还是其几天写的，这是最简单的一个直线裁剪算法了吧，它针对的是一个矩形和一条线段。并且还是边与坐标轴平行的矩形。
在实际应用上应该会经常用于屏幕对各种线段的裁剪吧。算法很简单效率也很高。
首先是算法的两种特例：平凡接受和平凡拒绝。
（图片来自《计算机图形学（OpenGL）》第三版）
当线段的两个端点都在矩形内部，则平凡接受，不需要裁剪。如图中的AB。而当线段的两个端点都在某条边的外边时，平凡拒绝，也不需要裁剪。如图中的CD。
检测这两种情况的方法可以先形成两个端点的码字，如下：
那么可以得到如下的几种码字：
如果两个点都在矩形内部，那么码字应该都是FFFF，则平凡接受，返回当前线段就好。而如果两个点的某一位都是T，则说明他们都在矩形某条边的外面，则平凡拒绝。如图3.17中的CD，对应的码字分别应是FTTF和FFTF，在第三位上都是T，他们都在矩形的右边，则平凡拒绝。
我们运行这样的算法来裁剪一条线段：
最后，代码如下：
1 #include <GL/gl.h>
2 #include <GL/glu.h>
3 #include <GL/glut.h>
4 #include <cmath>
5 #include <iostream>
6 using namespace std;
7
8 struct Point2D
9 {
10 float _x, _y;
11 Point2D()
12 {
13 _x = 0.0f;
14 _y = 0.0f;
15 }
16 Point2D(const Point2D& p)
17 {
18 _x = p._x;
19 _y = p._y;
20 }
21 Point2D(float xx, float yy)
22 {
23 _x = xx;
24 _y = yy;
25 }
26 Point2D& operator=(const Point2D& p)
27 {
28 _x = p._x;
29 _y = p._y;
30 return *this;
31 }
32 Point2D& operator+(const Point2D& p)
33 {
34 Point2D temp;
35 temp._x = _x + p._x;
36 temp._y = _y + p._y;
37 return temp;
38 }
39 Point2D& operator-(const Point2D& p)
40 {
41 Point2D temp(_x - p._x, _y - p._y);
42 return temp;
43 }
44 float operator*(const Point2D& p)
45 {
46 return _x * p._x + _y * p._y;
47 }
48
49 float length()
50 {
51 return sqrtf(_x * _x + _y * _y);
52 }
53 };
54
55 struct Line2D
56 {
57 Point2D _start;
58 Point2D _end;
59 float _length;
60
61 Line2D() : _start(), _end()
62 {
63 _length = 0.0f;
64 }
65 Line2D(const Point2D& start, const Point2D& end) : _start(start), _end(end)
66 {
67 }
68 Line2D(const Line2D& line) : _start(line._start), _end(line._end)
69 {}
70
71 float length()
72 {
73 _length = (_end - _start).length();
74 }
75
76 Line2D& operator = (const Line2D& line)
77 {
78 _start = line._start;
79 _end = line._end;
80 }
81 };
82
83 struct Rect
84 {
85 float _left;
86 float _right;
87 float _up;
88 float _down;
89
90 float width()
91 {
92 return _right - _left;
93 }
94 float height()
95 {
96 return _down - _up;
97 }
98 };
99
100 enum CutRes
101 {
102 CR_ACCEPTED = 0,
103 CR_REFUSED = 1,
104 };
105
106 enum CSBIT
107 {
108 CB_BELOW = 0x01,//0001
109 CB_RIGHT = 0x02,//0010
110 CB_ABOVE = 0x04,//0100
111 CB_LEFT = 0x08,//1000
112
113 CB_BELOW_INV = 0xfe,//1111 1110
114 CB_RIGHT_INV = 0xfd,//1111 1101
115 CB_ABOVE_INV = 0xfb,//1111 1011
116 CB_LEFT_INV = 0xf7,//1111 0111
117 };
118
119 typedef unsigned char KEY;
120
121 /*Global Varibles*/
122 const int SCREEN_WIDTH = 800;
123 const int SCREEN_HEIGHT = 600;
124 Point2D g_Start;
125 Point2D g_End;
126 Line2D src;
127 Line2D dest;
128 bool acc;
129 Rect g_Rect;
130 int g_Count;
131
132 KEY GenKey(const Point2D& p, const Rect& r)
133 {
134 KEY key = 0;
135
136 if(p._y > r._down)
137 {
138 key |= CB_BELOW;
139 }
140 if(p._y < r._up)
141 {
142 key |= CB_ABOVE;
143 }
144 if(p._x < r._left)
145 {
146 key |= CB_LEFT;
147 }
148 if(p._x > r._right)
149 {
150 key |= CB_RIGHT;
151 }
152
153 return key;
154 }
155
156 void ShowKey(KEY key)
157 {
158 if(key & CB_LEFT)
159 cout << "T";
160 else
161 cout << "F";
162
163 if(key & CB_ABOVE)
164 cout << "T";
165 else
166 cout << "F";
167
168 if(key & CB_RIGHT)
169 cout << "T";
170 else
171 cout << "F";
172
173 if(key & CB_BELOW)
174 cout << "T";
175 else
176 cout << "F";
177 }
178
179 /*
180 key: TTFF
181 left above right below
182 */
183 int Cohen_Sutherland(const Line2D& src, Line2D& dest, const Rect& rect)
184 {
185 cout << "===============In Cohen_Sutherland===============\n";
186 Point2D start = src._start;
187 Point2D end = src._end;
188 KEY s, e;
189 dest = src;
190
191 for(unsigned int i = 0; i < 4; ++i)
192 {
193 cout << "\nNow Line: start(" << start._x << ", " << start._y <<") end(" << end._x << ", " << end._y << ")\n";
194
195 s = GenKey(start, rect);
196 e = GenKey(end, rect);
197 cout << "Key of Line: start ";ShowKey(s);cout << " end: ";ShowKey(e); cout << endl;
198
199 if((s == e) && (s == 0))
200 {
201 //accept, all point inside the rect
202 dest._start = start;
203 dest._end = end;
204 return CR_ACCEPTED;
205 }
206 int _b = 1 << i;
207 if((s & _b) && (e & _b))
208 {
209 //all point at same side
210 return CR_REFUSED;
211 }
212
213 switch(i)
214 {
215 case 0:
216 {
217 //below
218 if(s & _b)
219 {
220 float scale = (rect._down - end._y) / (start._y - end._y);
221 start._x = (start._x - end._x) * scale + end._x;
222 start._y = rect._down;
223 cout << "Start Below Rect. Cutted: " << start._x << ", " << start._y << endl;
224 }
225 if(e & _b)
226 {
227 float scale = (rect._down - start._y) / (end._y - start._y);
228 end._x = (end._x - start._x) * scale + start._x;
229 end._y = rect._down;
230 cout << "end Below Rect. Cutted: " << end._x << ", " << end._y << endl;
231 }
232 }break;
233 case 1:
234 {
235 //right
236 if(s & _b)
237 {
238 float scale = (rect._right - end._x) / (start._x - end._x);
239 start._x = rect._right;
240 start._y = (start._y - end._y) * scale + end._y;
241 cout << "start right Rect. Cutted: " << start._x << ", " << start._y << endl;
242 }
243 if(e & _b)
244 {
245 float scale = (rect._right - start._x) / (end._x - start._x);
246 end._x = rect._right;
247 end._y = (end._y - start._y) * scale + start._y;
248 cout << "end right Rect. Cutted: " << end._x << ", " << end._y << endl;
249 }
250 }break;
251 case 2:
252 {
253 //above
254 if(s & _b)
255 {
256 float scale = (rect._up - end._y) / (start._y - end._y);
257 start._x = (start._x - end._x) * scale + end._x;
258 start._y = rect._up;
259 cout << "start above Rect. Cutted: " << start._x << ", " << start._y << endl;
260 }
261 if(e & _b)
262 {
263 float scale = (rect._up - start._y) / (end._y - start._y);
264 end._x = (end._x - start._x) * scale + start._x;
265 end._y = rect._up;
266 cout << "end above Rect. Cutted: " << end._x << ", " << end._y << endl;
267 }
268 }break;
269 case 3:
270 {
271 //left
272 if(s & _b)
273 {
274 float scale = (rect._left - end._x) / (start._x - end._x);
275 start._x = rect._left;
276 start._y = (start._y - end._y) * scale + end._y;
277 cout << "start left Rect. Cutted: " << start._x << ", " << start._y << endl;
278 }
279 if(e & _b)
280 {
281 float scale = (rect._left - start._x) / (end._x - start._x);
282 end._x = rect._left;
283 end._y = (end._y - start._y) * scale + start._y;
284 cout << "end left Rect. Cutted: " << end._x << ", " << end._y << endl;
285 }
286 }break;
287 }
288 }
289 s = GenKey(start, rect);
290 e = GenKey(end, rect);
291
292 cout << "At Last, Key of Line: start ";ShowKey(s);cout << " end: ";ShowKey(e); cout << endl;
293 if((s == e) && (s == 0))
294 {
295 //accept, all point inside the rect
296 dest._start = start;
297 dest._end = end;
298 return CR_ACCEPTED;
299 }
300 else
301 {
302 return CR_REFUSED;
303 }
304 }
305
306 void myInit()
307 {
308 /*
309 Output Info
310 */
311
312 g_Rect._up = 100;
313 g_Rect._down = 500;
314 g_Rect._left = 100;
315 g_Rect._right = 700;
316 g_Count = 0;
317 acc = false;
318 cout << "Rect: {" << g_Rect._left << ", " << g_Rect._up << ", " << g_Rect._right << ", "<< g_Rect._down << "}\n";
319
320 glClearColor((float)0x66 / 0x100, (float)0xcc / 0x100, 1.0, 0.0);
321 glColor3f(0.0f, 0.0f, 0.0f);//Map Color Black
322 glPointSize(1.0);
323 glMatrixMode(GL_PROJECTION);
324
325 glLoadIdentity();
326 gluOrtho2D(0.0, (GLdouble)SCREEN_WIDTH, (GLdouble)SCREEN_HEIGHT, 0.0);
327 glViewport(0.0, SCREEN_WIDTH, 0.0, SCREEN_HEIGHT);
328 }
329
330 void myMouse(int button, int state, int x, int y)
331 {
332 if(button != GLUT_LEFT_BUTTON || state != GLUT_DOWN)
333 return;
334
335 cout << "MyMouse Called with " << x << ", " << y << endl;
336 switch(g_Count)
337 {
338 case 0:
339 {
340 ++g_Count;
341 g_Start._x = x;
342 g_Start._y = y;
343 src._start = g_Start;
344 }break;
345 case 1:
346 {
347 ++g_Count;
348 g_End._x = x;
349 g_End._y = y;
350 src._end = g_End;
351 acc = Cohen_Sutherland(src, dest, g_Rect);
352 if(acc)
353 {
354 cout << "Refused.\n";
355 }
356 else
357 cout << "Accept.\n";
358
359 glutPostRedisplay();
360 }break;
361 case 2:
362 {
363 g_Start._x = x;
364 g_Start._y = y;
365 src._start = g_Start;
366 g_Count = 1;
367 }break;
368 }
369 }
370
371 void myDisplay()
372 {
373 glClear(GL_COLOR_BUFFER_BIT);
374
375 //Draw Rect
376
377 glColor3f(0.0f, 0.0f, 0.0f);//Rect
378 glPointSize(2.0);
379 glBegin(GL_LINE_STRIP);
380 glVertex2d(g_Rect._left, g_Rect._up);
381 glVertex2d(g_Rect._right, g_Rect._up);
382 glVertex2d(g_Rect._right, g_Rect._down);
383 glVertex2d(g_Rect._left, g_Rect._down);
384 glVertex2d(g_Rect._left, g_Rect._up);
385 glEnd();
386
387 if(g_Count == 2)
388 {
389 //Draw Line
390 glColor3f(1.0f, 0.0f, 0.0f);//Normal Line, Red
391 glPointSize(2.0);
392 glBegin(GL_LINES);
393 glVertex2d(src._start._x, src._start._y);
394 glVertex2d(src._end._x, src._end._y);
395 cout << "\nDraw Line\n";
396 if(acc == CR_ACCEPTED)
397 {
398 //Draw Cutted Line
399 glColor3f(0.0f, 1.0f, 0.0f);//Normal Line, Green
400 glPointSize(2.0);
401 glVertex2d(dest._start._x, dest._start._y);
402 glVertex2d(dest._end._x, dest._end._y);
403 cout << "\nDraw CutLine\n";
404 }
405 glEnd();
406 }
407
408 //glutSwapBuffers();
409 glFlush();
410 //cout << "Render Over\n";
411 }
412
413 int main(int argc, char* argv[])
414 {
415 glutInit(&argc, argv);
416 //glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB);
417 glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
418 glutInitWindowSize(SCREEN_WIDTH, SCREEN_HEIGHT);
419 glutInitWindowPosition(0, 0);
420 glutCreateWindow("Cohen Sutherland");
421 glutDisplayFunc(myDisplay);
422 glutMouseFunc(myMouse);
423
424 myInit();
425 glutMainLoop();
426
427 return 0;
428 }
Cohen_Sutherland_with_GL
程序最上面是一些数据结构的定义，包括Point2D、Line2D、Rect等。
然后码字我选择使用unsigned char类型的低四位，从高往低分别代表矩形的左、上、右、下。枚举类型CSBIT用来方便我进行位操作。
算法核心函数是Cohen_Sutherland函数，接受一条直线和一个矩形为参数，一条直线作为输出并返回是否拒绝。GenKey函数和showKey分别用来生成码字和以友好的方式显示码字。
其他则是OpenGL的东西了。程序运行后会有一个预先设定好的矩形，然后可以不断的通过鼠标点击选取起点和终点产生一条线段，并用之前的矩形进行裁剪。
运行效果：
时间： 2024-08-05 07:02:43