正十二面体旋转——外法线消隐

////////////////////////// //程序名称：立方体三视图及正等轴测图及其旋转 //功 能：鼠标左键单击时绕Z轴逆时针旋转10°,右键双击后退出程序 #include <math.h> #include <graphics.h> #include <stdio.h> #include <conio.h> #include <iostream> using namespace std; #define N 20 // N个点*** #define PI 3.1415926535 /* int facet_table[6][5]={{0,1,3,2,0},{0,4,5,1,0},{4,6,7,5,4}, {2,3,7,6,2},{0,2,6,4,0},{1,5,7,3,1}}; // 面表--内嵌环表 double points[N][4]={{0,0,0,1},{0,0,50,1},{80,0,0,1},{80,0,50,1}, {0,40,0,1},{0,40,50,1},{80,40,0,1},{80,40,50,1}}; // 六面体初始顶点表(三角形) */ /* int facet_table[4][4]={{0,2,1,0},{0,1,3,0},{0,3,2,0},{1,2,3,1}}; // 面表--内嵌环表 double points[N][4]={{0,0,0,1},{50,0,0,1},{25,30,0,1},{25,15,40,1}}; // 四面体初始顶点表(三角形) */ /* int facet_table[8][4]={{0,1,4,0},{1,2,4,1},{4,2,3,4}, {0,4,3,0},{0,3,5,0},{1,0,5,1},{1,5,2,1},{2,5,3,2}}; // 面表--内嵌环表 double points[N][4]={{50,0,10,1},{0,50,10,1},{-50,0,-10,1},{0,-50,-10,1}, {-10,-10,50,1},{10,10,-50,1}}; // 八面体初始顶点表(三角形) */ double a=1.618; int T=30; int facet_table[12][6]={ {3,16,17,7,14,3},{3,11,10,0,16,3},{0,12,4,17,16,0},{4,8,9,7,17,4},{6,15,14,7,9,6},{2,11,3,14,15,2}, {1,19,18,5,13,1},{0,10,1,13,12,0},{2,19,1,10,11,2}, {2,15,6,18,19,2},{5,18,6,9,8,5},{4,12,13,5,8,4} }; // 面表--内嵌环表 double points[N][4]={ {-T,-T,T,1},{-T,T,T,1},{T,T,T,1},{T,-T,T,1}, {-T,-T,-T,1},{-T,T,-T,1},{T,T,-T,1},{T,-T,-T,1}, {-1.0/a*T,0,-a*T,1},{1.0/a*T,0,-a*T,1},{-1.0/a*T,0,a*T,1},{1.0/a*T,0,a*T,1}, {-a*T,-1.0/a*T,0,1},{-a*T,1.0/a*T,0,1},{a*T,-1.0/a*T,0,1},{a*T,1.0/a*T,0,1}, {0,-a*T,1.0/a*T,1},{0,-a*T,-1.0/a*T,1},{0,a*T,-1.0/a*T,1},{0,a*T,1.0/a*T,1} }; // 十二面体初始顶点表(五边形) int facet=12; // 几个面*** int ring_points=5; // 一个面上几个点*** int cishu=0; void Blank(double NOW[][4],double T_x,double T_y,double times); // 画消隐图 void Matrix_Multiplication(double t[][4]); // 矩阵相乘及画图 void Number(double* x,double* y); // 输出点的编号 void Dotted_line(int x0,int y0,int x1,int y1,int color,int wheel); // 画虚线 int Mouse_event(); // 鼠标事件 void muti_Matrix_by_PPT(double Trans_points[N][4],double another[4][4]); // 旋转矩阵乘法专用函数 void ThreeD_rotate(int degree_x,int degree_y,int degree_z); // 参数分别为绕x,y,z逆时针旋转的角度 void lsometric_translation(); // 画正等轴测投影图变换 void three_facet_view(); // 画三视图 void initializer(); // 界面初始化 int main(){ initializer(); ThreeD_rotate(35,10,0); three_facet_view(); lsometric_translation(); if(!Mouse_event()) return 0; //停住 getch(); closegraph(); return 0; } void initializer(){ initgraph(800, 640); setbkcolor(WHITE); setcolor(WHITE); fillrectangle(0,0,800,640); setcolor(BLACK); rectangle(0,0,799,639); setcolor(BLACK); line(0,80,800,80); RECT r1 = {0, 0, 800, 80}; drawtext(_T("\n单击左键一次绕Z轴旋转10°\n\n双击右键可退出程序"), &r1, DT_CENTER | DT_VCENTER ); RECT r2 = {0, 81, 70, 100}; drawtext(_T("正视图"), &r2, DT_CENTER | DT_VCENTER ); RECT r3 = {0, 620, 70, 640}; drawtext(_T("俯视图"), &r3, DT_CENTER | DT_VCENTER ); RECT r4 = {730, 81, 800, 100}; drawtext(_T("侧视图"), &r4, DT_CENTER | DT_VCENTER ); RECT r5 = {700, 620, 800, 640}; drawtext(_T("正等轴测图"), &r5, DT_CENTER | DT_VCENTER ); HRGN rgn = CreateRectRgn(71, 101, 699, 619); // 将该矩形区域设置为裁剪区 setcliprgn(rgn); setcolor(BLACK); rectangle(0,0,800,640); setcolor(RED); } void muti_Matrix_by_PPT(double Trans_points[N][4],double another[4][4]){ int i,j,k; double New[N][4]={0}; for(i=0 ; i<N ; i++){ for(j=0 ; j<4 ; j++){ for(k=0 ; k<4 ; k++){ New[i][j]+=Trans_points[i][k]*another[k][j]; } } } for(i=0 ; i<N ; i++){ for(j=0 ; j<4 ; j++){ Trans_points[i][j]=New[i][j]; } } } void ThreeD_rotate(int degree_x,int degree_y,int degree_z){ double cita_x=degree_x*PI/180; double cita_y=degree_y*PI/180; double cita_z=degree_z*PI/180; double X_rotate[4][4]={{1,0,0,0},{0,cos(cita_x),sin(cita_x),0},{0,-sin(cita_x),cos(cita_x),0},{0,0,0,1}}; double Y_rotate[4][4]={{cos(cita_y),0,-sin(cita_y),0},{0,1,0,0},{sin(cita_y),0,cos(cita_y),0},{0,0,0,1}}; double Z_rotate[4][4]={{cos(cita_z),sin(cita_z),0,0},{-sin(cita_z),cos(cita_z),0,0},{0,0,1,0},{0,0,0,1}}; muti_Matrix_by_PPT(points,X_rotate); muti_Matrix_by_PPT(points,Y_rotate); muti_Matrix_by_PPT(points,Z_rotate); } void lsometric_translation(){ static double ex[4][4]; double beta=45,cita=180*atan(1.0/sqrt(2))/PI; //cita下,beta右 beta=beta*PI/180.0; cita=cita*PI/180.0; ex[0][0]=cos(beta); ex[0][2]=-sin(beta)*sin(cita); ex[1][0]=-sin(beta); ex[1][2]=-cos(beta)*sin(cita); ex[2][2]=cos(cita); ex[3][3]=1; Matrix_Multiplication(ex); } void three_facet_view(){ double one[4][4]={0},two[4][4]={0},thr[4][4]={0}; one[0][0]=1;one[2][2]=1;one[3][3]=1; two[0][0]=1;two[1][2]=-1;two[3][2]=-160;two[3][3]=1; thr[1][0]=-1;thr[2][2]=1;thr[3][0]=-160;thr[3][3]=1; Matrix_Multiplication(one); Matrix_Multiplication(two); Matrix_Multiplication(thr); } void Matrix_Multiplication(double ex[][4]){ double NOW[N][4]; int i,j,k; for(i=0 ; i<N ; i++){ for(j=0 ; j<4 ; j++){ NOW[i][j]=0; for(k=0 ; k<4 ; k++){ NOW[i][j]+=points[i][k]*ex[k][j]; } } } Blank(NOW,400,350,2); } void Blank(double NOW[][4],double T_x,double T_y,double times){ double x[N],y[N]; int i,j; cishu++; cishu=cishu%5; if(!cishu) cishu++; for(i=0 ; i<N ; i++){ if(cishu==4){ x[i]=NOW[i][0]*times+550; y[i]=NOW[i][2]*times+430; }else{ x[i]=-NOW[i][0]*times+225; y[i]=-NOW[i][2]*times+210; if(cishu==2) y[i]-=100; } } Number(x,y); double D,E,F,N_fa; int Xs,Ys,Zs,Xa,Ya,Za,Xb,Yb,Zb; int x1,y1,x2,y2; for(i=0 ; i<facet ; i++){ //facet个面 Xs=points[facet_table[i][0]][0];Ys=points[facet_table[i][0]][1];Zs=points[facet_table[i][0]][2]; Xa=points[facet_table[i][1]][0];Ya=points[facet_table[i][1]][1];Za=points[facet_table[i][1]][2]; Xb=points[facet_table[i][2]][0];Yb=points[facet_table[i][2]][1];Zb=points[facet_table[i][2]][2]; D=1.0*(Ya-Ys)*(Zb-Za)-(Za-Zs)*(Yb-Ya); E=1.0*(Za-Zs)*(Xb-Xa)-(Xa-Xs)*(Zb-Za); F=1.0*(Xa-Xs)*(Yb-Ya)-(Ya-Ys)*(Xb-Xa); if(-E==0) E=0; if(-D==0) D=0; if(-F==0) F=0; N_fa=sqrt(D*D+E*E+F*F); double COS; if(cishu==1){ COS=E*1.0/N_fa; }else if(cishu==3){ COS=D*1.0/N_fa; }else if(cishu==2){ COS=F*1.0/N_fa; }else if(cishu==4){ Xs=NOW[facet_table[i][0]][0];Ys=NOW[facet_table[i][0]][1];Zs=NOW[facet_table[i][0]][2]; Xa=NOW[facet_table[i][1]][0];Ya=NOW[facet_table[i][1]][1];Za=NOW[facet_table[i][1]][2]; Xb=NOW[facet_table[i][2]][0];Yb=NOW[facet_table[i][2]][1];Zb=NOW[facet_table[i][2]][2]; E=1.0*(Za-Zs)*(Xb-Xa)-(Xa-Xs)*(Zb-Za); COS=E*1.0/N_fa; } if(COS>0){ for(j=0 ; j<ring_points ; j++){ //ring_points个点 x1=x[facet_table[i][j]]; y1=y[facet_table[i][j]]; x2=x[facet_table[i][j+1]]; y2=y[facet_table[i][j+1]]; line(x1,y1,x2,y2); } }else{ for(j=0 ; j<ring_points ; j++){ //ring_points个点 x1=x[facet_table[i][j]]; y1=y[facet_table[i][j]]; x2=x[facet_table[i][j+1]]; y2=y[facet_table[i][j+1]]; Dotted_line(x1,y1,x2,y2,RED,0); } } } } void Number(double* x,double* y){ for(int i=0 ; i<N; i++){ circle(int(x[i]),int(y[i]),3); char str[10]; int a=i+1; sprintf(str,"%d",a); outtextxy(int(x[i]), int(y[i]),str); } } int z=0; void Putpixel(int x,int y,int color,int wheel){ z++; if(wheel==0 && z%4==0){ putpixel(x,y,color); } int i,j; for(i=0 ; i<2*wheel+1 ; i++){ for(j=int(wheel/2) ; j<2*wh