/*
* Copyright (C) 2015 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include "separate_rects.h"
#include <algorithm>
#include <assert.h>
#include <iostream>
#include <map>
#include <set>
#include <utility>
#include <vector>
namespace separate_rects {
enum EventType { START, END };
template <typename TId, typename TNum>
struct StartedRect {
IdSet<TId> id_set;
TNum left, top, bottom;
// Note that this->left is not part of the key. That field is only to mark the
// left edge of the rectangle.
bool operator<(const StartedRect<TId, TNum> &rhs) const {
return (top < rhs.top || (top == rhs.top && bottom < rhs.bottom)) ||
(top == rhs.top && bottom == rhs.bottom && id_set < rhs.id_set);
}
};
template <typename TId, typename TNum>
struct SweepEvent {
EventType type;
union {
TNum x;
TNum y;
};
TId rect_id;
bool operator<(const SweepEvent<TId, TNum> &rhs) const {
return (y < rhs.y || (y == rhs.y && rect_id < rhs.rect_id));
}
};
template <typename TNum>
std::ostream &operator<<(std::ostream &os, const Rect<TNum> &rect) {
return os << rect.bounds[0] << ", " << rect.bounds[1] << ", "
<< rect.bounds[2] << ", " << rect.bounds[3];
}
template <typename TUInt>
std::ostream &operator<<(std::ostream &os, const IdSet<TUInt> &obj) {
int bits = IdSet<TUInt>::max_elements;
TUInt mask = ((TUInt)0x1) << (bits - 1);
for (int i = 0; i < bits; i++)
os << ((obj.getBits() & (mask >> i)) ? "1" : "0");
return os;
}
template <typename TNum, typename TId>
void separate_rects(const std::vector<Rect<TNum>> &in,
std::vector<RectSet<TId, TNum>> *out) {
// Overview:
// This algorithm is a line sweep algorithm that travels from left to right.
// The sweep stops at each vertical edge of each input rectangle in sorted
// order of x-coordinate. At each stop, the sweep line is examined in order of
// y-coordinate from top to bottom. Along the way, a running set of rectangle
// IDs is either added to or subtracted from as the top and bottom edges are
// encountered, respectively. At each change of that running set, a copy of
// that set is recorded in along with the the y-coordinate it happened at in a
// list. This list is then interpreted as a sort of vertical cross section of
// our output set of non-overlapping rectangles. Based of the algorithm found
// at: http://stackoverflow.com/a/2755498
if (in.size() > IdSet<TId>::max_elements) {
return;
}
// Events are when the sweep line encounters the starting or ending edge of
// any input rectangle.
std::set<SweepEvent<TId, TNum>> sweep_h_events; // Left or right bounds
std::set<SweepEvent<TId, TNum>> sweep_v_events; // Top or bottom bounds
// A started rect is a rectangle whose left, top, bottom edge, and set of
// rectangle IDs is known. The key of this map includes all that information
// (except the left edge is never used to determine key equivalence or
// ordering),
std::map<StartedRect<TId, TNum>, bool> started_rects;
// This is cleared after every event. Its declaration is here to avoid
// reallocating a vector and its buffers every event.
std::vector<std::pair<TNum, IdSet<TId>>> active_regions;
// This pass will add rectangle start and end events to be triggered as the
// algorithm sweeps from left to right.
for (TId i = 0; i < in.size(); i++) {
const Rect<TNum> &rect = in[i];
// Filter out empty or invalid rects.
if (rect.left >= rect.right || rect.top >= rect.bottom)
continue;
SweepEvent<TId, TNum> evt;
evt.rect_id = i;
evt.type = START;
evt.x = rect.left;
sweep_h_events.insert(evt);
evt.type = END;
evt.x = rect.right;
sweep_h_events.insert(evt);
}
for (typename std::set<SweepEvent<TId, TNum>>::iterator it =
sweep_h_events.begin();
it != sweep_h_events.end(); ++it) {
const SweepEvent<TId, TNum> &h_evt = *it;
const Rect<TNum> &rect = in[h_evt.rect_id];
// During this event, we have encountered a vertical starting or ending edge
// of a rectangle so want to append or remove (respectively) that rectangles
// top and bottom from the vertical sweep line.
SweepEvent<TId, TNum> v_evt;
v_evt.rect_id = h_evt.rect_id;
if (h_evt.type == START) {
v_evt.type = START;
v_evt.y = rect.top;
sweep_v_events.insert(v_evt);
v_evt.type = END;
v_evt.y = rect.bottom;
sweep_v_events.insert(v_evt);
} else {
v_evt.type = START;
v_evt.y = rect.top;
typename std::set<SweepEvent<TId, TNum>>::iterator start_it =
sweep_v_events.find(v_evt);
assert(start_it != sweep_v_events.end());
sweep_v_events.erase(start_it);
v_evt.type = END;
v_evt.y = rect.bottom;
typename std::set<SweepEvent<TId, TNum>>::iterator end_it =
sweep_v_events.find(v_evt);
assert(end_it != sweep_v_events.end());
sweep_v_events.erase(end_it);
}
// Peeks ahead to see if there are other rectangles sharing a vertical edge
// with the current sweep line. If so, we want to continue marking up the
// sweep line before actually processing the rectangles the sweep line is
// intersecting.
typename std::set<SweepEvent<TId, TNum>>::iterator next_it = it;
++next_it;
if (next_it != sweep_h_events.end()) {
if (next_it->x == h_evt.x) {
continue;
}
}
#ifdef RECTS_DEBUG
std::cout << h_evt.x << std::endl;
#endif
// After the following for loop, active_regions will be a list of
// y-coordinates paired with the set of rectangle IDs that are intersect at
// that y-coordinate (and the current sweep line's x-coordinate). For
// example if the current sweep line were the left edge of a scene with only
// one rectangle of ID 0 and bounds (left, top, right, bottom) == (2, 3, 4,
// 5), active_regions will be [({ 0 }, 3), {}, 5].
active_regions.clear();
IdSet<TId> active_set;
for (typename std::set<SweepEvent<TId, TNum>>::iterator it =
sweep_v_events.begin();
it != sweep_v_events.end(); ++it) {
const SweepEvent<TId, TNum> &v_evt = *it;
if (v_evt.type == START) {
active_set.add(v_evt.rect_id);
} else {
active_set.subtract(v_evt.rect_id);
}
if (active_regions.size() > 0 && active_regions.back().first == v_evt.y) {
active_regions.back().second = active_set;
} else {
active_regions.push_back(std::make_pair(v_evt.y, active_set));
}
}
#ifdef RECTS_DEBUG
std::cout << "x:" << h_evt.x;
for (std::vector<std::pair<TNum, IdSet>>::iterator it =
active_regions.begin();
it != active_regions.end(); ++it) {
std::cout << " " << it->first << "(" << it->second << ")"
<< ",";
}
std::cout << std::endl;
#endif
// To determine which started rectangles are ending this event, we make them
// all as false, or unseen during this sweep line.
for (typename std::map<StartedRect<TId, TNum>, bool>::iterator it =
started_rects.begin();
it != started_rects.end(); ++it) {
it->second = false;
}
// This for loop will iterate all potential new rectangles and either
// discover it was already started (and then mark it true), or that it is a
// new rectangle and add it to the started rectangles. A started rectangle
// is unique if it has a distinct top, bottom, and set of rectangle IDs.
// This is tricky because a potential rectangle could be encountered here
// that has a non-unique top and bottom, so it shares geometry with an
// already started rectangle, but the set of rectangle IDs differs. In that
// case, we have a new rectangle, and the already existing started rectangle
// will not be marked as seen ("true" in the std::pair) and will get ended
// by the for loop after this one. This is as intended.
for (typename std::vector<std::pair<TNum, IdSet<TId>>>::iterator it =
active_regions.begin();
it != active_regions.end(); ++it) {
IdSet<TId> region_set = it->second;
if (region_set.isEmpty())
continue;
// An important property of active_regions is that each region where a set
// of rectangles applies is bounded at the bottom by the next (in the
// vector) region's starting y-coordinate.
typename std::vector<std::pair<TNum, IdSet<TId>>>::iterator next_it = it;
++next_it;
assert(next_it != active_regions.end());
TNum region_top = it->first;
TNum region_bottom = next_it->first;
StartedRect<TId, TNum> rect_key;
rect_key.id_set = region_set;
rect_key.left = h_evt.x;
rect_key.top = region_top;
rect_key.bottom = region_bottom;
// Remember that rect_key.left is ignored for the purposes of searching
// the started rects. This follows from the fact that a previously started
// rectangle would by definition have a left bound less than the current
// event's x-coordinate. We are interested in continuing the started
// rectangles by marking them seen (true) but we don't know, care, or wish
// to change the left bound at this point. If there are no matching
// rectangles for this region, start a new one and mark it as seen (true).
typename std::map<StartedRect<TId, TNum>, bool>::iterator
started_rect_it = started_rects.find(rect_key);
if (started_rect_it == started_rects.end()) {
started_rects[rect_key] = true;
} else {
started_rect_it->second = true;
}
}
// This for loop ends all rectangles that were unseen during this event.
// Because this is the first event where we didn't see this rectangle, it's
// right edge is exactly the current event's x-coordinate. With this, we
// have the final piece of information to output this rectangle's geometry
// and set of input rectangle IDs. To end a started rectangle, we erase it
// from the started_rects map and append the completed rectangle to the
// output vector.
for (typename std::map<StartedRect<TId, TNum>, bool>::iterator it =
started_rects.begin();
it != started_rects.end();
/* inc in body */) {
if (!it->second) {
const StartedRect<TId, TNum> &proto_rect = it->first;
Rect<TNum> out_rect;
out_rect.left = proto_rect.left;
out_rect.top = proto_rect.top;
out_rect.right = h_evt.x;
out_rect.bottom = proto_rect.bottom;
out->push_back(RectSet<TId, TNum>(proto_rect.id_set, out_rect));
started_rects.erase(it++); // Also increments out iterator.
#ifdef RECTS_DEBUG
std::cout << " <" << proto_rect.id_set << "(" << rect << ")"
<< std::endl;
#endif
} else {
// Remember this for loop has no built in increment step. We do it here.
++it;
}
}
}
}
void separate_frects_64(const std::vector<Rect<float>> &in,
std::vector<RectSet<uint64_t, float>> *out) {
separate_rects(in, out);
}
void separate_rects_64(const std::vector<Rect<int>> &in,
std::vector<RectSet<uint64_t, int>> *out) {
separate_rects(in, out);
}
} // namespace separate_rects
#ifdef RECTS_TEST
using namespace separate_rects;
int main(int argc, char **argv) {
#define RectSet RectSet<TId, TNum>
#define Rect Rect<TNum>
#define IdSet IdSet<TId>
typedef uint64_t TId;
typedef float TNum;
std::vector<Rect> in;
std::vector<RectSet> out;
std::vector<RectSet> expected_out;
in.push_back({0, 0, 4, 5});
in.push_back({2, 0, 6, 6});
in.push_back({4, 0, 8, 5});
in.push_back({0, 7, 8, 9});
in.push_back({10, 0, 18, 5});
in.push_back({12, 0, 16, 5});
in.push_back({20, 11, 24, 17});
in.push_back({22, 13, 26, 21});
in.push_back({32, 33, 36, 37});
in.push_back({30, 31, 38, 39});
in.push_back({40, 43, 48, 45});
in.push_back({44, 41, 46, 47});
in.push_back({50, 51, 52, 53});
in.push_back({50, 51, 52, 53});
in.push_back({50, 51, 52, 53});
in.push_back({0, 0, 0, 10});
in.push_back({0, 0, 10, 0});
in.push_back({10, 0, 0, 10});
in.push_back({0, 10, 10, 0});
for (int i = 0; i < 100000; i++) {
out.clear();
separate_rects(in, &out);
}
for (int i = 0; i < out.size(); i++) {
std::cout << out[i].id_set << "(" << out[i].rect << ")" << std::endl;
}
std::cout << "# of rects: " << out.size() << std::endl;
expected_out.push_back(RectSet(IdSet(0), Rect(0, 0, 2, 5)));
expected_out.push_back(RectSet(IdSet(1), Rect(2, 5, 6, 6)));
expected_out.push_back(RectSet(IdSet(1) | 0, Rect(2, 0, 4, 5)));
expected_out.push_back(RectSet(IdSet(1) | 2, Rect(4, 0, 6, 5)));
expected_out.push_back(RectSet(IdSet(2), Rect(6, 0, 8, 5)));
expected_out.push_back(RectSet(IdSet(3), Rect(0, 7, 8, 9)));
expected_out.push_back(RectSet(IdSet(4), Rect(10, 0, 12, 5)));
expected_out.push_back(RectSet(IdSet(5) | 4, Rect(12, 0, 16, 5)));
expected_out.push_back(RectSet(IdSet(4), Rect(16, 0, 18, 5)));
expected_out.push_back(RectSet(IdSet(6), Rect(20, 11, 22, 17)));
expected_out.push_back(RectSet(IdSet(6) | 7, Rect(22, 13, 24, 17)));
expected_out.push_back(RectSet(IdSet(6), Rect(22, 11, 24, 13)));
expected_out.push_back(RectSet(IdSet(7), Rect(22, 17, 24, 21)));
expected_out.push_back(RectSet(IdSet(7), Rect(24, 13, 26, 21)));
expected_out.push_back(RectSet(IdSet(9), Rect(30, 31, 32, 39)));
expected_out.push_back(RectSet(IdSet(8) | 9, Rect(32, 33, 36, 37)));
expected_out.push_back(RectSet(IdSet(9), Rect(32, 37, 36, 39)));
expected_out.push_back(RectSet(IdSet(9), Rect(32, 31, 36, 33)));
expected_out.push_back(RectSet(IdSet(9), Rect(36, 31, 38, 39)));
expected_out.push_back(RectSet(IdSet(10), Rect(40, 43, 44, 45)));
expected_out.push_back(RectSet(IdSet(10) | 11, Rect(44, 43, 46, 45)));
expected_out.push_back(RectSet(IdSet(11), Rect(44, 41, 46, 43)));
expected_out.push_back(RectSet(IdSet(11), Rect(44, 45, 46, 47)));
expected_out.push_back(RectSet(IdSet(10), Rect(46, 43, 48, 45)));
expected_out.push_back(RectSet(IdSet(12) | 13 | 14, Rect(50, 51, 52, 53)));
for (int i = 0; i < expected_out.size(); i++) {
RectSet &ex_out = expected_out[i];
if (std::find(out.begin(), out.end(), ex_out) == out.end()) {
std::cout << "Missing Rect: " << ex_out.id_set << "(" << ex_out.rect
<< ")" << std::endl;
}
}
for (int i = 0; i < out.size(); i++) {
RectSet &actual_out = out[i];
if (std::find(expected_out.begin(), expected_out.end(), actual_out) ==
expected_out.end()) {
std::cout << "Extra Rect: " << actual_out.id_set << "(" << actual_out.rect
<< ")" << std::endl;
}
}
return 0;
}
#endif