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时间:2020-09-27
《计算机图形学基于任意点的旋转变换ppt课件.ppt》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库。
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
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