【计算机图形学】裁剪算法（逐边裁剪法 & Weiler-Atherton裁剪法）

一 实验目的

1. 编写直线段、多边形裁剪算法
2. 熟悉逐边裁剪法、Weiler-Atherton裁剪法的使用

4：用逐边裁剪法实现多边形裁剪（代码最上方功能区注明是否处理退化边）

无退化实验结果如下图所示：
图形初始化：（红色部分为裁剪框，白色部分为待裁剪多边形）

点击左键进行裁剪：（黄色部分为裁剪后剩余多边形）

 

 

点击右键将裁剪图案右移：（黄色部分为裁剪后剩余多边形）

 

 

有退化实验结果如下图所示：
图形初始化：（红色部分为裁剪框，白色部分为待裁剪多边形）

 点击左键将裁剪图案右移：（黄色部分为裁剪后剩余多边形）

 

5：用Weiler-Atherton裁剪法实现多边形裁剪
实验结果如下图所示：

 说明：白色部分为原始多边形，红色部分为裁剪框，黄色部分为通过Weiler-Atherton裁剪法实现的裁剪多边形。

 

总结：

1. 上述两种裁剪法的代码实现方法，大致是按照PPT上的算法思路构建的。原始多边形是在全局里面预设的，由于时间紧张没有测试过其他多边形（以及水平很菜），可能存在bug没有找到并维护。望谅解。
2. 在实现本实验的过程中，调用了之前实验的函数（CSLineClip等），算是一种学以致用吧。

 

 

三 程序说明

Project中程序的调用：

将当前cpp文件的属性——常规——从生成中排除中选择否，其他文件选择是，即可运行当前的cpp文件

 

4题：无退化

// // 程序名称：多边形裁剪1-1 // 功    能：用逐边裁剪法实现多边形裁剪（无退化） // 编译环境：VS2019，EasyX_20220116 // 最后修改：2022-3-31 #include #include #include using namespace std; //框的边界 float XL = 5, XR = 140, YB = 74, YT = 149; POINT Edge[] = { {XR,YB},{XR,YT},{XL,YT},{XL,YB} }; //自定义多边形 POINT Vertex[] = { {110,84},{160,94},{90,169},{90,94},{70,90},{50,230}, {165,230},{175,89},{163,54} }; int inlen = 9; #define max 100 //判断顶点和裁剪边的内外关系 bool Inside(POINT test, POINT p0, POINT p1) {     if (p1.x > p0.x) {          //裁剪边是窗口的下边          if (test.y >= p0.y) {              return 1;          }     }     else if (p1.x < p0.x) {          //裁剪边是窗口的上边          if (test.y <= p0.y) {              return 1;          }     }     else if (p1.y > p0.y) {          //裁剪边是窗口的右边          if (test.x <= p0.x) {              return 1;          }     }     else if (p1.y < p0.y) {          //裁剪边是窗口的左边          if (test.x >= p0.x) {              return 1;          }     }     return 0; } //求多边形的一条边和裁剪边的交点 void Cross(POINT s, POINT p, POINT p0, POINT p1, POINT &i) {     if (p0.y == p1.y) {          //水平裁剪边          i.y = p0.y;          i.x = s.x + (p0.y - s.y) * (p.x - s.x) / (p.y - s.y);     }     else {          //竖直裁剪边          i.x = p0.x;          i.y = s.y + (p0.x - s.x) * (p.y - s.y) / (p.x - s.x);     } } //将新的多边形顶点加入原有顶点组 void Insert(POINT newpoint, int &mylen, POINT p[]) {     p[mylen].x = newpoint.x;     p[mylen].y = newpoint.y;     mylen++;     //顶点数+=1 } //裁剪算法 void SHClip(int mylen, POINT in[], int& outlen, POINT out[], POINT p0, POINT p1) {     POINT s, p, i;     outlen = 0;     s = in[mylen - 1];     for (int j = 0; j < mylen; j++) {          p = in[j];          if (Inside(p, p0, p1)) {              if (Inside(s, p0, p1)) {                   Insert(p, outlen, out);              }              else {                   Cross(s, p, p0, p1, i);                   Insert(i, outlen, out);                   Insert(p, outlen, out);              }          }          else if (Inside(s, p0, p1)) {              Cross(s, p, p0, p1, i);              Insert(i, outlen, out);          }          s = p;     } } int main() {     //接收框的信息     float x0, y0, x1, y1;     initgraph(640, 480);     //绘制自定的point多边形     setcolor(WHITE);     polygon(Vertex, 9);     //绘制框     setlinecolor(RED);     line(XL, YT, XR, YT);     line(XL, YB, XR, YB);     line(XL, YT, XL, YB);     line(XR, YT, XR, YB);     ExMessage m;     POINT outp1[max], outp2[max], outp3[max], outp4[max];     int len1, len2, len3, len4;     int times = 0;     while (1) {          m = getmessage(EX_MOUSE | EX_KEY);          //用户点击左键后生成裁剪图形          if (m.message == WM_LBUTTONDOWN) {                           //裁剪过程              //POINT Edge[] = { {XR,YB},{XR,YT},{XL,YT},{XL,YB} };              //右边窗口裁剪边              SHClip(inlen, Vertex, len1, outp1, Edge[0], Edge[1]);              //上边窗口裁剪边              SHClip(len1, outp1, len2, outp2, Edge[1], Edge[2]);              //左边窗口裁剪边              SHClip(len2, outp2, len3, outp3, Edge[2], Edge[3]);              //下边窗口裁剪边              SHClip(len3, outp3, len4, outp4, Edge[3], Edge[0]);              //连线过程              setcolor(YELLOW);              polygon(outp4, len4);              //原来的位置进行黄色标注裁剪                           times++;          }          //用户点击右键后在旁边空白处生成裁剪图形          else if (m.message == WM_RBUTTONDOWN) {              for (int i = 0; i < len4; i++) {                   outp4[i].x += 200;              }              setcolor(YELLOW);              polygon(outp4, len4);              times++;          }          if (times == 2) {              break;          }     }     _getch();                 // 按任意键继续     closegraph();         // 关闭绘图窗口     return 0; }

4题：有退化

// // 程序名称：多边形裁剪1-2 // 功    能：用逐边裁剪法实现多边形裁剪（有退化） // 编译环境：VS2019，EasyX_20220116 // 最后修改：2022-3-31 #include #include #include #include #include using namespace std; //框的边界 float XL = 5, XR = 140, YB = 74, YT = 149; POINT Edge[] = { {XR,YB},{XR,YT},{XL,YT},{XL,YB} }; //自定义多边形 POINT Vertex[] = { {110,84},{160,94},{90,169},{90,94},{70,90},{50,230}, {165,230},{175,89},{163,54} }; int inlen = 9; #define max 100 //判断顶点和裁剪边的内外关系 bool Inside(POINT test, POINT p0, POINT p1) {     if (p1.x > p0.x) {          //裁剪边是窗口的下边          if (test.y >= p0.y) {              return 1;          }     }     else if (p1.x < p0.x) {          //裁剪边是窗口的上边          if (test.y <= p0.y) {              return 1;          }     }     else if (p1.y > p0.y) {          //裁剪边是窗口的右边          if (test.x <= p0.x) {              return 1;          }     }     else if (p1.y < p0.y) {          //裁剪边是窗口的左边          if (test.x >= p0.x) {              return 1;          }     }     return 0; } //求多边形的一条边和裁剪边的交点 void Cross(POINT s, POINT p, POINT p0, POINT p1, POINT& i) {     if (p0.y == p1.y) {          //水平裁剪边          i.y = p0.y;          i.x = s.x + (p0.y - s.y) * (p.x - s.x) / (p.y - s.y);     }     else {          //竖直裁剪边          i.x = p0.x;          i.y = s.y + (p0.x - s.x) * (p.y - s.y) / (p.x - s.x);     } } //将新的多边形顶点加入原有顶点组 void Insert(POINT newpoint, int& mylen, POINT p[]) {     p[mylen].x = newpoint.x;     p[mylen].y = newpoint.y;     mylen++;     //顶点数+=1 } //裁剪算法 void SHClip(int mylen, POINT in[], int& outlen, POINT out[], POINT p0, POINT p1) {     POINT s, p, i;     outlen = 0;     s = in[mylen - 1];     for (int j = 0; j < mylen; j++) {          p = in[j];          if (Inside(p, p0, p1)) {              if (Inside(s, p0, p1)) {                   Insert(p, outlen, out);              }              else {                   Cross(s, p, p0, p1, i);                   Insert(i, outlen, out);                   Insert(p, outlen, out);              }          }          else if (Inside(s, p0, p1)) {              Cross(s, p, p0, p1, i);              Insert(i, outlen, out);          }          s = p;     } } //VS不让用快排啊=。= int cmp(void* a, void* b) {     return *(int*)a - *(int*)b; } int main() {     //接收框的信息     initgraph(640, 480);     //绘制自定的point多边形     setcolor(WHITE);     polygon(Vertex, 9);     //绘制框     setlinecolor(RED);     line(XL, YT, XR, YT);     line(XL, YB, XR, YB);     line(XL, YT, XL, YB);     line(XR, YT, XR, YB);     ExMessage m;     POINT outp1[max], outp2[max], outp3[max], outp4[max];     int len1, len2, len3, len4;     int times = 0;     while (1) {          m = getmessage(EX_MOUSE | EX_KEY);          //用户点击左键后生成裁剪图形          if (m.message == WM_LBUTTONDOWN) {              //裁剪过程              //POINT Edge[] = { {XR,YB},{XR,YT},{XL,YT},{XL,YB} };              //右边窗口裁剪边              SHClip(inlen, Vertex, len1, outp1, Edge[0], Edge[1]);              //上边窗口裁剪边              SHClip(len1, outp1, len2, outp2, Edge[1], Edge[2]);              //左边窗口裁剪边              SHClip(len2, outp2, len3, outp3, Edge[2], Edge[3]);              //下边窗口裁剪边              SHClip(len3, outp3, len4, outp4, Edge[3], Edge[0]);              //连线过程              //setcolor(YELLOW);              //polygon(outp4, len4);              //原来的位置进行黄色标注裁剪              /*closegraph();           // 关闭绘图窗口              for (int t = 0; t < len4; t++) {                   cout << outp4[t].x <<" " << outp4[t].y << endl;              }*/              //退化边，根据outp4修改吧              for (int i = 0; i < len4 - 1; i++) {                   int flag = 1;                   if (outp4[i].x == outp4[i + 1].x) {                       if (outp4[i].x == int(XL) || outp4[i].x == int(XR)) {                           flag = 0;                       }                  }                   if (outp4[i].y == outp4[i + 1].y) {                       if (outp4[i].y == int(YB) || outp4[i].y == int(YT)) {                           flag = 0;                       }                   }                   if (flag == 1) {                       setcolor(YELLOW);                       //+200像素，可能是为了，方便展示orz                       line(outp4[i].x + 200, outp4[i].y, outp4[i + 1].x + 200, outp4[i + 1].y);                   }              }                           //float XL = 5, XR = 140, YB = 74, YT = 149;              //{XR,YB},{XR,YT},{XL,YT},{XL,YB}              //{ {110,84},{160,94},{90,169},{90,94},{70,90},{50,230}, {165,230},{175,89},{163,54} };                           //将坐标值按从小到大排序，奇数线段依次连接。              int xl[10], xr[10], yb[10], yt[10];//记录和框重合的点              int cntl = 0, cntr = 0, cntb = 0, cntt = 0;              for (int t = 0; t < len4; t++) {                   if (outp4[t].x == int(XL)) {                       //有了一个x坐标了我还用啥二维数组存坐标啊，笑                       //[XL,y]                       xl[cntl++] = outp4[t].y;                   }                   if (outp4[t].x == int(XR)) {                       //[XR,y]                       xr[cntr++] = outp4[t].y;                   }                   if (outp4[t].y == int(YB)) {                       //[x,YB]                       yb[cntb++] = outp4[t].x;                   }                   if (outp4[t].y == int(YT)) {                       //[x,YB]                       yt[cntt++] = outp4[t].x;                   }              }              /*void selectSort(int& a, int alen) {                   for (int i = 0; i < alen - 1; i++) {                       int min = i;                       for (int j = i + 1; j < alen; j++) {                           if (a[j] < a[min]) {                                min = j;                           }                       }                       //swap elements                       int temp = a[min];                       a[min] = a[i];                       a[i] = temp;                   }              }*/              //为什么调用sort函数呢，突然的bug猝不及防。还是传统方法改好了。              //排序x,y坐标              //画left边              if (cntl != 0) {                   for (int i = 0; i < cntl - 1; i++) {                       int min = i;                       for (int j = i + 1; j < cntl; j++) {                           if (xl[j] < xl[min]) {                                min = j;                           }                       }                       int t = xl[min];                       xl[min] = xl[i];                       xl[i] = t;                   }                   for (int i = 0; i < cntl; i += 2) {                       setcolor(YELLOW);                       line(int(XL) + 200, xr[i], int(XL) + 200, xr[i + 1]);                   }              }              //画right边              if (cntr != 0) {                   for (int i = 0; i < cntr - 1; i++) {                       int min = i;                       for (int j = i + 1; j < cntr; j++) {                           if (xr[j] < xr[min]) {                                min = j;                           }                       }                       int t = xr[min];                       xr[min] = xr[i];                       xr[i] = t;                  }                   for (int i = 0; i < cntr; i += 2) {                       setcolor(YELLOW);                       line(int(XR) + 200, xr[i], int(XR) + 200, xr[i + 1]);                   }              }              //画bottom边              if (cntb != 0) {                   for (int i = 0; i < cntb - 1; i++) {                       int min = i;                       for (int j = i + 1; j < cntb; j++) {                           if (yb[j] < yb[min]) {                                min = j;                           }                       }                       int t = yb[min];                       yb[min] = yb[i];                       yb[i] = t;                   }                   for (int i = 0; i < cntb; i += 2) {                       setcolor(YELLOW);                       line(yb[i] + 200, int(YB), yb[i + 1] + 200, int(YB));                   }              }              //画top边              if (cntt != 0) {                   for (int i = 0; i < cntt - 1; i++) {                       int min = i;                       for (int j = i + 1; j < cntt; j++) {                           if (yt[j] < yt[min]) {                                min = j;                           }                       }                       int t = yt[min];                       yt[min] = yt[i];                       yt[i] = t;                   }                   for (int i = 0; i < cntt; i += 2) {                       setcolor(YELLOW);                       line(yt[i] + 200, int(YT), yt[i + 1] + 200, int(YT));                   }              }          }     }     _getch();                 // 按任意键继续     closegraph();         // 关闭绘图窗口     return 0; }

5题

// // 程序名称：多边形裁剪2 // 功    能：用Weiler-Atherton裁剪法实现多边形裁剪 // 编译环境：VS2019，EasyX_20220116 // 最后修改：2022-3-31 #include #include #include using namespace std; //框的边界 float XL = 20, XR = 150, YB = 200, YT = 450; POINT Edge[] = { {XR,YB},{XR,YT},{XL,YT},{XL,YB} }; //自定义多边形，顺时针排序点坐标 POINT Vertex[] = { {300,100},{100,400},{200,120},{50,300},{100,100} }; int inlen = 5, outlen = 0; int keepx[100], keepy[100]; //编码数值 #define LEFT 1 #define RIGHT 2 #define BOTTOM 4 #define TOP 8 //编码函数 int encode(float x, float y, int* code) {     int c = 0;     if (x < XL) {          c = c | LEFT;     }     else if (x > XR) {          c = c | RIGHT;     }     if (y < YB) {          c = c | BOTTOM;;     }     else if (y > YT) {          c = c | TOP;     }     *code = c;     return 0; } //CS裁剪 int CSLineClip(float x1, float y1, float x2, float y2) {     //记录原始点     float x10 = x1, y10 = y1, x20 = x2, y20 = y2;     int code1, code2, code;     float x, y;     encode(x1, y1, &code1);     encode(x2, y2, &code2);     while (code1 != 0 || code2 != 0) {          if ((code1 & code2) != 0) {              return 0;          }          code = code1;          if (code1 == 0) {              code = code2;          }          //找交点，通过边界找坐标值          if ((LEFT & code) != 0) {              x = XL;              y = y1 + (y2 - y1) * (XL - x1) / (x2 - x1);          }          else if ((RIGHT & code) != 0) {              x = XR;              y = y1 + (y2 - y1) * (XR - x1) / (x2 - x1);          }          else if ((BOTTOM & code) != 0) {              y = YB;              x = x1 + (x2 - x1) * (YB - y1) / (y2 - y1);          }          else if ((TOP & code) != 0) {              y = YT;              x = x1 + (x2 - x1) * (YT - y1) / (y2 - y1);          }          //更新范围内的交点          if (code == code1) {              x1 = x;              y1 = y;              encode(x, y, &code1);          }          else {              x2 = x;              y2 = y;              encode(x, y, &code2);          }     }     //最终端点是x1 y1, x2 y2     //由于本题的特殊性，一定有一个是原始点，那先在一开始记录下     //把求得的交点push到keep数组中     //记录原始点 float x10 = x1, y10 = y1, x20 = x2, y20 = y2;     if (x10 == x1 && y10 == y1) {          //1点和原始点一样，那2点是交点，存入2点          keepx[outlen] = x2;          keepy[outlen] = y2;          outlen++;//???换个名字就可以全局了     }     else if (x20 == x2 && y20 == y2) {          //2点和原始点一样，那1点是交点，存入1点          keepx[outlen] = x1;          keepy[outlen] = y1;          outlen++;     }     //画线     setlinecolor(YELLOW);     line(x1, y1, x2, y2);     return 0; } int main() {     initgraph(640, 480);     //绘制自定的point多边形     setcolor(WHITE);     polygon(Vertex, inlen);     setcolor(RED);     polygon(Edge, 4);     //寻找第一个从外部->内部的边，求交点     int startnum = -1, endnum = -1;     for (int i = 0; i < inlen; i++) {          int code1 = -1, code2 = -1;          //非末尾点判断          if (i < inlen - 1) {              encode(Vertex[i].x, Vertex[i].y, &code1);              encode(Vertex[i + 1].x, Vertex[i + 1].y, &code2);              if (code1 != 0 && code2 == 0) {                   //external to internal                   startnum = i;                   endnum = i + 1;                   break;              }          }          //末尾点判断          else {              encode(Vertex[inlen - 1].x, Vertex[inlen - 1].y, &code1);              encode(Vertex[0].x, Vertex[0].y, &code2);              if (code1 != 0 && code2 == 0) {                   //external to internal                   startnum = i;                   endnum = i + 1;                   break;              }          }     }     //看看框和多边形是否有交集     if (startnum == -1) {          //没找到交点          return 0;     }     /*else {          cout << startnum << " " << endnum; //输出判断     }*/     //设置全局count不行，给到主函数然后传参进去吧     //int count = 0;     //CSCLIP救我老命啊，直接求内外交点然后clip掉     CSLineClip(Vertex[startnum].x, Vertex[startnum].y, Vertex[endnum].x, Vertex[endnum].y);     int curnum = endnum;     int times = 1;//判断是否循环结束     while (1) {          int code1 = -1, code2 = -1;          int flag = -1;          //给起始点编码，看看是否在框内          if (curnum < inlen - 1) {              encode(Vertex[curnum].x, Vertex[curnum].y, &code1);              encode(Vertex[curnum + 1].x, Vertex[curnum + 1].y, &code2);              flag = 1;          }          else {              encode(Vertex[inlen - 1].x, Vertex[inlen - 1].y, &code1);              encode(Vertex[0].x, Vertex[0].y, &code2);              flag = 0;          }          //两个点都在框内          if (code1 == 0 && code2 == 0) {              setlinecolor(YELLOW);              if (flag == 1) {                   line(Vertex[curnum].x, Vertex[curnum].y, Vertex[curnum + 1].x, Vertex[curnum + 1].y);              }              else if (flag == 0) {                   line(Vertex[inlen - 1].x, Vertex[inlen - 1].y, Vertex[0].x, Vertex[0].y);              }          }          //起点内，终点外          else if (code1 == 0 && code2 != 0) {              if (flag == 1) {                   CSLineClip(Vertex[curnum].x, Vertex[curnum].y, Vertex[curnum + 1].x, Vertex[curnum + 1].y);              }              else if (flag == 0) {                   CSLineClip(Vertex[inlen - 1].x, Vertex[inlen - 1].y, Vertex[0].x, Vertex[0].y);              }          }          //起点外，终点内          else if (code1 != 0 && code2 == 0) {              if (flag == 1) {                   CSLineClip(Vertex[curnum].x, Vertex[curnum].y, Vertex[curnum + 1].x, Vertex[curnum + 1].y);              }              else if (flag == 0) {                   CSLineClip(Vertex[inlen - 1].x, Vertex[inlen - 1].y, Vertex[0].x, Vertex[0].y);              }          }          //起点外，终点外          else {              //不画线          }          //记录入框交点和出框交点，并连结          //当前线段判断完并连线完，给下一轮循环更新curnum          if (curnum == inlen - 1) {              curnum = 0;              times++;          }          else {              curnum++;              times++;          }          //判断循环退出          if (times == inlen) {              break;          }     }     for (int i = 0; i < outlen; i += 2) {          line(keepx[i], keepy[i], keepx[i + 1], keepy[i + 1]);     }     _getch();                 // 按任意键继续     closegraph();         // 关闭绘图窗口     //cout << outlen;     /*     //交点判断     for (int i = 0; i < outlen; i++) {          cout << keepx[i] << " " << keepy[i] << endl;     }     */     return 0; }