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ViewingIn3D,Chapter5,如何在二维平面上显示三维物体表示问题遮挡关系的反映真实感问题,投影,三维形体的表示,消隐,光照与着色,Thebasicquestionsof3Dgraphics,3Dviewingprocess,Conception,Projectionstransformpointsinacoordinatesystemofdimensionnintopointsinacoordinatesystemofdimensionlessthann.,Projection,Definition:Theprojectionofa3Dobjectisdefinedbystraightprojectionrays(calledprojectors)emanatingfromacenterofprojection,passingthrougheachpointoftheobject,andintersectingaprojectionplanetoformtheprojection.,Projections,ProjectionsParameter:projectioncenterprojectionplane,Theclassofprojections,PerspectiveProjectionThedistancebetweenthecenterofprojectionandtheprojectionplaneisfinite.ParallelProjectionThedistancebetweenthecenterofprojectionandtheprojectionplaneisinfinite.,Theclassofprojections,ThesubclassesofPlanarGeometricProjections.,ThreeOrthographicProjections,ThreeOrthographicProjections(三视图）,正平行投影（三视图）,FrontElevation,TopElevation,SideElevation,PerspectiveProjection,VanishingPoint.Theperspectiveprojectionsofanysetofparallellinesthatarenotparalleltotheprojectionplaneconvergetoavanishingpoint.AxisVanishingPointIfthesetoflinesisparalleltooneoftheprincipalaxes,thevanishingpointiscalledanaxisvanishingpoint.,ThestyleofPerspectiveProjection,Perspectiveprojectionsarecategorizedbytheirnumberofprincipalvanishingpointsandthereforebythenumberofaxestheprojectionplanecuts,One-pointperspectiveprojectionProjection-planecutsonlyoneofthreeaxes.Two-pointperspectiveprojectionProjection-planecutsonlytwoofthreeaxesatthesametime.Three-pointperspectiveprojectionProjection-planecutsallofthreeaxesatthesametime.,ThestyleofPerspectiveProjection,One-pointperspectiveprojection,Two-pointandThree-pointPerspectiveProjection,ThemathematicsofsimplePerspectiveProjection,ParameterEquationofLinePcP:,TheintersectionofthelinePPcwiththeprojectionplaneatz=0isintheXOYplane,One-pointperspectiveprojection,Undertheviewing-referencecoordinateofuvn,Suppose:projectionplanen=0,projectionreferencepoint(0,0,d),pointp(up,vp,np)ofthreedimspace,itsprojectionpointQ,LineParameterEq:,TransformationofOne-pointperspectiveprojection,举例,若假定投影参考点为(0,0,0),即观察坐标系的原点，投影平面为n=d,待投影的三维空间中的点是p(up,vp,np),投影点为Q,则直线方程是:,X,Z,右手用户坐标系,0,通常,在由三维物体转换成二维图形的假想相机模型中,物体首先被变换到在观察坐标系中描述,然后再投影到观察平面上成为二维图形.,观察坐标系中的简单一点透视,Y,在观察坐标系下,仍利用前述的简单一点透视的方法,可求观察坐标系上形体的一点(Xe,Ye,Ze)在视平面上的投影(Xs,Ys):,(Xw,Yw,Zw)是用户坐标系下的点(Xe,Ye,Ze)是观察坐标系下的点(X,Y,Z)是投影点,观察坐标系中的简单一点透视,在观察坐标系中,视点为原点,(Xc,Yc,Zc)为(0,0,0),用户坐标系下的点(Xw,Yw,Zw)为(Xe,Ye,Ze),则有:,观察坐标系中的简单一点透视,如何完成从世界坐标系到观察坐标系的变换？,观察变换,完成工作：在世界坐标系下定义出观察坐标系，并推导世界坐标系到观察坐标系的变换矩阵。实现步骤：定义观察坐标系世界坐标系变换到观察坐标系,观察坐标系的定义,VUP：观察正向,观察坐标系是依赖于投影平面（照相机的底片）建立的。,观察坐标系的定义,坐标原点：用户指定的观察点作为观察坐标系原点，记为,Z坐标轴用户指定观察平面法向VPN作为Z轴正向，记为：,通常可令,观察坐标系的定义,观察坐标系的定义：选择向上观察向量VUP向上观察向量只需不与N方向平行即可，记为：V,令：,再令：,显然U同时垂直于N和V矢量。,则U、V、N两两垂直。,令：,定义Ouvn为观察坐标系（右手坐标系）。,u,右手观察坐标系,V,v,n,世界坐标系到观察坐标系,等价于建模变换过程引入观察坐标系记号：,变换矩阵：,
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