#include <algorithm> #include <cmath> #include <cstdio> #include <vector> namespace pk { namespace geometry { template<class T> class exact_value_comparator { public: bool equal(const T& v1, const T& v2) { return (v1 == v2); } }; template<class T> class epsilon_value_comparator { public: bool equal(const T& v1, const T& v2, const T& epsilon = 0.000000001) { return (fabs(v1 - v2) < epsilon); } }; template<class T> class value_comparators {}; template<> class value_comparators<int> { public: typedef exact_value_comparator<int> comparator_type; }; template<> class value_comparators<long long> { public: typedef exact_value_comparator<long long> comparator_type; }; template<> class value_comparators<double> { public: typedef epsilon_value_comparator<double> comparator_type; }; template<> class value_comparators<long double> { public: typedef epsilon_value_comparator<long double> comparator_type; }; } // namespace geometry } // namespace pk namespace pk { namespace geometry { /** * WARNING: Take possible overflow into account. */ template<class Point> typename Point::value_type det(const Point& p1, const Point& p2, const Point& p3) { return (p1.x * p2.y + p2.x * p3.y + p3.x * p1.y - p1.x * p3.y - p2.x * p1.y - p3.x * p2.y); } } // namespace geometry } // namespace pk namespace pk { namespace geometry { template<class Point> double points_collinear(const Point& p1, const Point& p2, const Point& p3) { typename value_comparators<typename Point::value_type>::comparator_type comp; return comp.equal(det(p1, p2, p3), typename Point::value_type(0)); } } // namespace geometry } // namespace pk namespace pk { namespace geometry { /** * True if a given point is on a given line segment. * * If the point exactly equals one of the line segment's ends, * it is on the line segment (function returns true). */ template<class Point, class LineSegment> bool point_on_line_segment(const Point& p, const LineSegment& ls) { if(!points_collinear(p, ls.p1, ls.p2)) return false; if(std::min(ls.p1.x, ls.p2.x) > p.x) return false; if(std::max(ls.p1.x, ls.p2.x) < p.x) return false; if(std::min(ls.p1.y, ls.p2.y) > p.y) return false; if(std::max(ls.p1.y, ls.p2.y) < p.y) return false; return true; } } // namespace geometry } // namespace pk namespace pk { namespace geometry { template<class LineSegment> bool line_segments_intersect(const LineSegment& ls1, const LineSegment& ls2) { if(point_on_line_segment(ls1.p1, ls2) || point_on_line_segment(ls1.p2, ls2)) return true; if(point_on_line_segment(ls2.p1, ls1) || point_on_line_segment(ls2.p2, ls1)) return true; typedef typename LineSegment::point_type::value_type value_type; value_type d1 = det(ls1.p1, ls1.p2, ls2.p1); value_type d2 = det(ls1.p1, ls1.p2, ls2.p2); if((d1 < value_type(0)) && (d2 < value_type(0))) return false; if((d1 > value_type(0)) && (d2 > value_type(0))) return false; d1 = det(ls2.p1, ls2.p2, ls1.p1); d2 = det(ls2.p1, ls2.p2, ls1.p2); if((d1 < value_type(0)) && (d2 < value_type(0))) return false; if((d1 > value_type(0)) && (d2 > value_type(0))) return false; return true; } } // namespace geometry } // namespace pk struct PointDouble { typedef long double value_type; PointDouble() {} PointDouble(const long double x_, const long double y_) : x(x_), y(y_) {} long double x, y; }; struct LineSegmentDouble { typedef PointDouble point_type; LineSegmentDouble() {} LineSegmentDouble(const PointDouble& p1_, const PointDouble& p2_) : p1(p1_), p2(p2_) {} PointDouble p1, p2; }; bool operator<(const PointDouble& left, const PointDouble& right) { if(left.y < right.y) return true; if(left.y > right.y) return false; return (left.x < right.x); } template<class LineSegment> PointDouble get_line_segments_intersection(const LineSegment& ls1, const LineSegment& ls2) { if(pk::geometry::point_on_line_segment(ls1.p1, ls2)) return PointDouble(ls1.p1.x, ls1.p1.y); if(pk::geometry::point_on_line_segment(ls1.p2, ls2)) return PointDouble(ls1.p2.x, ls1.p2.y); if(pk::geometry::point_on_line_segment(ls2.p1, ls1)) return PointDouble(ls2.p1.x, ls2.p1.y); if(pk::geometry::point_on_line_segment(ls2.p2, ls1)) return PointDouble(ls2.p2.x, ls2.p2.y); const long double x1 = ls1.p1.x; const long double x2 = ls1.p2.x; const long double x3 = ls2.p1.x; const long double x4 = ls2.p2.x; const long double y1 = ls1.p1.y; const long double y2 = ls1.p2.y; const long double y3 = ls2.p1.y; const long double y4 = ls2.p2.y; const long double u = ((x4-x3)*(y1-y3) - (y4-y3)*(x1-x3)) / ((y4-y3)*(x2-x1) - (x4-x3)*(y2-y1)); return PointDouble(x1 + u * (x2-x1), y1 + u * (y2-y1)); } struct Point { typedef int value_type; Point() {} Point(const int x_, const int y_) : x(x_), y(y_) {} int x, y; }; struct LineSegment { typedef Point point_type; LineSegment() {} LineSegment(const Point& p1_, const Point& p2_) : p1(p1_), p2(p2_) {} Point p1, p2; }; std::vector<LineSegment> line_segments; std::vector<LineSegment> valid_line_segments; std::vector<int> valid_line_segments_dets; bool all_others_dets_positive(const Point& p1, const Point& p2, const int i, const int j) { for(int a = 0; a < line_segments.size(); ++a) { if((a == i) || (a == j)) continue; if((pk::geometry::det(p1, p2, line_segments[a].p1) < 0) && (pk::geometry::det(p1, p2, line_segments[a].p2) < 0)) return false; } return true; } bool all_others_dets_negative(const Point& p1, const Point& p2, const int i, const int j) { for(int a = 0; a < line_segments.size(); ++a) { if((a == i) || (a == j)) continue; if((pk::geometry::det(p1, p2, line_segments[a].p1) > 0) && (pk::geometry::det(p1, p2, line_segments[a].p2) > 0)) return false; } return true; } void check_if_valid_line_segment(const Point& p1, const Point& p2, const Point& p3, const Point& p4, const int i, const int j) { const auto d1 = pk::geometry::det(p1, p2, p3); const auto d2 = pk::geometry::det(p1, p2, p4); if((d1 <= 0) && (d2 <= 0)) { if(all_others_dets_positive(p1, p2, i, j)) { valid_line_segments.emplace_back(p1, p2); valid_line_segments_dets.push_back(1); } } if((d1 >= 0) && (d2 >= 0)) { if(all_others_dets_negative(p1, p2, i, j)) { valid_line_segments.emplace_back(p1, p2); valid_line_segments_dets.push_back(-1); } } } bool turning_left(const PointDouble& p1, const PointDouble& p2, const PointDouble& p3) { return (pk::geometry::det(p1, p2, p3) >= 0.0); } bool is_valid_intersection_point(const PointDouble& p) { for(int i = 0; i < valid_line_segments.size(); ++i) { if(pk::geometry::point_on_line_segment( p, LineSegmentDouble( PointDouble(valid_line_segments[i].p1.x, valid_line_segments[i].p1.y), PointDouble(valid_line_segments[i].p2.x, valid_line_segments[i].p2.y)))) continue; const auto d = pk::geometry::det( PointDouble(valid_line_segments[i].p1.x, valid_line_segments[i].p1.y), PointDouble(valid_line_segments[i].p2.x, valid_line_segments[i].p2.y), p); if((d > 0) && (valid_line_segments_dets[i] < 0)) return false; if((d < 0) && (valid_line_segments_dets[i] > 0)) return false; } return true; } int main() { int n; scanf("%d", &n); for(int i = 0; i < n; ++i) { int ax, ay, bx, by; scanf("%d%d%d%d", &ax, &ay, &bx, &by); line_segments.emplace_back(Point(ax, ay), Point(bx, by)); } for(int i = 0; i < line_segments.size(); ++i) { for(int j = i+1; j < line_segments.size(); ++j) { check_if_valid_line_segment( line_segments[i].p1, line_segments[j].p1, line_segments[i].p2, line_segments[j].p2, i, j); check_if_valid_line_segment( line_segments[i].p2, line_segments[j].p1, line_segments[i].p1, line_segments[j].p2, i, j); check_if_valid_line_segment( line_segments[i].p1, line_segments[j].p2, line_segments[i].p2, line_segments[j].p1, i, j); check_if_valid_line_segment( line_segments[i].p2, line_segments[j].p2, line_segments[i].p1, line_segments[j].p1, i, j); } } std::vector<PointDouble> intersection_points; for(int i = 0; i < valid_line_segments.size(); ++i) { for(int j = i + 1; j < valid_line_segments.size(); ++j) { if(pk::geometry::line_segments_intersect(valid_line_segments[i], valid_line_segments[j])) intersection_points.push_back(get_line_segments_intersection(valid_line_segments[i], valid_line_segments[j])); } } std::vector<PointDouble> valid_intersection_points; for(const auto& p : intersection_points) { if(is_valid_intersection_point(p)) valid_intersection_points.push_back(p); } if(valid_intersection_points.size() < 3) { printf("0.0000000000000\n"); return 0; } std::sort(valid_intersection_points.begin(), valid_intersection_points.end()); std::vector<PointDouble> upper; for(int i = 0; i < valid_intersection_points.size(); ++i) { while((upper.size() >= 2) && turning_left(upper[upper.size()-2], upper[upper.size()-1], valid_intersection_points[i])) upper.pop_back(); upper.push_back(valid_intersection_points[i]); } std::reverse(valid_intersection_points.begin(), valid_intersection_points.end()); std::vector<PointDouble> lower; for(int i = 0; i < valid_intersection_points.size(); ++i) { while((lower.size() >= 2) && turning_left(lower[lower.size()-2], lower[lower.size()-1], valid_intersection_points[i])) lower.pop_back(); lower.push_back(valid_intersection_points[i]); } for(int i = 1; i < lower.size(); ++i) upper.push_back(lower[i]); upper.push_back(upper[1]); long double result = 0.0; for(int i = 1; i < (upper.size()-1); ++i) result += (upper[i-1].x - upper[i+1].x) * upper[i].y; if(result < 0.0) result = -result; printf("%.13Lf\n", result / 2.0); }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 | #include <algorithm> #include <cmath> #include <cstdio> #include <vector> namespace pk { namespace geometry { template<class T> class exact_value_comparator { public: bool equal(const T& v1, const T& v2) { return (v1 == v2); } }; template<class T> class epsilon_value_comparator { public: bool equal(const T& v1, const T& v2, const T& epsilon = 0.000000001) { return (fabs(v1 - v2) < epsilon); } }; template<class T> class value_comparators {}; template<> class value_comparators<int> { public: typedef exact_value_comparator<int> comparator_type; }; template<> class value_comparators<long long> { public: typedef exact_value_comparator<long long> comparator_type; }; template<> class value_comparators<double> { public: typedef epsilon_value_comparator<double> comparator_type; }; template<> class value_comparators<long double> { public: typedef epsilon_value_comparator<long double> comparator_type; }; } // namespace geometry } // namespace pk namespace pk { namespace geometry { /** * WARNING: Take possible overflow into account. */ template<class Point> typename Point::value_type det(const Point& p1, const Point& p2, const Point& p3) { return (p1.x * p2.y + p2.x * p3.y + p3.x * p1.y - p1.x * p3.y - p2.x * p1.y - p3.x * p2.y); } } // namespace geometry } // namespace pk namespace pk { namespace geometry { template<class Point> double points_collinear(const Point& p1, const Point& p2, const Point& p3) { typename value_comparators<typename Point::value_type>::comparator_type comp; return comp.equal(det(p1, p2, p3), typename Point::value_type(0)); } } // namespace geometry } // namespace pk namespace pk { namespace geometry { /** * True if a given point is on a given line segment. * * If the point exactly equals one of the line segment's ends, * it is on the line segment (function returns true). */ template<class Point, class LineSegment> bool point_on_line_segment(const Point& p, const LineSegment& ls) { if(!points_collinear(p, ls.p1, ls.p2)) return false; if(std::min(ls.p1.x, ls.p2.x) > p.x) return false; if(std::max(ls.p1.x, ls.p2.x) < p.x) return false; if(std::min(ls.p1.y, ls.p2.y) > p.y) return false; if(std::max(ls.p1.y, ls.p2.y) < p.y) return false; return true; } } // namespace geometry } // namespace pk namespace pk { namespace geometry { template<class LineSegment> bool line_segments_intersect(const LineSegment& ls1, const LineSegment& ls2) { if(point_on_line_segment(ls1.p1, ls2) || point_on_line_segment(ls1.p2, ls2)) return true; if(point_on_line_segment(ls2.p1, ls1) || point_on_line_segment(ls2.p2, ls1)) return true; typedef typename LineSegment::point_type::value_type value_type; value_type d1 = det(ls1.p1, ls1.p2, ls2.p1); value_type d2 = det(ls1.p1, ls1.p2, ls2.p2); if((d1 < value_type(0)) && (d2 < value_type(0))) return false; if((d1 > value_type(0)) && (d2 > value_type(0))) return false; d1 = det(ls2.p1, ls2.p2, ls1.p1); d2 = det(ls2.p1, ls2.p2, ls1.p2); if((d1 < value_type(0)) && (d2 < value_type(0))) return false; if((d1 > value_type(0)) && (d2 > value_type(0))) return false; return true; } } // namespace geometry } // namespace pk struct PointDouble { typedef long double value_type; PointDouble() {} PointDouble(const long double x_, const long double y_) : x(x_), y(y_) {} long double x, y; }; struct LineSegmentDouble { typedef PointDouble point_type; LineSegmentDouble() {} LineSegmentDouble(const PointDouble& p1_, const PointDouble& p2_) : p1(p1_), p2(p2_) {} PointDouble p1, p2; }; bool operator<(const PointDouble& left, const PointDouble& right) { if(left.y < right.y) return true; if(left.y > right.y) return false; return (left.x < right.x); } template<class LineSegment> PointDouble get_line_segments_intersection(const LineSegment& ls1, const LineSegment& ls2) { if(pk::geometry::point_on_line_segment(ls1.p1, ls2)) return PointDouble(ls1.p1.x, ls1.p1.y); if(pk::geometry::point_on_line_segment(ls1.p2, ls2)) return PointDouble(ls1.p2.x, ls1.p2.y); if(pk::geometry::point_on_line_segment(ls2.p1, ls1)) return PointDouble(ls2.p1.x, ls2.p1.y); if(pk::geometry::point_on_line_segment(ls2.p2, ls1)) return PointDouble(ls2.p2.x, ls2.p2.y); const long double x1 = ls1.p1.x; const long double x2 = ls1.p2.x; const long double x3 = ls2.p1.x; const long double x4 = ls2.p2.x; const long double y1 = ls1.p1.y; const long double y2 = ls1.p2.y; const long double y3 = ls2.p1.y; const long double y4 = ls2.p2.y; const long double u = ((x4-x3)*(y1-y3) - (y4-y3)*(x1-x3)) / ((y4-y3)*(x2-x1) - (x4-x3)*(y2-y1)); return PointDouble(x1 + u * (x2-x1), y1 + u * (y2-y1)); } struct Point { typedef int value_type; Point() {} Point(const int x_, const int y_) : x(x_), y(y_) {} int x, y; }; struct LineSegment { typedef Point point_type; LineSegment() {} LineSegment(const Point& p1_, const Point& p2_) : p1(p1_), p2(p2_) {} Point p1, p2; }; std::vector<LineSegment> line_segments; std::vector<LineSegment> valid_line_segments; std::vector<int> valid_line_segments_dets; bool all_others_dets_positive(const Point& p1, const Point& p2, const int i, const int j) { for(int a = 0; a < line_segments.size(); ++a) { if((a == i) || (a == j)) continue; if((pk::geometry::det(p1, p2, line_segments[a].p1) < 0) && (pk::geometry::det(p1, p2, line_segments[a].p2) < 0)) return false; } return true; } bool all_others_dets_negative(const Point& p1, const Point& p2, const int i, const int j) { for(int a = 0; a < line_segments.size(); ++a) { if((a == i) || (a == j)) continue; if((pk::geometry::det(p1, p2, line_segments[a].p1) > 0) && (pk::geometry::det(p1, p2, line_segments[a].p2) > 0)) return false; } return true; } void check_if_valid_line_segment(const Point& p1, const Point& p2, const Point& p3, const Point& p4, const int i, const int j) { const auto d1 = pk::geometry::det(p1, p2, p3); const auto d2 = pk::geometry::det(p1, p2, p4); if((d1 <= 0) && (d2 <= 0)) { if(all_others_dets_positive(p1, p2, i, j)) { valid_line_segments.emplace_back(p1, p2); valid_line_segments_dets.push_back(1); } } if((d1 >= 0) && (d2 >= 0)) { if(all_others_dets_negative(p1, p2, i, j)) { valid_line_segments.emplace_back(p1, p2); valid_line_segments_dets.push_back(-1); } } } bool turning_left(const PointDouble& p1, const PointDouble& p2, const PointDouble& p3) { return (pk::geometry::det(p1, p2, p3) >= 0.0); } bool is_valid_intersection_point(const PointDouble& p) { for(int i = 0; i < valid_line_segments.size(); ++i) { if(pk::geometry::point_on_line_segment( p, LineSegmentDouble( PointDouble(valid_line_segments[i].p1.x, valid_line_segments[i].p1.y), PointDouble(valid_line_segments[i].p2.x, valid_line_segments[i].p2.y)))) continue; const auto d = pk::geometry::det( PointDouble(valid_line_segments[i].p1.x, valid_line_segments[i].p1.y), PointDouble(valid_line_segments[i].p2.x, valid_line_segments[i].p2.y), p); if((d > 0) && (valid_line_segments_dets[i] < 0)) return false; if((d < 0) && (valid_line_segments_dets[i] > 0)) return false; } return true; } int main() { int n; scanf("%d", &n); for(int i = 0; i < n; ++i) { int ax, ay, bx, by; scanf("%d%d%d%d", &ax, &ay, &bx, &by); line_segments.emplace_back(Point(ax, ay), Point(bx, by)); } for(int i = 0; i < line_segments.size(); ++i) { for(int j = i+1; j < line_segments.size(); ++j) { check_if_valid_line_segment( line_segments[i].p1, line_segments[j].p1, line_segments[i].p2, line_segments[j].p2, i, j); check_if_valid_line_segment( line_segments[i].p2, line_segments[j].p1, line_segments[i].p1, line_segments[j].p2, i, j); check_if_valid_line_segment( line_segments[i].p1, line_segments[j].p2, line_segments[i].p2, line_segments[j].p1, i, j); check_if_valid_line_segment( line_segments[i].p2, line_segments[j].p2, line_segments[i].p1, line_segments[j].p1, i, j); } } std::vector<PointDouble> intersection_points; for(int i = 0; i < valid_line_segments.size(); ++i) { for(int j = i + 1; j < valid_line_segments.size(); ++j) { if(pk::geometry::line_segments_intersect(valid_line_segments[i], valid_line_segments[j])) intersection_points.push_back(get_line_segments_intersection(valid_line_segments[i], valid_line_segments[j])); } } std::vector<PointDouble> valid_intersection_points; for(const auto& p : intersection_points) { if(is_valid_intersection_point(p)) valid_intersection_points.push_back(p); } if(valid_intersection_points.size() < 3) { printf("0.0000000000000\n"); return 0; } std::sort(valid_intersection_points.begin(), valid_intersection_points.end()); std::vector<PointDouble> upper; for(int i = 0; i < valid_intersection_points.size(); ++i) { while((upper.size() >= 2) && turning_left(upper[upper.size()-2], upper[upper.size()-1], valid_intersection_points[i])) upper.pop_back(); upper.push_back(valid_intersection_points[i]); } std::reverse(valid_intersection_points.begin(), valid_intersection_points.end()); std::vector<PointDouble> lower; for(int i = 0; i < valid_intersection_points.size(); ++i) { while((lower.size() >= 2) && turning_left(lower[lower.size()-2], lower[lower.size()-1], valid_intersection_points[i])) lower.pop_back(); lower.push_back(valid_intersection_points[i]); } for(int i = 1; i < lower.size(); ++i) upper.push_back(lower[i]); upper.push_back(upper[1]); long double result = 0.0; for(int i = 1; i < (upper.size()-1); ++i) result += (upper[i-1].x - upper[i+1].x) * upper[i].y; if(result < 0.0) result = -result; printf("%.13Lf\n", result / 2.0); } |