标签：chapter pivot out 角度 ons eject click 计算机 sed
Nicholl-Lee-Nicholl二维线段裁剪算法相对于Cohen-Sutherland和Liang-Barsky算法来说，在求交点之前进行了线段端点相对于几个区域的判断，可以确切的知道要求交点的边的信息。
此方法只在二维空间裁剪时使用，C-S和L-B裁剪方法则可应用到三维空间。
算法步骤：
1 先使用C-S裁剪算法的区域码判断方法，去除一部分在裁剪区域外面的线段、显示在完全在裁剪区域内的线段。其他不能判断的情况，采用NLN算法进行裁剪。
2 p1和p2若有一点在区域内，必要时交换端点以确保p1在区域内。
分别计算p1到裁剪区域四个顶点斜率m1-m4（从左下端点顺时针的4个顶点），判断线段斜率m与m1-m4的关系，决定计算哪条边与线段的交点。交点值赋给p2.
3 p1和p2有一个点在区域0001（左侧），必要时交换端点以确保p1在0001内。
因为p2在区域内的情况被步骤2覆盖，因此p1为线段与左边界的交点。
分别计算m1-m4，判断线段斜率m与m1-m4的关系，决定计算哪条边与线段的交点。此交点赋值给p2.
4 p1和p2有一个点在区域1001（左上角），必要时交换端点以确保p1在1001内。
同样p2在区域内的情况被步骤2覆盖。
分别计算m1-m4，判断线段斜率m与m1-m4的关系（注意此处需要判断m2与m4的大小，决定计算哪条边与线段的交点）。分别计算p1和p2。
5 对于其他6种情况，分别判断p1和p2的位置，在不同的区域，将线段和裁剪区域旋转相应的角度，重复步骤2-4进行裁剪。裁剪完成后再将线段旋转回原来的位置。
1 #include <GLUT/GLUT.h> 2 #include <iostream> 3 #include <math.h> 4 #include "lineNLN.h" 5 #include "linebres.h" 6 7 GLfloat m1, m2, m3, m4; 8 9 const GLint winLeftBitCode = 0x1; // 直接为1也没问题 10 const GLint winRightBitCode = 0x2; 11 const GLint winBottomBitCode = 0x4; 12 const GLint winTopBitCode = 0x8; 13 14 typedef GLfloat Matrix3x3 [3][3]; 15 Matrix3x3 matRotate; 16 Matrix3x3 matComposite; 17 const GLdouble pi = 3.14159; 18 GLfloat delta; 19 wcPt2D center; 20 21 inline GLint inside (GLint code) 22 { 23 return GLint (!(code)); 24 } 25 inline GLint reject (GLint code1, GLint code2) 26 { 27 return GLint (code1 & code2); 28 } 29 inline GLint accept (GLint code1, GLint code2) 30 { 31 return GLint (!(code1 | code2)); 32 } 33 34 GLubyte encode (wcPt2D pt, wcPt2D winMin, wcPt2D winMax) 35 { 36 GLubyte code = 0x00; 37 38 if(pt.getx() < winMin.getx()) 39 code = code | winLeftBitCode; 40 if(pt.getx() > winMax.getx()) 41 code = code | winRightBitCode; 42 if(pt.gety() < winMin.gety()) 43 code = code | winBottomBitCode; 44 if(pt.gety() > winMax.gety()) 45 code = code | winTopBitCode; 46 47 return code; 48 } 49 50 void swapPts (wcPt2D * p1, wcPt2D * p2) // TODO 为什么要用指针？ 51 { 52 wcPt2D tmp; 53 tmp = * p1; * p1 = * p2; * p2 = tmp; 54 } 55 56 void swapCode (GLubyte * c1, GLubyte * c2) 57 { 58 GLubyte tmp; 59 tmp = * c1; * c1 = * c2; * c2 = tmp; 60 } 61 62 void renewWinVertexes (wcPt2D * winMin, wcPt2D * winMax) 63 { 64 wcPt2D tmp1, tmp2; 65 tmp1.setCoords(fmin(winMin->getx(), winMax->getx()), fmin(winMin->gety(), winMax->gety())); 66 tmp2.setCoords(fmax(winMin->getx(), winMax->getx()), fmax(winMin->gety(), winMax->gety())); 67 * winMin = tmp1; 68 * winMax = tmp2; 69 } 70 71 void matrix3x3SetIdentity (Matrix3x3 matIden3x3) 72 { 73 GLint row, col; 74 for(row = 0; row < 3; row++) 75 { 76 for(col = 0; col < 3; col++) 77 { 78 matIden3x3[row][col] = (row == col); 79 } 80 } 81 } 82 83 void matrix3x3Premultiply (Matrix3x3 m1, Matrix3x3 m2) 84 { 85 GLint row, col; 86 Matrix3x3 matTemp; 87 88 for(row = 0; row < 3; row++) 89 { 90 for(col = 0; col < 3; col++) 91 { 92 matTemp[row][col] = m1[row][0] * m2 [0][col] + m1[row][1] * m2 [1][col] + m1[row][2] * m2 [2][col]; 93 } 94 } 95 96 for(row = 0; row < 3; row++) 97 { 98 for(col = 0; col < 3; col++) 99 { 100 m2[row][col] = matTemp[row][col]; 101 } 102 } 103 } 104 105 void rotate2D (wcPt2D pivotPt, GLfloat theta) 106 { 107 matrix3x3SetIdentity(matRotate); 108 109 matRotate[0][0] = cos(theta); 110 matRotate[0][1] = -sin(theta); 111 matRotate[0][2] = pivotPt.getx() * (1 - cos(theta)) + pivotPt.gety() * sin(theta); 112 matRotate[1][0] = sin(theta); 113 matRotate[1][1] = cos(theta); 114 matRotate[1][2] = pivotPt.gety() * (1 - cos(theta)) + pivotPt.getx() * sin(theta); 115 } 116 117 void transformVerts2D (wcPt2D * verts) 118 { 119 GLfloat tempx, tempy; 120 121 tempx = matRotate[0][0] * verts->getx() + matRotate[0][1] * verts->gety() + matRotate[0][2]; 122 tempy = matRotate[1][0] * verts->getx() + matRotate[1][1] * verts->gety() + matRotate[1][2]; 123 124 verts->setCoords(tempx, tempy); 125 } 126 127 void slopeWith4Vertexes (wcPt2D winMin, wcPt2D winMax, wcPt2D p1) 128 { 129 m1 = (p1.gety() - winMin.gety()) / (p1.getx() - winMin.getx()); 130 m2 = (p1.gety() - winMax.gety()) / (p1.getx() - winMin.getx()); 131 m3 = (p1.gety() - winMax.gety()) / (p1.getx() - winMax.getx()); 132 m4 = (p1.gety() - winMin.gety()) / (p1.getx() - winMax.getx()); 133 134 // std::cout << "slope : m1 : " << m1 << " m2 : " << m2 << " m3 : " << m3 << " m4 : " << m4 << std::endl; 135 } 136 137 void lineClipNLN (wcPt2D winMin, wcPt2D winMax, wcPt2D p1, wcPt2D p2) 138 { 139 GLubyte code1, code2; 140 GLint plotLine = false, done = false; 141 GLfloat m = 0.0; 142 143 while (!done) 144 { 145 code1 = encode(p1, winMin, winMax); 146 code2 = encode(p2, winMin, winMax); 147 if(accept(code1, code2)) 148 { 149 plotLine = true; 150 done = true; 151 } 152 else 153 { 154 if(reject(code1, code2)) 155 { 156 std::cout << "1 rejected line!" << std::endl; 157 done = true; 158 } 159 else 160 { 161 // 有一个点在裁剪区域内 162 if(inside(code1) || inside(code2)) 163 { 164 plotLine = true; 165 done = true; 166 if(!inside(code1)) 167 { 168 swapPts(&p1, &p2); 169 swapCode(&code1, &code2); 170 } 171 wcPt2D topLeft, bottomRight; 172 topLeft.setCoords(winMin.getx(), winMax.gety()); 173 bottomRight.setCoords(winMax.getx(), winMin.gety()); 174 if(p1.equals(winMin) || p1.equals(winMax) || p1.equals(topLeft) || p1.equals(bottomRight)) 175 { 176 p2.setCoords(p1.getx(), p1.gety()); 177 } 178 else 179 { 180 slopeWith4Vertexes(winMin, winMax, p1); 181 182 if(p1.getx() != p2.getx()) 183 { 184 m = (p2.gety() - p1.gety()) / (p2.getx() - p1.getx()); 185 186 if(m <= m1 && m >= m2 && (code2 & winLeftBitCode)) 187 {//L 188 p2.setCoords(winMin.getx(), p1.gety() + m * (winMin.getx() - p1.getx())); 189 } 190 else if(m <= m3 && m >= m4 && (code2 & winRightBitCode)) 191 {//R 192 p2.setCoords(winMax.getx(), p1.gety() + m * (winMax.getx() - p1.getx())); 193 } 194 else if((m > m3 || m < m2) && (code2 & winTopBitCode)) 195 {//T 196 p2.setCoords(p1.getx() + (winMax.gety() - p1.gety())/m, winMax.gety()); 197 } 198 else if((m > m1 || m < m4) && (code2 & winBottomBitCode)) 199 {//B 200 p2.setCoords(p1.getx() + (winMin.gety() - p1.gety())/m, winMin.gety()); 201 } 202 } 203 else 204 { 205 if(p2.gety() > winMax.gety()) 206 { 207 p2.setCoords(p2.getx(), winMax.gety()); 208 } 209 else 210 { 211 p2.setCoords(p2.getx(), winMin.gety()); 212 } 213 } 214 } 215 } 216 else 217 { 218 if(code1 == 0x01 || code2 == 0x01) 219 // 有一个点的区域码是0001，即在裁剪区域正左侧，L的情况在上一个if中包含，这里只会有LT，LR，LB和rejected的情况 220 { 221 if(code1 != 0x01) 222 { 223 swapPts(&p1, &p2); 224 swapCode(&code1, &code2); 225 } 226 slopeWith4Vertexes(winMin, winMax, p1); 227 if(p1.getx() != p2.getx()) 228 { 229 m = (p2.gety() - p1.gety()) / (p2.getx() - p1.getx()); 230 } 231 if(m < m1 || m > m2) 232 { 233 std::cout << "2 rejected line!" << std::endl; 234 done = true; 235 } 236 else 237 { 238 p1.setCoords(winMin.getx(), p1.gety() + m * (winMin.getx() - p1.getx())); 239 if((m <= m2 && m >= m3) && (code2 & winTopBitCode)) 240 {//LT 241 p2.setCoords(p1.getx() + (winMax.gety() - p1.gety())/m, winMax.gety()); 242 } 243 else if((m < m3 && m >= m4) && (code2 & winRightBitCode)) 244 {//LR 245 p2.setCoords(winMax.getx(), p1.gety() + m * (winMax.getx() - p1.getx())); 246 } 247 else if((m < m4 && m >= m1) && (code2 & winBottomBitCode)) 248 {//LB 249 p2.setCoords(p1.getx() + (winMin.gety() - p1.gety())/m, winMin.gety()); 250 } 251 plotLine = true; 252 done = true; 253 } 254 } 255 else if(code1 == (winLeftBitCode | winTopBitCode) || code2 == (winLeftBitCode | winTopBitCode)) 256 // 有一个点在裁剪区域外左上角的情况，这里的L、T情况已经在第一个if里包含 257 { 258 if(code1 != (winLeftBitCode | winTopBitCode)) 259 { 260 swapPts(&p1, &p2); 261 swapCode(&code1, &code2); 262 } 263 264 slopeWith4Vertexes(winMin, winMax, p1); 265 if(p1.getx() != p2.getx()) 266 { 267 m = (p2.gety() - p1.gety()) / (p2.getx() - p1.getx()); 268 } 269 if(m > m3 || m < m1) 270 { 271 std::cout << "3 rejected line!" << std::endl; 272 done = true; 273 } 274 else 275 { 276 plotLine = true; 277 done = true; 278 if(m <= m3 && m >= m4) 279 { 280 p2.setCoords(winMax.getx(), p1.gety() + m * (winMax.getx() - p1.getx())); 281 if(m2 > m4 && m <= m2) 282 {//LR 283 p1.setCoords(winMin.getx(), p1.gety() + m * (winMin.getx() - p1.getx())); 284 } 285 else 286 {//TR 287 p1.setCoords(p1.getx() + (winMax.gety() - p1.gety())/m, winMax.gety()); 288 } 289 } 290 else if(m < m4 && m >= m1) 291 { 292 p2.setCoords(p1.getx() + (winMin.gety() - p1.gety())/m, winMin.gety()); 293 if(m2 < m4 && m >= m2) 294 {//TB 295 p1.setCoords(p1.getx() + (winMax.gety() - p1.gety())/m, winMax.gety()); 296 } 297 else 298 {//LB 299 p1.setCoords(winMin.getx(), p1.gety() + m * (winMin.getx() - p1.getx())); 300 } 301 } 302 } 303 } 304 else 305 { 306 center.setCoords((winMin.getx() + winMax.getx())/2, (winMin.gety() + winMax.gety())/2); 307 308 if(code1 == (winLeftBitCode | winBottomBitCode) || code2 == (winLeftBitCode | winBottomBitCode)) 309 {//LB 310 delta = -pi/2; 311 } 312 else if(code1 == winBottomBitCode || code2 == winBottomBitCode) 313 {//B 314 delta = -pi/2; 315 } 316 else if(code1 == (winBottomBitCode | winRightBitCode) || code2 == (winBottomBitCode | winRightBitCode)) 317 {//BR 318 delta = pi; 319 } 320 else if(code1 == winRightBitCode || code2 == winRightBitCode) 321 {//R 322 delta = pi; 323 } 324 else if(code1 == (winRightBitCode | winTopBitCode) || code2 == (winRightBitCode | winTopBitCode)) 325 {//TR 326 delta = pi/2; 327 } 328 else if(code1 == winTopBitCode || code2 == winTopBitCode) 329 {//T 330 delta = pi/2; 331 } 332 rotate2D(center, delta); 333 transformVerts2D(&p1); 334 transformVerts2D(&p2); 335 transformVerts2D(&winMin); 336 transformVerts2D(&winMax); 337 renewWinVertexes(&winMin, &winMax); 338 } 339 } 340 } 341 } 342 } 343 344 if(plotLine) 345 { 346 if(delta != 0) 347 { 348 rotate2D(center, -delta); 349 transformVerts2D(&p1); 350 transformVerts2D(&p2); 351 } 352 lineBres(round(p1.getx()), round(p1.gety()), round(p2.getx()), round(p2.gety())); 353 } 354 delta = 0; 355 }
完整代码路径：https://github.com/p0e0o0p0l0e0/Computer_Graphics/tree/f9a7ad1987586445d780de2461d423af0dd9ba6a
[计算机图形学 with OpenGL] Chapter8 习题8.12 NLN二维线段裁剪算法实现
标签：chapter pivot out 角度 ons eject click 计算机 sed
原文地址：http://www.cnblogs.com/p0e0o0p0l0e0/p/6931194.html
