1 /* 2 * Copyright (C) 2015 The Android Open Source Project 3 * 4 * Licensed under the Apache License, Version 2.0 (the "License"); 5 * you may not use this file except in compliance with the License. 6 * You may obtain a copy of the License at 7 * 8 * http://www.apache.org/licenses/LICENSE-2.0 9 * 10 * Unless required by applicable law or agreed to in writing, software 11 * distributed under the License is distributed on an "AS IS" BASIS, 12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 13 * See the License for the specific language governing permissions and 14 * limitations under the License. 15 */ 16 17 #include "seperate_rects.h" 18 #include <algorithm> 19 #include <assert.h> 20 #include <iostream> 21 #include <map> 22 #include <set> 23 #include <utility> 24 #include <vector> 25 26 namespace seperate_rects { 27 28 enum EventType { START, END }; 29 30 template <typename TId, typename TNum> 31 struct StartedRect { 32 IdSet<TId> id_set; 33 TNum left, top, bottom; 34 35 // Note that this->left is not part of the key. That field is only to mark the 36 // left edge of the rectangle. 37 bool operator<(const StartedRect<TId, TNum> &rhs) const { 38 return (top < rhs.top || (top == rhs.top && bottom < rhs.bottom)) || 39 (top == rhs.top && bottom == rhs.bottom && id_set < rhs.id_set); 40 } 41 }; 42 43 template <typename TId, typename TNum> 44 struct SweepEvent { 45 EventType type; 46 union { 47 TNum x; 48 TNum y; 49 }; 50 51 TId rect_id; 52 53 bool operator<(const SweepEvent<TId, TNum> &rhs) const { 54 return (y < rhs.y || (y == rhs.y && rect_id < rhs.rect_id)); 55 } 56 }; 57 58 template <typename TNum> 59 std::ostream &operator<<(std::ostream &os, const Rect<TNum> &rect) { 60 return os << rect.bounds[0] << ", " << rect.bounds[1] << ", " 61 << rect.bounds[2] << ", " << rect.bounds[3]; 62 } 63 64 template <typename TUInt> 65 std::ostream &operator<<(std::ostream &os, const IdSet<TUInt> &obj) { 66 int bits = IdSet<TUInt>::max_elements; 67 TUInt mask = ((TUInt)0x1) << (bits - 1); 68 for (int i = 0; i < bits; i++) 69 os << ((obj.getBits() & (mask >> i)) ? "1" : "0"); 70 return os; 71 } 72 73 template <typename TNum, typename TId> 74 void seperate_rects(const std::vector<Rect<TNum> > &in, 75 std::vector<RectSet<TId, TNum> > *out) { 76 // Overview: 77 // This algorithm is a line sweep algorithm that travels from left to right. 78 // The sweep stops at each vertical edge of each input rectangle in sorted 79 // order of x-coordinate. At each stop, the sweep line is examined in order of 80 // y-coordinate from top to bottom. Along the way, a running set of rectangle 81 // IDs is either added to or subtracted from as the top and bottom edges are 82 // encountered, respectively. At each change of that running set, a copy of 83 // that set is recorded in along with the the y-coordinate it happened at in a 84 // list. This list is then interpreted as a sort of vertical cross section of 85 // our output set of non-overlapping rectangles. Based of the algorithm found 86 // at: http://stackoverflow.com/a/2755498 87 88 if (in.size() > IdSet<TNum>::max_elements) { 89 return; 90 } 91 92 // Events are when the sweep line encounters the starting or ending edge of 93 // any input rectangle. 94 std::set<SweepEvent<TId, TNum> > sweep_h_events; // Left or right bounds 95 std::set<SweepEvent<TId, TNum> > sweep_v_events; // Top or bottom bounds 96 97 // A started rect is a rectangle whose left, top, bottom edge, and set of 98 // rectangle IDs is known. The key of this map includes all that information 99 // (except the left edge is never used to determine key equivalence or 100 // ordering), 101 std::map<StartedRect<TId, TNum>, bool> started_rects; 102 103 // This is cleared after every event. Its declaration is here to avoid 104 // reallocating a vector and its buffers every event. 105 std::vector<std::pair<TNum, IdSet<TId> > > active_regions; 106 107 // This pass will add rectangle start and end events to be triggered as the 108 // algorithm sweeps from left to right. 109 for (TId i = 0; i < in.size(); i++) { 110 const Rect<TNum> &rect = in[i]; 111 SweepEvent<TId, TNum> evt; 112 evt.rect_id = i; 113 114 evt.type = START; 115 evt.x = rect.left; 116 sweep_h_events.insert(evt); 117 118 evt.type = END; 119 evt.x = rect.right; 120 sweep_h_events.insert(evt); 121 } 122 123 for (typename std::set<SweepEvent<TId, TNum> >::iterator it = 124 sweep_h_events.begin(); 125 it != sweep_h_events.end(); ++it) { 126 const SweepEvent<TId, TNum> &h_evt = *it; 127 const Rect<TNum> &rect = in[h_evt.rect_id]; 128 129 // During this event, we have encountered a vertical starting or ending edge 130 // of a rectangle so want to append or remove (respectively) that rectangles 131 // top and bottom from the vertical sweep line. 132 SweepEvent<TId, TNum> v_evt; 133 v_evt.rect_id = h_evt.rect_id; 134 if (h_evt.type == START) { 135 v_evt.type = START; 136 v_evt.y = rect.top; 137 sweep_v_events.insert(v_evt); 138 139 v_evt.type = END; 140 v_evt.y = rect.bottom; 141 sweep_v_events.insert(v_evt); 142 } else { 143 v_evt.type = START; 144 v_evt.y = rect.top; 145 typename std::set<SweepEvent<TId, TNum> >::iterator start_it = 146 sweep_v_events.find(v_evt); 147 assert(start_it != sweep_v_events.end()); 148 sweep_v_events.erase(start_it); 149 150 v_evt.type = END; 151 v_evt.y = rect.bottom; 152 typename std::set<SweepEvent<TId, TNum> >::iterator end_it = 153 sweep_v_events.find(v_evt); 154 assert(end_it != sweep_v_events.end()); 155 sweep_v_events.erase(end_it); 156 } 157 158 // Peeks ahead to see if there are other rectangles sharing a vertical edge 159 // with the current sweep line. If so, we want to continue marking up the 160 // sweep line before actually processing the rectangles the sweep line is 161 // intersecting. 162 typename std::set<SweepEvent<TId, TNum> >::iterator next_it = it; 163 ++next_it; 164 if (next_it != sweep_h_events.end()) { 165 if (next_it->x == h_evt.x) { 166 continue; 167 } 168 } 169 170 #ifdef RECTS_DEBUG 171 std::cout << h_evt.x << std::endl; 172 #endif 173 174 // After the following for loop, active_regions will be a list of 175 // y-coordinates paired with the set of rectangle IDs that are intersect at 176 // that y-coordinate (and the current sweep line's x-coordinate). For 177 // example if the current sweep line were the left edge of a scene with only 178 // one rectangle of ID 0 and bounds (left, top, right, bottom) == (2, 3, 4, 179 // 5), active_regions will be [({ 0 }, 3), {}, 5]. 180 active_regions.clear(); 181 IdSet<TId> active_set; 182 for (typename std::set<SweepEvent<TId, TNum> >::iterator it = 183 sweep_v_events.begin(); 184 it != sweep_v_events.end(); ++it) { 185 const SweepEvent<TId, TNum> &v_evt = *it; 186 187 if (v_evt.type == START) { 188 active_set.add(v_evt.rect_id); 189 } else { 190 active_set.subtract(v_evt.rect_id); 191 } 192 193 if (active_regions.size() > 0 && active_regions.back().first == v_evt.y) { 194 active_regions.back().second = active_set; 195 } else { 196 active_regions.push_back(std::make_pair(v_evt.y, active_set)); 197 } 198 } 199 200 #ifdef RECTS_DEBUG 201 std::cout << "x:" << h_evt.x; 202 for (std::vector<std::pair<TNum, IdSet> >::iterator it = 203 active_regions.begin(); 204 it != active_regions.end(); ++it) { 205 std::cout << " " << it->first << "(" << it->second << ")" 206 << ","; 207 } 208 std::cout << std::endl; 209 #endif 210 211 // To determine which started rectangles are ending this event, we make them 212 // all as false, or unseen during this sweep line. 213 for (typename std::map<StartedRect<TId, TNum>, bool>::iterator it = 214 started_rects.begin(); 215 it != started_rects.end(); ++it) { 216 it->second = false; 217 } 218 219 // This for loop will iterate all potential new rectangles and either 220 // discover it was already started (and then mark it true), or that it is a 221 // new rectangle and add it to the started rectangles. A started rectangle 222 // is unique if it has a distinct top, bottom, and set of rectangle IDs. 223 // This is tricky because a potential rectangle could be encountered here 224 // that has a non-unique top and bottom, so it shares geometry with an 225 // already started rectangle, but the set of rectangle IDs differs. In that 226 // case, we have a new rectangle, and the already existing started rectangle 227 // will not be marked as seen ("true" in the std::pair) and will get ended 228 // by the for loop after this one. This is as intended. 229 for (typename std::vector<std::pair<TNum, IdSet<TId> > >::iterator it = 230 active_regions.begin(); 231 it != active_regions.end(); ++it) { 232 IdSet<TId> region_set = it->second; 233 234 if (region_set.isEmpty()) 235 continue; 236 237 // An important property of active_regions is that each region where a set 238 // of rectangles applies is bounded at the bottom by the next (in the 239 // vector) region's starting y-coordinate. 240 typename std::vector<std::pair<TNum, IdSet<TId> > >::iterator next_it = 241 it; 242 ++next_it; 243 assert(next_it != active_regions.end()); 244 245 TNum region_top = it->first; 246 TNum region_bottom = next_it->first; 247 248 StartedRect<TId, TNum> rect_key; 249 rect_key.id_set = region_set; 250 rect_key.left = h_evt.x; 251 rect_key.top = region_top; 252 rect_key.bottom = region_bottom; 253 254 // Remember that rect_key.left is ignored for the purposes of searching 255 // the started rects. This follows from the fact that a previously started 256 // rectangle would by definition have a left bound less than the current 257 // event's x-coordinate. We are interested in continuing the started 258 // rectangles by marking them seen (true) but we don't know, care, or wish 259 // to change the left bound at this point. If there are no matching 260 // rectangles for this region, start a new one and mark it as seen (true). 261 typename std::map<StartedRect<TId, TNum>, bool>::iterator 262 started_rect_it = started_rects.find(rect_key); 263 if (started_rect_it == started_rects.end()) { 264 started_rects[rect_key] = true; 265 } else { 266 started_rect_it->second = true; 267 } 268 } 269 270 // This for loop ends all rectangles that were unseen during this event. 271 // Because this is the first event where we didn't see this rectangle, it's 272 // right edge is exactly the current event's x-coordinate. With this, we 273 // have the final piece of information to output this rectangle's geometry 274 // and set of input rectangle IDs. To end a started rectangle, we erase it 275 // from the started_rects map and append the completed rectangle to the 276 // output vector. 277 for (typename std::map<StartedRect<TId, TNum>, bool>::iterator it = 278 started_rects.begin(); 279 it != started_rects.end(); 280 /* inc in body */) { 281 if (!it->second) { 282 const StartedRect<TId, TNum> &proto_rect = it->first; 283 Rect<TNum> out_rect; 284 out_rect.left = proto_rect.left; 285 out_rect.top = proto_rect.top; 286 out_rect.right = h_evt.x; 287 out_rect.bottom = proto_rect.bottom; 288 out->push_back(RectSet<TId, TNum>(proto_rect.id_set, out_rect)); 289 started_rects.erase(it++); // Also increments out iterator. 290 291 #ifdef RECTS_DEBUG 292 std::cout << " <" << proto_rect.id_set << "(" << rect << ")" 293 << std::endl; 294 #endif 295 } else { 296 // Remember this for loop has no built in increment step. We do it here. 297 ++it; 298 } 299 } 300 } 301 } 302 303 void seperate_frects_64(const std::vector<Rect<float> > &in, 304 std::vector<RectSet<uint64_t, float> > *out) { 305 seperate_rects(in, out); 306 } 307 308 } // namespace seperate_rects 309 310 #ifdef RECTS_TEST 311 312 using namespace seperate_rects; 313 314 int main(int argc, char **argv) { 315 #define RectSet RectSet<TId, TNum> 316 #define Rect Rect<TNum> 317 #define IdSet IdSet<TId> 318 typedef uint64_t TId; 319 typedef float TNum; 320 321 std::vector<Rect> in; 322 std::vector<RectSet> out; 323 std::vector<RectSet> expected_out; 324 325 in.push_back({0, 0, 4, 5}); 326 in.push_back({2, 0, 6, 6}); 327 in.push_back({4, 0, 8, 5}); 328 in.push_back({0, 7, 8, 9}); 329 330 in.push_back({10, 0, 18, 5}); 331 in.push_back({12, 0, 16, 5}); 332 333 in.push_back({20, 11, 24, 17}); 334 in.push_back({22, 13, 26, 21}); 335 in.push_back({32, 33, 36, 37}); 336 in.push_back({30, 31, 38, 39}); 337 338 in.push_back({40, 43, 48, 45}); 339 in.push_back({44, 41, 46, 47}); 340 341 in.push_back({50, 51, 52, 53}); 342 in.push_back({50, 51, 52, 53}); 343 in.push_back({50, 51, 52, 53}); 344 345 for (int i = 0; i < 100000; i++) { 346 out.clear(); 347 seperate_rects(in, &out); 348 } 349 350 for (int i = 0; i < out.size(); i++) { 351 std::cout << out[i].id_set << "(" << out[i].rect << ")" << std::endl; 352 } 353 354 std::cout << "# of rects: " << out.size() << std::endl; 355 356 expected_out.push_back(RectSet(IdSet(0), Rect(0, 0, 2, 5))); 357 expected_out.push_back(RectSet(IdSet(1), Rect(2, 5, 6, 6))); 358 expected_out.push_back(RectSet(IdSet(1) | 0, Rect(2, 0, 4, 5))); 359 expected_out.push_back(RectSet(IdSet(1) | 2, Rect(4, 0, 6, 5))); 360 expected_out.push_back(RectSet(IdSet(2), Rect(6, 0, 8, 5))); 361 expected_out.push_back(RectSet(IdSet(3), Rect(0, 7, 8, 9))); 362 expected_out.push_back(RectSet(IdSet(4), Rect(10, 0, 12, 5))); 363 expected_out.push_back(RectSet(IdSet(5) | 4, Rect(12, 0, 16, 5))); 364 expected_out.push_back(RectSet(IdSet(4), Rect(16, 0, 18, 5))); 365 expected_out.push_back(RectSet(IdSet(6), Rect(20, 11, 22, 17))); 366 expected_out.push_back(RectSet(IdSet(6) | 7, Rect(22, 13, 24, 17))); 367 expected_out.push_back(RectSet(IdSet(6), Rect(22, 11, 24, 13))); 368 expected_out.push_back(RectSet(IdSet(7), Rect(22, 17, 24, 21))); 369 expected_out.push_back(RectSet(IdSet(7), Rect(24, 13, 26, 21))); 370 expected_out.push_back(RectSet(IdSet(9), Rect(30, 31, 32, 39))); 371 expected_out.push_back(RectSet(IdSet(8) | 9, Rect(32, 33, 36, 37))); 372 expected_out.push_back(RectSet(IdSet(9), Rect(32, 37, 36, 39))); 373 expected_out.push_back(RectSet(IdSet(9), Rect(32, 31, 36, 33))); 374 expected_out.push_back(RectSet(IdSet(9), Rect(36, 31, 38, 39))); 375 expected_out.push_back(RectSet(IdSet(10), Rect(40, 43, 44, 45))); 376 expected_out.push_back(RectSet(IdSet(10) | 11, Rect(44, 43, 46, 45))); 377 expected_out.push_back(RectSet(IdSet(11), Rect(44, 41, 46, 43))); 378 expected_out.push_back(RectSet(IdSet(11), Rect(44, 45, 46, 47))); 379 expected_out.push_back(RectSet(IdSet(10), Rect(46, 43, 48, 45))); 380 expected_out.push_back(RectSet(IdSet(12) | 13 | 14, Rect(50, 51, 52, 53))); 381 382 for (int i = 0; i < expected_out.size(); i++) { 383 RectSet &ex_out = expected_out[i]; 384 if (std::find(out.begin(), out.end(), ex_out) == out.end()) { 385 std::cout << "Missing Rect: " << ex_out.id_set << "(" << ex_out.rect 386 << ")" << std::endl; 387 } 388 } 389 390 for (int i = 0; i < out.size(); i++) { 391 RectSet &actual_out = out[i]; 392 if (std::find(expected_out.begin(), expected_out.end(), actual_out) == 393 expected_out.end()) { 394 std::cout << "Extra Rect: " << actual_out.id_set << "(" << actual_out.rect 395 << ")" << std::endl; 396 } 397 } 398 399 return 0; 400 } 401 402 #endif 403
