计算机图形学第5章习题

1、计算机图形学基础华东理工大学计算机系华东理工大学计算机系 谢晓玲谢晓玲习题习题5.2/P149o5.2 5.2 用用DDADDA算法、中点算法、中点BresenhamBresenham算法和改进算法和改进BresenhamBresenham算法扫描转换直线段算法扫描转换直线段P1P2P1P2，其中，其中P1P1为为(0,0)(0,0)、 P2P2为为(8,6)(8,6)。DDADDA算法：算法：已知已知P1(0,0)P1(0,0)、P2(8,6)P2(8,6)，则：则：dx=8, dy=6dx=8, dy=6dxdydxdy并且并且k1k0 D Di i0,D0,Di+1i+1=D=Di i+

2、2(dx-dy) (x+2(dx-dy) (xi i+1,y+1,yi i+1)+1) D Di i 0,D0,Di+1i+1=D=Di i-2dy (x-2dy (xi i+1,y+1,yi i) )2(0k1)2(0k1) D D0 0=-dx+2dy =-dx+2dy dx=-1,dy0 D Di i0,D0,Di+1i+1=D=Di i+2(dy-dx) (x+2(dy-dx) (xi i-1,y-1,yi i-1)-1) D Di i 0,D0,Di+1i+1=D=Di i+2dy (x+2dy (xi i-1,y-1,yi i) )3(-1k0)3(-1k0) D D0 0=-dx

3、-2dy=-dx-2dy dx=1,dy0 D Di i0,D0 D Di i0,D0,dy=1 D Di i0,D0,Di+1i+1=D=Di i+2(dx-dy) (x+2(dx-dy) (xi i+1,y+1,yi i+1)+1) D Di i 0,D0,Di+1i+1=D=Di i+2dx (x+2dx (xi i,y,yi i+1) )6(k6(k1) ) D D0 0=-2dx+2dy =-2dx+2dy dx0,dy=-1 D Di i0,D0,Di+1i+1=D=Di i-2dx (x-2dx (xi i,y,yi i-1)-1) D Di i 0,D0,Di+1i+1=D=D

4、i i+2(dy-dx) (x+2(dy-dx) (xi i-1,y-1,yi i-1) )7(k-1)7(k-1) D D0 0=2dx+dy=2dx+dy dx0,dy=1 D Di i0,D0,dy=-1 D Di i0,D1k1，则将，则将x,yx,y位置对调；位置对调；o如果如果 x0 x0，则，则dxdx取负数取负数o如果如果 y0y0，则，则dydy取负数取负数已知已知1(0k1)1(0k1)时的时的中点中点BresenhamBresenham算法函数：算法函数：void MidBresenhamLine(int x0,int y0,int x1,int y1,int color

5、);void MidBresenhamLine(int x0,int y0,int x1,int y1,int color);1(0k1) 1(0k1) (x0,y0),(x1,y1) MidBresenhamLine(x0,y0,x1,y1,15)MidBresenhamLine(x0,y0,x1,y1,15)2(0k1) 2(0k1) (x0,y0),(x1,y1) MidBresenhamLine(-x0,-y0,-x1,-y1,15)MidBresenhamLine(-x0,-y0,-x1,-y1,15)3(-1k0)3(-1k0) (x0,y0),(x1,y1) MidBresenh

6、amLine(x0,-y0,x1,-y1,15)MidBresenhamLine(x0,-y0,x1,-y1,15)4(-1k0) 4(-1k0) (x0,y0),(x1,y1) MidBresenhamLine(-x0,y0,-x1,y1,15)MidBresenhamLine(-x0,y0,-x1,y1,15)5(k1) 5(k1) (x0,y0),(x1,y1) MidBresenhamLine(y0,x0,y1,x1,15)MidBresenhamLine(y0,x0,y1,x1,15)6(k1) 6(k1) (x0,y0),(x1,y1) MidBresenhamLine(-y0,-

7、x0,-y1,-x1,15)MidBresenhamLine(-y0,-x0,-y1,-x1,15)7(k-1) 7(k-1) (x0,y0),(x1,y1) MidBresenhamLine(y0,-x0,y1,-x1,15)MidBresenhamLine(y0,-x0,y1,-x1,15)8(k-1) 8(k-1) (x0,y0),(x1,y1) MidBresenhamLine(-y0,x0,-y1,x1,15)MidBresenhamLine(-y0,x0,-y1,x1,15)习题习题5.6/P1495.6 5.6 试用中点试用中点BresenhamBresenham算法扫描转换圆心

8、在原点、算法扫描转换圆心在原点、半径为半径为8 8的园。的园。已知已知d d0 0=1-R=-7=1-R=-7i (xi yi) di 2x+3 2(x-y)+50 (0, 8) -7 3(1, 8) -4 5 (2, 8) 1 -7(3, 7) -6 9(4, 7) 3-1(5, 6) 2 3(6, 5) 5 7习题习题5.11/P1495.11 5.11 采用扫描转换算法对图所示多边形进行填充，采用扫描转换算法对图所示多边形进行填充，试写出试写出ETET表和当扫描线表和当扫描线y=4y=4时的有效边表时的有效边表AETAET表。表。设节点的数据结构：设节点的数据结构： 多边形多边形ETET

9、表表6543211, 3, 1/26,6,-11,1,7,5,03,3,-13,6,1/46,5,1xmin ymax 1/k nextAETAET表表按按p119p119的的规则规则1 ，得交点：，得交点：(1,1)(7,1)(1,1)(7,1)、(2,2)(3,2)(2,2)(3,2)、(3,2)(7,2)(3,2)(7,2)、(4,3)(7,3)(4,3)(7,3)、(4,4)(6,4)(4,4)(6,4)、(6,4)(7,4)(6,4)(7,4)、(4,5)(5,5)(4,5)(5,5)6543211, 3, 1/26,6,-11,1,7,5,03,3,-13,6,1/46,5,16543211, 3, 1/23.75,6,1/47,5,01.5,3,1/23,3,-16,6,-13,6,1/47,5,03.25,6,1/47,5,06,5, 17,5