计算机图形学3D图形表示方式.ppt

Viewing In 3D,Chapter 5,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,The basic questions of 3D graphics,3D viewing process,Conception,Projections transform points in a coordinate system of dimension n into points in a coordinate system of dimension less than n.,Projection,Definition: The projection of a 3D object is defined by straight projection rays (called projectors) emanating from a center of projection, passing through each point of the object, and intersecting a projection plane to form the projection.,Projections,Projections Parameter : projection center projection plane,The class of projections,Perspective Projection The distance between the center of projection and the projection plane is finite. Parallel Projection The distance between the center of projection and the projection plane is infinite.,The class of projections,The subclasses of Planar Geometric Projections.,Three Orthographic Projections,Three Orthographic Projections(三视图）,正平行投影（三视图）,Front Elevation,Top Elevation,Side Elevation,Perspective Projection,Vanishing Point. The perspective projections of any set of parallel lines that are not parallel to the projection plane converge to a vanishing point. Axis Vanishing Point If the set of lines is parallel to one of the principal axes, the vanishing point is called an axis vanishing point.,The style of Perspective Projection,Perspective projections are categorized by their number of principal vanishing points and therefore by the number of axes the projection plane cuts,One-point perspective projection Projection-plane cuts only one of three axes. Two-point perspective projection Projection-plane cuts only two of three axes at the same time. Three-point perspective projection Projection-plane cuts all of three axes at the same time.,The style of Perspective Projection,One-point perspective projection,Two-point and Three-point Perspective Projection,The mathematics of simple Perspective Projection,Parameter Equation of Line PcP:,The intersection of the line PPc with the projection plane at z=0 is in the XOY plane,One-point perspective projection,Under the viewing-reference coordinate of uvn, Suppose :projection plane n=0,projection reference point (0,0,d),point p(up,vp,np) of three dim space,its projection point Q,Line Parameter Eq:,Transformation of One-point perspective projection,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