWyt--VxlVxrVybVyt--VxlVxrvybVytCont.VxlVxrVybVytNDC-to-DCtransfor

5、mationNDC:[-1，1][-a，a]DC:[0，M-1][0，N-1]Consideringitsdiscretefeature:[-0.5，M-1.5][-0.5，N-1.5]ThesamelineartransformationastheW-to-VtransformationWhereas:Flowchartof2DviewWC世界坐标系内的变换NDC规格化坐标系到设备坐标系的变换对窗口区进行裁剪WCDC设备输出二维图形显示流程窗口到视图区的规格化变换WCExercisesExercise4.1Exercise4.2Exerc

6、ise4.34.33DtransformationsTranslate(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:Wherea

7、s:Translate记为：ScaletransformationAboutoriginCont.AboutarbitrarypointThearbitraryreferencepointis:Cont.Aboutarbitrarypointtranslate,scaleaboutorigin,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：XYZ

8、RotatetransformationRotateaboutXaxisEquallywithchangingthecoordinatesystem[x,y,z]tothecoo