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Added Wave Function Collapse functionality
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// Copyright 2018 Wouter van Oortmerssen. All rights reserved. | ||
// | ||
// 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. | ||
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// Very simple tile based Wave Function Collapse ("Simple Tiled Model") implementation. | ||
// See: https://github.com/mxgmn/WaveFunctionCollapse | ||
// Derives adjacencies from an example rather than explicitly specified neighbors. | ||
// Does not do any symmetries/rotations unless they're in the example. | ||
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// Algorithm has a lot of similarities to A* in how its implemented. | ||
// Uses bitmasks to store the set of possible tiles, which currently limits the number of | ||
// unique tiles to 64. This restriction cool be lifted by using std::bitset instead. | ||
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// In my testing, generates a 50x50 tile map in <1 msec. 58% of such maps are conflict free. | ||
// At 100x100 that is 3 msec and 34%. | ||
// At 200x200 that is 24 msec and 13% | ||
// At 400x400 that is 205 msec and ~1% | ||
// Algorithm may need to extended to flood more than 2 neighbor levels to make it suitable | ||
// for really gigantic maps. | ||
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// inmap & outmap must point to row-major 2D arrays of the given size. | ||
// each in tile char must be in range 0..127, of which max 64 may actually be in use (may be | ||
// sparse). | ||
// Returns false if too many unique tiles in input. | ||
template<typename T> bool WaveFunctionCollapse(const int2 &insize, const char **inmap, | ||
const int2 &outsize, char **outmap, | ||
RandomNumberGenerator<T> &rnd, | ||
int &num_contradictions) { | ||
num_contradictions = 0; | ||
typedef uint64_t bitmask_t; | ||
const auto nbits = sizeof(bitmask_t) * 8; | ||
array<int, 256> tile_lookup; | ||
tile_lookup.fill(-1); | ||
struct Tile { bitmask_t sides[4] = {}; size_t freq = 0; char tidx = 0; }; | ||
vector<Tile> tiles; | ||
int2 neighbors[] = { { 0, 1 }, { 1, 0 }, { 0, -1 }, { -1, 0 } }; | ||
// Collect unique tiles and their frequency of occurrence. | ||
for (int iny = 0; iny < insize.y; iny++) { | ||
for (int inx = 0; inx < insize.x; inx++) { | ||
auto t = inmap[iny][inx]; | ||
if (tile_lookup[t] < 0) { | ||
// We use a bitmask_t mask for valid neighbors. | ||
if (tiles.size() == nbits - 1) return false; | ||
tile_lookup[t] = (int)tiles.size(); | ||
tiles.push_back(Tile()); | ||
} | ||
auto &tile = tiles[tile_lookup[t]]; | ||
tile.freq++; | ||
tile.tidx = t; | ||
} | ||
} | ||
// Construct valid neighbor bitmasks. | ||
for (int iny = 0; iny < insize.y; iny++) { | ||
for (int inx = 0; inx < insize.x; inx++) { | ||
auto t = inmap[iny][inx]; | ||
auto &tile = tiles[tile_lookup[t]]; | ||
int ni = 0; | ||
for (auto n : neighbors) { | ||
auto p = (n + int2(inx, iny) + insize) % insize; | ||
auto tn = inmap[p.y][p.x]; | ||
assert(tile_lookup[tn] >= 0); | ||
tile.sides[ni] |= 1 << tile_lookup[tn]; | ||
ni++; | ||
} | ||
} | ||
} | ||
size_t most_common_tile_id = 0; | ||
size_t most_common_tile_freq = 0; | ||
for (auto &tile : tiles) if (tile.freq > most_common_tile_freq) { | ||
most_common_tile_freq = tile.freq; | ||
most_common_tile_id = &tile - &tiles[0]; | ||
} | ||
// Track an open list (much like A*) of next options, sorted by best candidate at the end. | ||
list<pair<int2, int>> open, temp; | ||
// Store a bitmask per output cell of remaining possible choices. | ||
auto max_bitmask = (1 << tiles.size()) - 1; | ||
enum class State : uchar { NEW, OPEN, CLOSED }; | ||
struct Cell { | ||
bitmask_t wf; | ||
uchar popcnt = 0; | ||
State state = State::NEW; | ||
decltype(open)::iterator it; | ||
Cell(bitmask_t wf, uchar popcnt) : wf(wf), popcnt(popcnt) {} | ||
}; | ||
vector<vector<Cell>> cells(outsize.y, vector<Cell>(outsize.x, Cell(max_bitmask, tiles.size()))); | ||
auto start = rndivec<int, 2>(rnd, outsize); | ||
open.push_back({ start, 0 }); // Start. | ||
auto &scell = cells[start.y][start.x]; | ||
scell.state = State::OPEN; | ||
scell.it = open.begin(); | ||
// Pick tiles until no more possible. | ||
while (!open.empty()) { | ||
// Simply picking the first list item results in the same chance of conflicts as | ||
// random picks over equal options, but it is assumed the latter could generate more | ||
// interesting maps. | ||
size_t num_candidates = 1; | ||
auto numopts_0 = cells[open.back().first.y][open.back().first.x].popcnt; | ||
for (auto it = ++open.rbegin(); it != open.rend(); ++it) | ||
if (numopts_0 == cells[it->first.y][it->first.x].popcnt && | ||
open.back().second == it->second) | ||
num_candidates++; | ||
else | ||
break; | ||
auto candidate_i = rnd(num_candidates); | ||
auto candidate_it = --open.end(); | ||
for (int i = 0; i < candidate_i; i++) --candidate_it; | ||
auto cur = candidate_it->first; | ||
temp.splice(temp.end(), open, candidate_it); | ||
auto &cell = cells[cur.y][cur.x]; | ||
assert(cell.state == State::OPEN); | ||
cell.state = State::CLOSED; | ||
bool contradiction = !cell.popcnt; | ||
if (contradiction) { | ||
num_contradictions++; | ||
// Rather than failing right here, fill in the whole map as best as possible just in | ||
// case a map with bad tile neighbors is still useful to the caller. | ||
// As a heuristic lets just use the most common tile, as that will likely have the | ||
// most neighbor options. | ||
cell.wf = 1 << most_common_tile_id; | ||
cell.popcnt = 1; | ||
} | ||
// From our options, pick one randomly, weighted by frequency of tile occurrence. | ||
// First find total frequency. | ||
size_t total_freq = 0; | ||
for (size_t i = 0; i < tiles.size(); i++) if (cell.wf & (1 << i)) total_freq += tiles[i].freq; | ||
auto freqpick = rnd(total_freq); | ||
// Now pick. | ||
size_t picked = 0; | ||
for (size_t i = 0; i < tiles.size(); i++) if (cell.wf & (1 << i)) { | ||
picked = i; | ||
if ((freqpick -= tiles[i].freq) <= 0) break; | ||
} | ||
assert(freqpick <= 0); | ||
// Modify the picked tile. | ||
auto &tile = tiles[picked]; | ||
outmap[cur.y][cur.x] = tile.tidx; | ||
cell.wf = 1 << picked; // Exactly one option remains. | ||
cell.popcnt = 1; | ||
// Now lets cycle thru neighbors, reduce their options (and maybe their neighbors options), | ||
// and add them to the open list for next pick. | ||
int ni = 0; | ||
for (auto n : neighbors) { | ||
auto p = (cur + n + outsize) % outsize; | ||
auto &ncell = cells[p.y][p.x]; | ||
if (ncell.state != State::CLOSED) { | ||
ncell.wf &= tile.sides[ni]; // Reduce options. | ||
ncell.popcnt = PopCount(ncell.wf); | ||
int totalnnumopts = 0; | ||
if (!contradiction) { | ||
// Hardcoded second level of neighbors of neighbors, to reduce chance of | ||
// contradiction. | ||
// Only do this when our current tile isn't a contradiction, to avoid | ||
// artificially shrinking options. | ||
int nni = 0; | ||
for (auto nn : neighbors) { | ||
auto pnn = (p + nn + outsize) % outsize; | ||
auto &nncell = cells[pnn.y][pnn.x]; | ||
if (nncell.state != State::CLOSED) { | ||
// Collect the superset of possible options. If we remove anything but | ||
// these, we are guaranteed the direct neigbor always has a possible | ||
//pick. | ||
bitmask_t superopts = 0; | ||
for (size_t i = 0; i < tiles.size(); i++) | ||
if (ncell.wf & (1 << i)) | ||
superopts |= tiles[i].sides[nni]; | ||
nncell.wf &= superopts; | ||
nncell.popcnt = PopCount(nncell.wf); | ||
} | ||
totalnnumopts += nncell.popcnt; | ||
nni++; | ||
} | ||
} | ||
if (ncell.state == State::OPEN) { | ||
// Already in the open list, remove it for it to be re-added just in case | ||
// its location is not optimal anymore. | ||
totalnnumopts = min(totalnnumopts, ncell.it->second); | ||
temp.splice(temp.end(), open, ncell.it); // Avoid alloc. | ||
} | ||
// Insert this neighbor, sorted by lowest possibilities. | ||
// Use total possibilities of neighbors as a tie-breaker to avoid causing | ||
// contradictions by needless surrounding of tiles. | ||
decltype(open)::iterator dit = open.begin(); | ||
for (auto it = open.rbegin(); it != open.rend(); ++it) { | ||
auto onumopts = cells[it->first.y][it->first.x].popcnt; | ||
if (onumopts > ncell.popcnt || | ||
(onumopts == ncell.popcnt && it->second >= totalnnumopts)) { | ||
dit = it.base(); | ||
break; | ||
} | ||
} | ||
if (temp.empty()) temp.push_back({}); | ||
open.splice(dit, temp, ncell.it = temp.begin()); | ||
*ncell.it = { p, totalnnumopts }; | ||
ncell.state = State::OPEN; | ||
} | ||
ni++; | ||
} | ||
} | ||
return true; | ||
} |
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// Example of using Wave Function Collapse to generate gameworlds based on tiles. | ||
// Using ascii chars here for simplicity. | ||
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// Using """ string literals so we don't have to escape \ :( | ||
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tilemap :== [ | ||
""" /--\ """, | ||
""" | | """, | ||
""" | | """, | ||
"""/--J L--\ """, | ||
"""| | """, | ||
"""| | """, | ||
"""L--\ /--J """, | ||
""" | | """, | ||
""" | | """, | ||
""" L--J """, | ||
""" """, | ||
] | ||
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benchmark :== false | ||
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if benchmark: | ||
no_conflicts := 0 | ||
for(1000) i: | ||
outmap, conflicts := wave_function_collapse(tilemap, xy { 100, 100 }) | ||
print i + ": " + conflicts | ||
if not conflicts: no_conflicts++ | ||
print no_conflicts | ||
print seconds_elapsed() | ||
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else: | ||
// Just print a single no-conflict example. | ||
for(100) i: | ||
outmap, conflicts := wave_function_collapse(tilemap, xy { 100, 50 }) | ||
if not conflicts: | ||
print "iteration: " + i | ||
for(outmap) s: print s | ||
return from program | ||
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/* | ||
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prints: | ||
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| | /-\ /-------J | | L-J /--J | ||
| /--J | | | | | | | ||
| | | L-J | | /-\ | | ||
-----------J /-J | | | /------------\ | | | / | ||
| L-\ /----J | | | | | | | | ||
| | | /--J | | | L----J | | ||
| | L-\ | | | | | | ||
----\ | L-\ | | /-\ /-J | | L | ||
| | | | | | | | L-------------\ | /---\ | ||
| | | /-----J L-J L--J | L-\ | | | ||
| | | | | | | | | ||
| | | | /-------\ | | | | | ||
| | | | | | | L----J | | ||
| | /---------J L-----\ | /---J | | | ||
/-J | | | /-----J | /-J /----J | ||
| | | | /----\ | | | | | ||
| | | /-\ /----J | | | | | | | ||
| | | | | | | | | | | /------J | ||
| | | | | /-J /--\ /-----J | | | | | | ||
| L-J | | | | | | | | | /--J | | ||
L-----\ | | | | L--J | L---\ | | | /--\ /----\ | ||
| /---\ | | | | | | L------J | | | | | | ||
| | | | | | | | | | | | | | | ||
--\ | | L-----J | | | | | | | | | L-- | ||
| | | | L--\ | /--------J | | | | /--J | ||
--J /--J | /-\ | | | | | /--J | | | /----- | ||
| L---\ | | | | | | | | | L---J | | ||
| | | | | | | | | /----\ | | | | ||
| L--J | | | | | /-\ | | | | | /----\ L----\ | ||
| | | L-J | | | | | | | | | | | | ||
L------------\ | | L-------J | | | | | | | | | | ||
| | | | | | | | | | L--\ | | ||
/-------------J | | /---\ | L------J | | | | | | | ||
| /-J | | | /---J | | | | | | | ||
| | L------\ | L---\ | | | | L--\ /--J | | ||
| /-\ L-\ | | | | | L-----\ | | | | | ||
| | | | | | | | /----\ | /-\ | L--\ | | | | ||
--\ | | | | L---J | L--\ | | | | | | | | | L | ||
| | | | | | | | /-J | L-J | | | | | ||
L-J L-J L---------\ | | | | | /--J | | | | ||
| L-\ | | | | | | | L---\ | ||
----\ /---\ | | L------J | | | | | | /-- | ||
| | | | | | | L--\ | | | | | ||
| L---J | /---J | | | L--J | | | ||
| | /--\ | /--\ | | | | | | ||
L------\ /-----J | | | | | | | /--J | | | ||
| /--\ | | | | L--J | | | | | | ||
| | | | | | | /-\ L-------\ | L----------\ | | | ||
| | L---J | | | | | | | | L--J | ||
| | | | | | | L-J | | ||
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*/ | ||
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