【计算机图形学】图形变换（平移变换、比例变换、旋转变换、对称变换、错切变换、复合变换）

一 实验目的

1. 编写图形各种变换的算法

二 实验内容

1：自行设计基本图案，完成1-5种简单变换

实验结果如下图所示：
图形初始化：

 

第一次点击左键，实现平移变换：

 

 

 
第二次点击左键，实现比例变换（同时伴有平移变换）：

 

 
第三次点击左键，实现对称变换（以平行y轴方向的直线为对称轴）：

 

 
第四次点击左键，实现对称变换（以平行x轴方向的直线为对称轴）：

 

第五次点击左键，实现错切变换（沿x轴方向关于y错切）：

 

第六次点击左键，实现错切变换（沿y轴方向关于x错切）：

 

 

2：在实验题3-1的基础上实现多步复合变换，设计动画效果

代码来源：https://blog.csdn.net/weixin_42815846/article/details/113099023

实验结果如下图所示：
初始化界面：

 按任意键后出现动画效果：

 

 

三 程序说明

最终的实验代码如下表所示：

1题

// // 程序名称：实验3-1 // 功    能：实现预设图像的平移变换、比例变换等变换 // 编译环境：VS2019，EasyX_20220116 // 最后修改：2022-4-5 #include #include #include #include using namespace std; #define pi 3.1415926535 int main() {     POINT t1[] = { {200,200} , {200,20} , {220,80} };     POINT t2[] = { {200,200} , {200,20} , {180,80} };     int len = 3;     float Tx = 50, Ty = 50;//平移     float Sx = 0.5, Sy = 0.5;//比例     float angle = 45 * pi / 180;//旋转，没做出来QwQ     float C = 0.5, B = -0.5;//错切     //initialize graph     initgraph(640, 480);     //勾画初始图案     setfillcolor(RED);     fillpolygon(t1, 3);     polygon(t2, 3);     //record the times of changing     int times = 0;     ExMessage m;     //全是单步变换。     while (1) {          m = getmessage(EX_MOUSE | EX_KEY);          float cur1x[3], cur1y[3], cur2x[3], cur2y[3];          //平移          if (m.message == WM_LBUTTONDOWN && times == 0) {              for (int i = 0; i < len; i++) {                   t1[i].x += Tx;                   t1[i].y += Ty;                   t2[i].x += Tx;                   t2[i].y += Ty;              }              setfillcolor(RED);              fillpolygon(t1, 3);              polygon(t2, 3);              times++;          }          //比例          else if (m.message == WM_LBUTTONDOWN && times == 1) {              for (int i = 0; i < len; i++) {                   t1[i].x += 50;                   t2[i].x += 50;              }              //以一顶点为缩放点              for (int i = 1; i < len; i++) {                   t1[i].x = Sx * (t1[i].x - t1[0].x) + t1[0].x;                   t2[i].x = Sx * (t2[i].x - t2[0].x) + t2[0].x;                   t1[i].y = Sy * (t1[i].y - t1[0].y) + t1[0].y;                   t2[i].y = Sy * (t2[i].y - t2[0].y) + t2[0].y;              }              setfillcolor(RED);              fillpolygon(t1, 3);              polygon(t2, 3);              times++;          }          //对称 about x axis          else if (m.message == WM_LBUTTONDOWN && times == 2) {              float mid = t1[0].y;              for (int i = 0; i < len; i++) {                   t1[i].y = 2 * mid - t1[i].y;                   t2[i].y = 2 * mid - t2[i].y;              }              setfillcolor(RED);              fillpolygon(t1, 3);              polygon(t2, 3);              times++;          }          //对称 about y axis          else if (m.message == WM_LBUTTONDOWN && times == 3) {              float midx = t1[2].x;              for (int i = 0; i < len; i++) {                   t1[i].x = 2 * midx - t1[i].x;                   t2[i].x = 2 * midx - t2[i].x;                   //float cur1x[3], cur1y[3], cur2x[3], cur2y[3];                   cur1x[i] = t1[i].x;                   cur1y[i] = t1[i].y;                   cur2x[i] = t2[i].x;                   cur2y[i] = t2[i].y;              }              setfillcolor(RED);              fillpolygon(t1, 3);              polygon(t2, 3);              times++;          }          //错切 沿x轴方向关于y错切（x = x + cy）          else if (m.message == WM_LBUTTONDOWN && times == 4) {              for (int i = 0; i < len; i++) {                   t1[i].x += C * t1[i].y;                   t2[i].x += C * t2[i].y;              }              setfillcolor(RED);              fillpolygon(t1, 3);              polygon(t2, 3);              times++;          }          //错切 沿y轴方向关于x错切（y = y + bx）          else if (m.message == WM_LBUTTONDOWN && times == 5) {              for (int i = 0; i < len; i++) {                   /*                   //float cur1x[3], cur1y[3], cur2x[3], cur2y[3];                   cur1x[i] = t1[i].x;                   cur1y[i] = t1[i].y;                   cur2x[i] = t2[i].x;                   cur2y[i] = t2[i].y;                   */                   //t1[i].y += B * t1[i].x;                   //t2[i].y += B * t2[i].x;                   t1[i].y = cur1y[i] + B * cur1x[i];                   t1[i].x = cur1x[i];                   t2[i].y = cur2y[i] + B * cur2x[i];                   t2[i].x = cur2x[i];              }              setfillcolor(RED);              fillpolygon(t1, 3);              polygon(t2, 3);              times++;          }     }     _getch();     closegraph();     return 0; }

2题

// // 程序名称：实验3-2 // 功    能：实现预设图像的复合变换 // 编译环境：VS2019，EasyX_20220116 // 最后修改：2022-4-5 #include #include #include #include #include #include using namespace std; #define PI 3.1415926535 int dimension = 3, num = 4; double points[50][2] = { {150,150},{150,200},{200,200},{200,150} }; //初始化 void initialize() {     initgraph(800, 640);     setbkcolor(WHITE);     setcolor(WHITE);     fillrectangle(0, 0, 800, 640);     setcolor(BLACK);     line(0, 80, 800, 80);     setcolor(BLACK);     line(0, 80, 800, 80);     //说明框矩形     RECT r = { 0,0,800,80 };     drawtext(_T("\n\n依次展示旋转，放大，平移，关于直线对称，关于x错切"), &r, DT_CENTER | DT_VCENTER);     HRGN rgn = CreateRectRgn(1, 81, 799, 639);     setcliprgn(rgn);         setcolor(BLACK);     rectangle(0, 0, 800, 640);     setcolor(RED); } //矩阵乘法 void multiply(double a[5][5], int ar, int ac, double b[5][5], int br, int bc) {     if (ac != br) {          cout << "matrix invalid";          return;     }     double c[5][5];     for (int i = 0; i < ar; i++) {          for (int j = 0; j < bc; j++) {              c[i][j] = 0;          }     }     for (int i = 0; i < ar; i++) {          for (int j = 0; j < bc; j++) {              for (int k = 0; k < ac; k++) {                   c[i][j] += a[i][k] * b[k][j];              }          }     }     for (int i = 0; i < ar; i++) {          for (int j = 0; j < bc; j++) {              b[i][j] = c[i][j];          }     } } //平移变换 void trans(double tx, double ty) {     double T[5][5] = { {1,0,tx},{0,1,ty},{0,0,1} };     double point[5][5];     for (int i = 0; i < num; i++) {          point[0][0] = points[i][0];          point[1][0] = points[i][1];          point[2][0] = 1;          multiply(T, dimension, dimension, point, dimension, 1);          points[i][0] = point[0][0];          points[i][1] = point[1][0];     } } //旋转变换 void rotate(double degree) {     double theta = degree / 180 * PI;     double R[5][5] = { {cos(theta),-sin(theta),0},{sin(theta),cos(theta),0},{0,0,1} };     double point[5][5];     for (int i = 0; i < num; i++) {          point[0][0] = points[i][0];          point[1][0] = points[i][1];          point[2][0] = 1;          multiply(R, dimension, dimension, point, dimension, 1);          points[i][0] = point[0][0];          points[i][1] = point[1][0];     } } //缩放变换 void scale(double sx, double sy) {     double S[5][5] = { {sx,0,0},{0,sy,0},{0,0,1} };     double point[5][5];     for (int i = 0; i < num; i++) {          point[0][0] = points[i][0];          point[1][0] = points[i][1];          point[2][0] = 1;          multiply(S, dimension, dimension, point, dimension, 1);          points[i][0] = point[0][0];          points[i][1] = point[1][0];     } } //对称变换 void symmetry(int flag) {     if (flag == 0) {          for (int i = 0; i < num; i++) {              points[i][1] = -points[i][1];          }     }     else if (flag == 1) {          for (int i = 0; i < num; i++) {              points[i][0] = -points[i][0];          }     }     else {          return;     } } void anysymmetry(int x1, int y1, int x2, int y2) {     double k = 0, b = 0;     if (x1 == x2) {          trans(-x1, 0);          symmetry(1);          trans(x1, 0);     }     else if (y1 == y2) {          trans(0, -y1);          symmetry(0);          trans(0, y1);     }     else {          k = double((y1 - y2) / (x1 - x2));          b = y1 - k * x1;          trans(0, -b);          rotate(-atan(k) * 180 * 1.0 / PI);          symmetry(0);          rotate(atan(k) * 180 * 1.0 / PI);          trans(0, b);     } } //输出图形 void paint() {     for (int i = 0; i < num; i++) {          if (i == num - 1) {              line(points[i][0], points[i][1], points[0][0], points[0][1]);              break;          }          line(points[i][0], points[i][1], points[i + 1][0], points[i + 1][1]);     } } //错切变换 void cut(int flag, int degree) {     double point[5][5];     if (flag == 0) {          double C[5][5] = { {1,0,0},{tan(double(degree) / 180 * PI),1,0},{0,0,1} };          for (int i = 0; i < num; i++) {              point[0][0] = points[i][0];              point[1][0] = points[i][1];              point[2][0] = 1;              multiply(C, dimension, dimension, point, dimension, 1);              points[i][0] = point[0][0];              points[i][1] = point[1][0];          }     }     else if (flag == 1) {          double C[5][5] = { {1,tan(double(degree) / 180 * PI),0},{0,1,0},{0,0,1} };          for (int i = 0; i < num; i++) {              point[0][0] = points[i][0];              point[1][0] = points[i][1];              point[2][0] = 1;              multiply(C, dimension, dimension, point, dimension, 1);              points[i][0] = point[0][0];              points[i][1] = point[1][0];          }     }     else if (flag == 2) {          double C[5][5] = { {1,tan(double(degree) / 180 * PI),0},{tan(double(degree) / 180 * PI),1,0},{0,0,1} };          for (int i = 0; i < num; i++) {              point[0][0] = points[i][0];              point[1][0] = points[i][1];              point[2][0] = 1;              multiply(C, dimension, dimension, point, dimension, 1);              points[i][0] = point[0][0];              points[i][1] = point[1][0];          }     }     else {          return;     } } //复合变换 void multitrans() {     paint();     int i = 50;     while (i > 0) {          i--;          Sleep(50);          clearcliprgn();          trans(-150, -150);          rotate(-20);          trans(150, 150);          paint();     }     i = 8;     while (i > 0) {          i--;          Sleep(250);          scale(1.1, 1.1);          clearcliprgn();          paint();     }     i = 40;     while (i > 0) {          i--;          Sleep(50);          trans(-1, -1);          clearcliprgn();          paint();     }     i = 4;     while (i > 0) {          i--;          Sleep(250);          anysymmetry(250, 100, 300, 560);          clearcliprgn();          setcolor(BLACK);          line(250, 100, 300, 560);          setcolor(RED);          paint();     }     i = 20;     while (i > 0) {          i--;          Sleep(150);          cut(0, 1);          clearcliprgn();          paint();     } } //主函数 int main() {     initialize();     _getch();     multitrans();     _getch();     closegraph();     return 0; }