計(jì)算機(jī)圖形學(xué)第5章習(xí)題教學(xué)文案

計(jì)算機(jī)圖形學(xué)第5章習(xí)題i(xiyi)di(xi+1,yi+1)di+2(dx-dy)

di-2dy0(0,0)-4(1,1)-4+4=0(1,1)0(2,1) 0-12=-12(2,1)-12(3,2) -12+4=-8(3,2)-8(4,3)-8+4=-4(4,3)-4(5,4)-4+4=0(5,4)0(6,4) 0-12=-12(6,4)-12(7,5)-12+4=-8(7,5)-8(8,6)習(xí)題5.2/P149②中點(diǎn)Bresenham算法：dx=8,dy=6,2(dx-dy)=4,-2dy=-12,d0=dx-2dy=-4習(xí)題5.2/P149③改進(jìn)Bresenham算法：dx=8,dy=6,2dx=16,2dy=12,e0=-dx=-8i(xiyi)eiei+2dy(xi+1,yi+1)ei-2dx0(0,0)-8-8+12=4(1,1)4-16=-12(1,1)-12-12+12=0(2,1)(2,1)00+12=12(3,2)12-16=-4(3,2)-4-4+12=8(4,3)8-16=-8(4,3)-8-8+12=4(5,4)4-16=-12(5,4)-12-12+12=0(6,4)(6,4)00+12=12(7,5)12-16=-4(7,5)-4-4+12=8(8,6)5.3試用中點(diǎn)Bresenham算法畫(huà)直線段的原理，推導(dǎo)斜率在[-1,0]之間的直線段繪制過(guò)程。∵k[-1,0]，即|k|1∴取|dx|=1①取dx=1,dy=-k設(shè)di=F(xi+1,yi-0.5)=yi-0.5-k(xi+1)-b當(dāng)di0,下一點(diǎn)(xi+1,yi)di+1=F(xi+2,yi-0.5)=di-k當(dāng)di0,下一點(diǎn)(xi+1,yi-1)di+1=F(xi+2,yi-1.5)=di-1-kd0=F(x0+1,y0-0.5)=-(k+0.5)令Di=2dxdi,得D0=-(dx+2dy),D與d同號(hào)當(dāng)Di0,下一點(diǎn)(xi,yi-1),Di+1=Di-2dy當(dāng)Di0,下一點(diǎn)(xi+1,yi-1),Di+1=Di-2(dx+dy)習(xí)題5.3/P149yi-1yixi+1xi第四象限yi-2xi+2②取dx=-1,dy=k設(shè)di=F(xi-1,yi+0.5)=yi+0.5-k(xi-1)-b當(dāng)di0,下一點(diǎn)(xi-1,yi)di+1=F(xi-2,yi+0.5)=di+k當(dāng)di0,下一點(diǎn)(xi-1,yi+1)di+1=F(xi-2,yi+1.5)=di+1+kd0=F(x0-1,y0+0.5)=0.5+k令Di=2dxdi,得D0=dx+2dy,D與d異號(hào)當(dāng)Di0,下一點(diǎn)(xi-1,yi),Di+1=Di+2dy當(dāng)Di0,下一點(diǎn)(xi-1,yi+1),Di+1=Di+2(dx+dy)習(xí)題5.3/P149yi+1yixi-1xi第二象限yi+2xi-2|k|≤1習(xí)題5.4/P149

5.4將中點(diǎn)Bresenham算法畫(huà)直線段，推廣到任意斜率的直線段。13421(0≤k≤1)D0=dx-2dydx=1,dy>0

Di<0,Di+1=Di+2(dx-dy)(xi+1,yi+1) Di0,Di+1=Di-2dy(xi+1,yi)2(0≤k≤1)D0=-dx+2dy

dx=-1,dy<0

Di<0,Di+1=Di+2(dy-dx)(xi-1,yi-1) Di0,Di+1=Di+2dy(xi-1,yi)3(-1≤k≤0)D0=-dx-2dydx=1,dy<0

Di<0,Di+1=Di-2dy(xi+1,yi) Di0,Di+1=Di-2(dx+dy)(xi+1,yi-1)4(-1≤k≤0)D0=dx+2dydx=-1,dy>0

Di<0,Di+1=Di+2dy(xi-1,yi) Di0,Di+1=Di+2(dx+dy)(xi-1,yi+1)習(xí)題5.4/P14958765(k≥1)D0=2dx-dydx>0,dy=1

Di<0,Di+1=Di+2(dx-dy)(xi+1,yi+1) Di0,Di+1=Di+2dx(xi,yi+1)6(k≥1)D0=-2dx+2dy

dx<0,dy=-1

Di<0,Di+1=Di-2dx(xi,yi-1) Di0,Di+1=Di+2(dy-dx)(xi-1,yi-1)7(k≤-1)D0=2dx+dydx<0,dy=1

Di<0,Di+1=Di+2(dx+dy)(xi-1,yi+1) Di0,Di+1=Di+2dx(xi,yi+1)8(k≤-1)D0=-2dx-dydx>0,dy=-1

Di<0,Di+1=Di-2(dx+dy)(xi,yi-1) Di0,Di+1=Di-2dx(xi+1,yi-1)|k|≥1習(xí)題5.4/P149推而廣之：如果k>1，則將x,y位置對(duì)調(diào)；如果x<0，則dx取負(fù)數(shù)如果y<0，則dy取負(fù)數(shù)已知1(0≤k≤1)時(shí)的中點(diǎn)Bresenham算法函數(shù)：voidMidBresenhamLine(intx0,inty0,intx1,inty1,intcolor);1(0≤k≤1)(x0,y0),(x1,y1)MidBresenhamLine(x0,y0,x1,y1,15)2(0≤k≤1)(x0,y0),(x1,y1)MidBresenhamLine(-x0,-y0,-x1,-y1,15)3(-1≤k≤0)(x0,y0),(x1,y1)MidBresenhamLine(x0,-y0,x1,-y1,15)4(-1≤k≤0)(x0,y0),(x1,y1)MidBresenhamLine(-x0,y0,-x1,y1,15)5(k≥1)(x0,y0),(x1,y1)MidBresenhamLine(y0,x0,y1,x1,15)6(k≥1)(x0,y0),(x1,y1)MidBresenhamLine(-y0,-x0,-y1,-x1,15)7(k≤-1)(x0,y0),(x1,y1)MidBresenhamLine(y0,-x0,y1,-x1,15)8(k≤-1)(x0,y0),(x1,y1)MidBresenhamLine(-y0,x0,-y1,x1,15)習(xí)題5.6/P1495.6試用中點(diǎn)Bresenham算法掃描轉(zhuǎn)換圓心在原點(diǎn)、半徑為8的園。已知d0=1-R=-7i(xiyi)di2x+3

2(x-y)+50(0,8)-73(1,8)-45 (2,8)1 -7(3,7)-69(4,7)3 -1(5,6)2 3(6,5)5 7習(xí)題5.11/P1495.11采用掃描轉(zhuǎn)換算法對(duì)圖所示多邊形進(jìn)行填充，試寫(xiě)出ET表和當(dāng)掃描線y=4時(shí)的有效邊表AET表。設(shè)節(jié)點(diǎn)的數(shù)據(jù)結(jié)構(gòu)：

多邊形 ET表6543211,3,1/26,6,-11,1,∞7,5,03,3,-13,6,1/46,5,1xminymax1/knextAET表∴按p119的規(guī)則1，得交點(diǎn)：(1,1)(7,1)、(2,2)(3,2)、(3,2)(7,2)、(4,3)(7,3)、(4,4)(6,4)、(6,4)(7,4)、(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