图形学第7章习题ppt课件

计算机图形学基础,华东理工大学计算机系谢晓玲,习题7.4/P227,7.4将图7-40中物体ABCDEFGH进行如下变换的变换矩阵，写出复合变换后图形各顶点的规范化齐次坐标，并画出复合变换后的图形。平移，使点C与点p(1,-1,0)重合。绕z轴旋转60。解：T1=T(0,-2,0)=1000010000100-201,T2=Rz(60)=1/23/200-3/21/20000100001T=T1T2=T(0,-2,0)Rz(60)=1/23/200-3/21/20000103-101,A00013-101B10011/2+33/2-101C11011/2+3/23/2-1/201D0101T=3/2-1/201E00213-121F10211/2+33/2-121G11211/2+3/23/2-1/221H01213/2-1/221,D,C,四舍五入得：A2-101B2001C1001D1-101E2-121F2021G1021H1-121,A,G,1,1,2,-1,x,y,z,-2,2,B,E,F,G,H,习题7.4/P227,7.4将图7-40中物体ABCDEFGH进行如下变换的变换矩阵，写出复合变换后图形各顶点的规范化齐次坐标，并画出复合变换后的图形。平移，使点C与点p(1,-1,0)重合。相对于点p(1,-1,0)绕z轴旋转60。解：T1=T(0,-2,0)T2=T(-1,1,0)Rz(60)T(1,-1,0)T=T1T2=T(0,-2,0)T(-1,1,0)Rz(60)T(1,-1,0),T=T(0,-2,0)T(-1,1,0)Rz(60)T(1,-1,0)=100010001/23/200100001000100-3/21/200010000100010001000100-201-110100011-101=1/23/200-3/21/2000010(1+3)/2-(3+3)/201,T=T(0,-2,0)T(-1,1,0)Rz(60)T(1,-1,0)=1/23/200-3/21/2000010(1+3)/2-(3+3)/201A0001(1+3)/2-(3+3)/201B10011+3/2-3/201C11011-101D0101T=1/2-1-3/201E0021(1+3)/2-(3+3)/221F10211+3/2-3/221G11211-121H01211/2-1-3/221,四舍五入得：A1-201B2-101C1-101D0-201E1-221F2-121G1-121H1-221,习题7.5/P228,7.5将图7-41中四面体ABCD进行如下变换的变换矩阵，写出复合变换后图形各顶点的规范化齐次坐标，并画出复合变换后的图形。关于P点整体放大2倍。关于y轴进行对称变换。解：T1=T(-2,2,-2)S(2)T(2,-2,2)T2=TFy()T=T(-2,2,-2)S(2)T(2,-2,2)TFy(),100020001000-1000T=010002000100010000100020001000-10-22-2100012-2210001-2000=020000-202221A2001-2221B2101T=-2421C01012421D11110401得A(-2,2,2)、B(-2,4,2)、C(2,4,2)、D(0,4,0),7.6假定直线AB的两个端点为A(0,0,0)和B(2,2,2)，试写出绕AB旋转30的三维复合变换矩阵。第一步，使得AB与z轴重合TRx：绕x轴旋转(45)TRx(45)=100001/21/200-1/21/200001B2221TRx(45)=20221B,习题7.6/P228,TRy：绕y轴旋转-AB=23sin(-)=-sin=-1/3cos(-)=cos=2/3TRy(-)=2/301/300100-1/302/300001第二步，绕z轴（AB”）旋转30TRz(30)=3/21/200-1/23/20000100001,第三步，绕y轴逆旋转-，绕x轴逆旋转Try-1(-)=Try()=2/30-1/3001001/302/300001TRx-1(45)=TRx(-45)=100001/2-1/2001/21/200001第四步，T=TRx(45)TRy(-)TRz(30)Try-1(-)TRx-1(45),7.7试作出图7-41中四面体的三视图，平移矢量均为1，要求写出变换矩阵。V主视图（xoz）Tv=Txoz=1000000000100001A20012001AB2101TXOZ=2001BC01010001CD11111011D,习题7.7/P228,H俯视图（xoy）Tv=TxoyTRx(-90)T(0,0,-1)=100010001000=1000010000-10010000-1000000100000100000001000100-1100-11A200120-11AB2101Tv=20-21BC010100-21CD111110-21D,W侧视图（yoz）Tv=TyozTRz(90)T(-1,0,0)=000001001000=00000100-10000100-1000001000100001001000010001-1001-1001A2001-1001AB2101Tv=-2001BC0101-2001CD1111-2011D,7.8试推导正轴测图的投影矩阵，并写出图7-41四面体经过正等测变换或二测变换（=30）后各顶点的齐次坐标。正轴测图的投影矩阵T=TRy(-)TRx()Txoy=cos-0-sin-01000100001000cossin00100sin-0cos-00sincos00000000100010001,习题7.8/P228,正轴测图的投影矩阵正等测的投影矩阵sin=cos=1/2;sin=1/3,cos=2/3T=1/2-1/60002/300-1/2-1/6000001,正等测的投影矩阵A20011/2-1/600B210102/300C0101-1/2-1/600D11110001=2-2/301200102/3010001四舍五入得：A(1,-1,0)、B(1,0,0)、C(0,1,0)、D(0,0,0),二测变换（=30）的投影矩阵sin=cos=1/2;sin=1/2,cos=3/2T=1/2-1/220003/200-1/2-1/22000001A20012-1/201AB2101T=2-1/2+3/201BC010103/201CD11110-1/201D四舍五入得：A(1,-1,0),B(1,0,0),C(0,1,0)，D(0,-1,0),7.9求图7-41四面体经过斜等测变换或斜二测变换（=30）后各顶点的齐次坐标。T=10000100cotcoscotsin000001斜等测（cot=1、=30）的投影矩阵T=100001003/21/2000001,习题7.9/P228,斜等测（cot=1、=30）的投影矩阵A200110002001AB21010100=2101BC01013/21/2000101CD111100011+3/23/201D四舍五入得：A(2,0,0),B(2,1,0),C(0,1,0)，D(2,1,0),斜二测（cot=1/2、=30）的投影矩阵A200110002001AB21010100=2101BC01013/41/4000101CD111100011+3/45/401D四舍五入得：A(2,0,0),B(2,1,0),C(0,1,0)，D(1,1,0),7.10求图7-40中平面多面体经过二点透视变换后各顶点的齐次坐标。给定p=-1，q=1，r=-1，=30，l=n=1，m=-1。二点透视将顶点（0,0,0）平移（l,m,n)绕y轴旋转角度（90）二点透视变换向xoy平面(z=0)进行正投影变换,习题7.10/P228,1000cos0sin0100p1000T=01000100010001000000-sin0cos0001r0000lmn1000100011000cos00pcos-rsin=0100000psin+rcoslcos+nsinm0p(lcos+nsin)+r(ncos-lsin)+1=3/200(1-3)/201001/200-(1+3)/2(3+1)/2-101-3,T=3/200(1-3)/201001/200-(1+3)/2(3+1)/2-101-300011.366-10-0.73210012.232-10-1.09811012.23200-1.0980101T=1.36600-0.73200212.366-10-3.46410213.232-10-3.83011213.23200-3.83001212.36600-3.464,四舍五入得：-2101-2101-2001=-2001-1001-1001-1001-1001,得规范化坐标：A-1.8661.36601B-2.030.9101C-2.03001D-1.866001E-0.680.28801F-0.840.2601G-0.84001H-0.68001,7.10求图7-40中平面多面体经过一点透视或二点透视变换后各顶点的齐次坐标。给定l=m=1，n=-1，d=-3，=30。一点透视(l=m=1，n=-1，d=-3)T=1000=1000010001000001/d000-1/3lm01+n/d1104/300011104/33/43/4011