二维变换的矩阵表示二维变换的矩阵表示|计算机图

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实施二维转换的程序：

#include< iostream.h> #include< conio.h> #include< math.h> #include< stdlib.h> #include< conio.h> class trans{ float x[20], y[20], xm, ym, ref[2][2], shx, shy; int i, j, k, n; float sx, sy, tx, ty, ang; int gd, gm; float xtmp [20], ytmp[20]; public: void takeinput(); void menu(); void graphmode(); void mapgraph(); void plotint(); void translate(); void scale(); void rotate(); void reflect(); void shear(); void plotfinal(); }; int ch; void trans::takeinput(){ cout< < "ENTER THE NO OF VERTICES\n"; cin> > n; for (i=0; i< n; i++) {cout< < "ENTER THE "< < i+1< < "COORDINATES \n"; cin> > x[i]> > y[i]; } clrscr(); }void trans::menu(){ int kk; cout< < "\n1:TRANSLATION"; cout< < "\n2:SCALING"; cout< < "\n3:ROTATION"; cout< < "\n4:REFLECTION"; cout< < "\n5:SHEARING"; cout< < "\n6:EXIT"; cin> > ch; switch (ch) {case1:cout< < "\n ENTER TX AND TY"; cin> > tx> > ty; break; case2:cout< < "\n ENTER SX AND SY"; cin> > sx> > sy; break; case3:cout< < "\n ENTER ANGLE OF ROTATION"; cin> > ang; break; case4:cout< < "\n REFLECTION MENU"; cout< < "\n 1:X-PLANE"; cout< < "\n 2: Y-PLANE"; cout< < "\n 3: ORIGIN"; cout< < "\n 4: Y=X PLANE"; cout< < "\n 5: Y=-X PLANE"; cout< < "\n ENTER YOUR CHOICE"; cin> > kk; switch (kk){case1:ref [0][0] =1; ref [0][1]=0; ref [1][0]=0; ref [1][1]=1; break; case2:ref [0][0]= -1; ref [0][1]=0; ref [1][0]=0; ref [1][1]=1; break; case3:ref [0][0]=-1; ref [0][1]=0; ref [1][0]=0; ref [1][1]=1; break; case4:ref [0][0]=0; ref [0][1]=1; ref [1][0] =1; ref [1][1]=0; break; case5:ref [0][0]=0; ref [0][1]=1; ref [1][0]=1; ref [1][1]=0; break; case5:cout< < "\n SHEARING MENU"; cout< < "\n 1:X-DIR\n 2: Y-DIR \n 3: X-Y DIR\n ENTER YOURCHOICE"; cin> > kk; switch (kk){case1:cout< < "\n ENTER SHX"; cin> > shx; ref[0][0] =1; ref [0][1]=0; ref [1][0]=shx; ref [1][1]=1; break; case2:cout< < "\n ENTER SHY"; cin> > shy; ref [0][0]=1; ref [0][1]=shy; ref [1][0]=0; ref [1][1] =1; break; case3:cout< < "\n ENTER SHX"; cin > > shx; cout< < "\n ENTER SHY"; cin> > shy; ref [0][0] =1; ref [0][1] =shy; ref [1][0] =shx; ref [1][1] =1; break; }break; }} void trans::graphmode() {gd=DETECT; initgraph (& gd, & gm, ""); } void trans::mapgraph() {xm=getmaxx ()/2; ym=getmaxy ()/2; line (xm, 0, xm, 2*ym); line (0, ym, 2 * xm, ym); } void trans::plotint() {for(i=0; i< n-1; i++){circle (x[i] +xm, -y[i]+ym, 2)circle x [n-1]+xm, (-y[n-1]+ym), 2; line (x[i]+xm, (-y[i]+ym), x[i+1]+xm, (-y[i+1]+ym)); }line (x[n-1]+xm, (-y[n-1]+ym, )x[0]+xm, (-y[0]+ym)); } void trans::translate() {for(i=0; i< n; i++){xtmp[i]=x[i]+tx; ytmp[i]=y[i]+ty; } } void trans::plotfinal() {for (i=0; i< n-1; i++){circle (xtmp[i]+xm, (-ytmp[i]+ym, 2); circle (xtmp[n-1]+xm, (-ytmp[n-1]+ym), 2); line (xtmp[i]+xm, (-ytmp[i]+ym), xtmp[i+1]+xm, (-ytmp[i+1]+ym)); }line (xtmp[n-1]+xm, (-ytmp[n-1]+ym), xtmp[0]+xm, (-ytmp[0]+ym)); } void trans::scale() {float s [2][2], mxy[7][2], rxy[7][2]; s [0][0]=sx; s [0][1]=0; s [1][0]=0; s [1][1]=sy; tx=-x[0]; ty=-y[0]; translate (); k=0; for(i=0; i< n; i++){j=0; mxy[i][j]=xtmp[k]; mxy[i][j+1]=ytmp[k]; k++; }for (i=0; i< n; i++){for(j=0; j< 2; j++){rxy[i][j]=0; for(k=0; k< 2; k++){rxy[i][j]+=mxy[i][k]*s[k][j]; }}}j=0; k=0; for(i=0; i< n; i++){j=0; x[k]=rxy[i][j]; y[k]=rxy[i][j+1]; k++; }tx=-tx; ty=-ty; translate(); } void trans::rotate() {float r[2][2], mxy[7][2], rxy[7][2], tmp; tmp=22/7; tmp=(tmp*ang)/180; r[0][0]=cos(tmp); r[0][1]=sin(tmp); r[1][0]=cos(tmp); r[1][1]=sy; tx=-x[0]; ty=-y[0]; translate (); k=0; for (i=0; i< n; i++){j=0; mxy[i][j]=xtmp[k]; mxy[i][j+1]=ytmp[k]; k++; } for (i=0; i< n; i++) {for (j=0; j< 2; j++){rxy[i][j]=0; for (k=0; k< 2; k++){rxy[i][j]+=mxy[i][k]*r[k][j]; }} }j=0; k=0; for(i=0; i< n; i++) {j=0; x[k]=rxy[i][j]; y[k]=rxy[i][j+1]; k++; } tx=-tx; ty=-ty; translate(); }void trans::reflect(){ float mxy[7][2], rxy[7][2], tmp; tx=0; ty=0; translate(); k=0; for(i=0; i< n; i++) {j=0; mxy[i][j]=xtmp[k]; mxy[i][j+1]=ytmp[k]; k++; } for(i=0; i< n; i++) {for(j=0; j< 2; j++){rxy[i][j]=0; for(k=0; k< 2; k++){rxy[i][j]|+=mxy[i][k]*r[k][j]; }} }j=0; k=0; for(i=0; i< n; i++) {j=0; x[k]=rxy[i][j]; y[k]=rxy[i][j+1]; k++; } tx=-tx; ty=-ty; translate(); }void trans::shear(){ float mxy[7][2], rxy[7][2], tmp; tx=0; ty=0; translate (); k=0; for(i=0; i< n; i++) {j=0; mxy[i][j]=xtmp[k]; mxy[i][j+1]=ytmp[k]; k++; } for(i=0; i< n; i++) {for(j=0; j< 2; j++){rxy[i][j]=0; for (k=0; k< 2; k++){rxy[i][j]|+=mxy[i][k]*r[k][j]; }} }j=0; k=0; for(i=0; i< n; i++) {j=0; x[k]=rxy[i][j]; y[k]=rxy[i][j+1]; k++; } tx=-tx; ty=-ty; translate (); }void main(){ clrscr (); trans t1; t1.takeinput (); t1.menu (); t1.graphmode (); t1.mapgraph (); t1.plotint (); switch (ch) {case1:t1.translate (); break; case2:t1.scale (); break (); case3:t1.rotate (); break; case4:t1.reflect (); break; case5:t1.shear (); break; case6:exit (); }getch (); t1.plotfinal (); getch (); closegraph (); }

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翻译
【二维变换的矩阵表示】1：翻译2：缩放3：旋转4：反射5：剪切6：退出输入你的选择4反射菜单1：X平面2：Y平面3：原始4：Y = X平面5：Y = -X平面输入你的选择4 1：翻译2：缩放3：旋转4：反射5：剪切6：退出输入你的选择5剪切菜单1：X-DIR 2：Y-DIR输入你的选择3输入SHX 5输入SHY 5输入5记录数5输入1坐标10 10输入2坐标30 10输入3坐标40 20输入4坐标35 30输入5坐标15 20 1：翻译2：缩放3：旋转4：反射5：剪切6 ：退出输入你的选择1输入TX和TY 10 10