一 实验目的
- 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 <graphics.h> #include <conio.h> #include <iostream> #include <math.h> 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 <graphics.h> #include <conio.h> #include <iostream> #include <math.h> #include <malloc.h> #include <stdio.h> 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; } |
