Detect all closed polygons given a set of line segments

Repeat poly detection by cutting the detected polygon/cycle ears (free point connected to two lines), eliminating the detected lines picked two times and collinear remaining lines until no cycle is detected.

See how fast it is:

$ time ./app

nPolys:241 dissolveSteps:2 lines:514

real 0m0.080s

user 0m0.063s

sys 0m0.016s

Originally I tried the approach of Alfredo Ferreira (https://web.ist.utl.pt/alfredo.ferreira/publications/12EPCG-PolygonDetection.pdf) and for the lines from main.cpp it took more than 15 minutes! Plus that it uses a few matrixes with the size of the number of vertives squared!

While it is impossible to use, I began simplifying the algorithm using a recursion algorightm (see function BuildCycle() ).

I kept the original idea of breaking the line segments by their intersections, but without the sweep line method.

It makes sure that no line segments are crossed (collinear) and that the polygon is convex. Plus that each line segment point is taken maximum 2 times (it is connected to another line segment).

With a bit of care, the algo can be optimized at least ten times (remove recursion, precompute similar points using indices, we already know the intersections (optimize AddLineId), ...), but I leave that as a homework ;) Right now the detector has no limitation and by optimizing it, it could be used for very large line sets.

PolyDetector can be reused by taking advantage of the caching previously done (processed set, neighbors graph ...).

bool PolyCycle::AddLineId(PolyDetector &pd, uint32_t id)
{
    auto l = pd.findLine(id);
    if (!l) return false;

    l->test0 = 0; // a cnt
    l->test1 = 0; // b cnt

    for (auto &id1 : idx)
    {
        auto l1 = pd.findLine(id1);
        if (!l1) continue;

        if (!pointsDiffer(l->a, l1->a) || !pointsDiffer(l->a, l1->b))
        {
            if (Collinear(l->a, l1->a, l1->b) && Collinear(l->b, l1->a, l1->b)) // collinear points
                return false;
            l->test0++;
        }
        if (!pointsDiffer(l->b, l1->a) || !pointsDiffer(l->b, l1->b))
        {
            if (Collinear(l->a, l1->a, l1->b) && Collinear(l->b, l1->a, l1->b)) // collinear points
                return false;
            l->test1++;
        }

        if (l->test0 >= 2 || l->test1 >= 2)
        {
            //logoutf("line %u can't be added to cycle! ta:%d tb:%d ids: [%s]", id, l->test0, l->test1, idxToString().c_str());
            return false;
        }

        PolyLine ls(l->center, l1->center);
        for (auto &id2 : idx)
        {
            if (id2 != id && id2 != id1)
            {
                auto l2 = pd.findLine(id2);
                if (l2 && ls.PolyIntersects(*l2))
                {
                    return false;
                }
            }
        }
    }
    idx.insert(id);
    return true;
}

bool PolyDetector::BuildCycle(uint32_t id, PolyCycle cycle) // as value!
{
    //if (cycle.idx.size() >= 15) // limit the number of poly edges? maybe someone needs that
    //    return true;

    auto l = findLine(id);
    if (!l)
        return true;

    if (_neighbors[id].size() < 4) // connected / line splitted
    {
        return true;
    }

    if (!silent)
        cycle.print((std::string("[PROC:") + std::to_string(id) + std::string("]")).c_str());

    // cycle closed! -> cache it
    if (cycle.canBeClosed(id))
    {
        cycle.isClosed = true;

        if (!silent)
            cycle.print("[CLOSED] ");

        if (!similarCycle(_cycles, cycle))
        {
            _cycles.push_back(cycle);
            if (!silent)
                cycle.print("[ACCEPTED] ");
            //logoutf("nCycles:%u", uint32_t(_cycles.size()));
        }
        else
        {
            if (!silent)
                cycle.print("[CYCLE_EXISTS] ");
        }

        return true;
    }

    // the cycle should be discarded
    if (!cycle.AddLineId(*this, l->id))
    {
        return true;
    }

    // don't return to the same path again
    if (CycleProcessed(cycle.idx))
    {
        if (!silent)
            cycle.print("[PROCESSED!] ");
        return true;
    }
    processed.insert(cycle.idx);

    // recur neighbors
    for (auto &nid : _neighbors[id])
    {
        if (_neighbors[nid].size() < 4) continue;
        if (cycle.canBeClosed(nid) || !cycle.contains(nid))
        {
            if (!silent)
                cycle.print((std::string("[NEIGN:") + std::to_string(nid) + std::string("]")).c_str());
            BuildCycle(nid, cycle); // recur
        }
    }

    return true;
}

Very simple line neighbor graph, where the key is [line id] and the value is a [list of neighbors], sorted by the line segment center distance!

// Build neighbors
    std::vector<uint32_t> neigh;
    _neighbors.clear();
    for (uint32_t i = 0; i < lines.size(); ++i)
    {
        auto &l1 = lines[i];
        neigh.clear();
        for (uint32_t j = i + 1; j < lines.size(); ++j)
        {
            auto &l2 = lines[j];
            if (l1.HasCommonPoints(l2))
            {
                neigh.push_back(j);
            }
        }
        if (!neigh.empty())
        {
            std::sort(neigh.begin(), neigh.end(), [this, &i, &l1](const uint32_t &a, const uint32_t &b) {
                auto da = lines[a].center.squaredist(l1.center);
                auto db = lines[b].center.squaredist(l1.center);
                return da < db;
            });
            for (auto &n : neigh)
            {
                _neighbors[i].push_back(n);
                _neighbors[n].push_back(i);
            }
        }
    }

And now start the algo:

for (auto &kv : _neighbors) // point by point
    {
        if (_neighbors[kv.first].size() < 4) continue; // connected
        PolyCycle cycle;
        cycle.startIdx = kv.first;
        BuildCycle(kv.first, cycle);
    }

Very simple: pass the list of line segments in 2D, detect and process the detected polygons.

    std::vector<PolyLine> lines = {
        { { 0.481273, 19.263916 }, { 2.672669, -20.676010 } },
    ....
    };
    PolyDetector pd; // can be reused
    for (auto &l : lines)
        pd.AddLine(l);

    if (!pd.DetectPolygons()) // can be reused
    {
        logoutf("%s", "WARN: cannot detect polys!");
        return -1;
    }

    for (auto &poly : pd.polys) // here are the detected polys
    {
        for (auto &p : poly.p)
        {
            logoutf("[%u] p:{%f %f}", poly.id, p.x, p.y);
        }
    }

[100] p:{-5.966534 -16.157389} [100] p:{-5.985141 -16.163368} [100] p:{-6.596913 -14.281137} [104] p:{-5.753591 -16.088951} [104] p:{-5.921042 -16.142767} [104] p:{-7.055668 -11.525142} [106] p:{-4.095016 -15.555901} [106] p:{-5.739954 -16.136740} [106] p:{-5.753591 -16.088951} [110] p:{-1.943092 -14.864294} [110] p:{-1.957186 -14.801019} [110] p:{-4.095016 -15.555901} [112] p:{-6.583131 -15.457682} [112] p:{-7.130582 -13.257606} [112] p:{-8.761721 -8.122437} [114] p:{-1.003788 -14.845609} [114] p:{-1.850288 -15.280960} [114] p:{-1.884779 -15.126103} [116] p:{0.464259 -14.090594} [116] p:{-1.003788 -14.845609} [116] p:{-1.884779 -15.126103} [116] p:{-1.943092 -14.864294} [120] p:{0.464259 -14.090594} [120] p:{0.845067 -14.256959} [120] p:{0.995011 -13.920016} [120] p:{-1.003788 -14.845609} [124] p:{-6.596913 -14.281137} [124] p:{-7.672495 -11.079787} [124] p:{-7.787011 -10.619578} [126] p:{0.845067 -14.256959} [126] p:{0.995011 -13.920016} [126] p:{2.279338 -13.507246} [126] p:{2.295142 -13.795278} [128] p:{0.464259 -14.090594} [128] p:{0.995011 -13.920016} [128] p:{1.054096 -13.787243} [131] p:{0.995011 -13.920016} [131] p:{1.054096 -13.787243} [131] p:{1.361359 -13.629218} [131] p:{2.268456 -13.308915} [131] p:{2.279338 -13.507246} [133] p:{2.279338 -13.507246} [133] p:{2.295142 -13.795278} [133] p:{3.840607 -13.005469} [133] p:{3.898518 -13.284785} [135] p:{1.054096 -13.787243} [135] p:{1.080247 -13.728479} [135] p:{1.361359 -13.629218} [139] p:{1.361359 -13.629218} [139] p:{2.260654 -13.166713} [139] p:{2.268456 -13.308915} [141] p:{2.268456 -13.308915} [141] p:{2.279338 -13.507246} [141] p:{3.791984 -12.770947} [141] p:{3.840607 -13.005469} [143] p:{2.260654 -13.166713} [143] p:{2.268456 -13.308915} [143] p:{3.718580 -12.416905} [143] p:{3.791984 -12.770947} [145] p:{23.993586 -6.528498} [145] p:{24.577854 -6.700784} [145] p:{3.840607 -13.005469} [145] p:{3.898518 -13.284785} [147] p:{-7.130582 -13.257606} [147] p:{-7.672495 -11.079787} [147] p:{-8.761721 -8.122437} [147] p:{-9.490391 -5.669026} [149] p:{2.158531 -11.305436} [149] p:{2.260654 -13.166713} [149] p:{3.065557 -9.267232} [149] p:{3.718580 -12.416905} [14] p:{-3.623546 -24.298502} [14] p:{-3.812639 -24.723419} [14] p:{-4.919745 -20.217789} [151] p:{22.618740 -6.123089} [151] p:{23.993586 -6.528498} [151] p:{3.791984 -12.770947} [151] p:{3.840607 -13.005469} [153] p:{18.384180 -4.874419} [153] p:{22.618740 -6.123089} [153] p:{3.718580 -12.416905} [153] p:{3.791984 -12.770947} [155] p:{18.384180 -4.874419} [155] p:{3.065557 -9.267232} [155] p:{3.718580 -12.416905} [155] p:{6.570628 -1.390888} [157] p:{-7.055668 -11.525142} [157] p:{-8.794989 -4.446561} [157] p:{-9.039429 -4.572016} [159] p:{1.680041 -2.584581} [159] p:{2.158531 -11.305436} [159] p:{3.065557 -9.267232} [161] p:{-7.672495 -11.079787} [161] p:{-7.787011 -10.619578} [161] p:{-9.490391 -5.669026} [161] p:{-9.650656 -4.885727} [161] p:{-9.713459 -4.917960} [163] p:{-7.787011 -10.619578} [163] p:{-9.263258 -4.686897} [163] p:{-9.650656 -4.885727} [166] p:{1.623343 -1.551223} [166] p:{1.680041 -2.584581} [166] p:{3.065557 -9.267232} [166] p:{4.469060 -0.771186} [166] p:{6.570628 -1.390888} [170] p:{-8.761721 -8.122437} [170] p:{-9.490391 -5.669026} [170] p:{-9.738426 -4.930776} [170] p:{-9.770322 -4.947144} [178] p:{-9.490391 -5.669026} [178] p:{-9.713459 -4.917960} [178] p:{-9.738426 -4.930776} [183] p:{-9.770322 -4.947144} [183] p:{-9.850037 -4.696186} [183] p:{-9.917417 -5.022640} [183] p:{-9.975594 -4.730603} [185] p:{-9.738426 -4.930776} [185] p:{-9.770322 -4.947144} [185] p:{-9.820008 -4.687955} [185] p:{-9.850037 -4.696186} [187] p:{-9.713459 -4.917960} [187] p:{-9.738426 -4.930776} [187] p:{-9.784650 -4.678263} [187] p:{-9.820008 -4.687955} [189] p:{-9.650656 -4.885727} [189] p:{-9.713459 -4.917960} [189] p:{-9.723531 -4.661512} [189] p:{-9.784650 -4.678263} [191] p:{-9.263258 -4.686897} [191] p:{-9.298562 -4.545022} [191] p:{-9.650656 -4.885727} [191] p:{-9.723531 -4.661512} [194] p:{-10.205222 -3.577986} [194] p:{-9.850037 -4.696186} [194] p:{-9.975594 -4.730603} [196] p:{-10.205222 -3.577986} [196] p:{-10.223121 -3.488138} [196] p:{-9.820008 -4.687955} [196] p:{-9.850037 -4.696186} [198] p:{-10.223121 -3.488138} [198] p:{-10.396303 -2.618845} [198] p:{-9.784650 -4.678263} [198] p:{-9.820008 -4.687955} [19] p:{-3.460271 -23.931604} [19] p:{-3.494256 -24.007971} [19] p:{-3.916646 -22.527483} [200] p:{-9.039429 -4.572016} [200] p:{-9.065367 -4.481102} [200] p:{-9.263258 -4.686897} [200] p:{-9.298562 -4.545022} [202] p:{-10.396303 -2.618845} [202] p:{-10.410321 -2.548471} [202] p:{-9.723531 -4.661512} [202] p:{-9.784650 -4.678263} [204] p:{-10.410321 -2.548471} [204] p:{-10.446211 -2.368323} [204] p:{-9.298562 -4.545022} [204] p:{-9.723531 -4.661512} [204] p:{-9.893959 -2.152269} [206] p:{-8.794989 -4.446561} [206] p:{-8.804099 -4.409484} [206] p:{-9.039429 -4.572016} [206] p:{-9.065367 -4.481102} [208] p:{-9.065367 -4.481102} [208] p:{-9.298562 -4.545022} [208] p:{-9.746279 -2.094493} [208] p:{-9.893959 -2.152269} [210] p:{-8.804099 -4.409484} [210] p:{-9.065367 -4.481102} [210] p:{-9.405672 -1.961240} [210] p:{-9.746279 -2.094493} [212] p:{-8.629501 -4.361626} [212] p:{-8.794989 -4.446561} [212] p:{-8.804099 -4.409484} [216] p:{-4.532474 -3.238592} [216] p:{-4.728305 -2.359363} [216] p:{-8.629501 -4.361626} [219] p:{-10.205222 -3.577986} [219] p:{-10.223121 -3.488138} [219] p:{-10.418082 -2.907860} [227] p:{-15.334239 -1.867071} [227] p:{-17.146812 -2.402270} [227] p:{-20.989971 -2.829295} [227] p:{-22.073826 -3.120804} [229] p:{-10.418082 -2.907860} [229] p:{-10.573626 -2.418170} [229] p:{-10.581562 -2.421275} [22] p:{-3.400043 -23.796263} [22] p:{-3.460271 -23.931604} [22] p:{-3.916646 -22.527483} [22] p:{-4.425184 -20.745045} [232] p:{-14.743880 -1.692756} [232] p:{-15.334239 -1.867071} [232] p:{-18.325047 -2.112545} [232] p:{-20.989971 -2.829295} [236] p:{1.474267 -1.592087} [236] p:{1.623343 -1.551223} [236] p:{1.680041 -2.584581} [238] p:{-10.410321 -2.548471} [238] p:{-10.446211 -2.368323} [238] p:{-10.466318 -2.376189} [240] p:{-10.573626 -2.418170} [240] p:{-10.581562 -2.421275} [240] p:{-10.869467 -1.486810} [240] p:{-10.894306 -1.490433} [244] p:{-10.894306 -1.490433} [244] p:{-10.974771 -1.250936} [244] p:{-13.347639 -1.529087} [244] p:{-15.334239 -1.867071} [244] p:{-17.146812 -2.402270} [250] p:{-10.087907 -1.372831} [250] p:{-10.446211 -2.368323} [250] p:{-10.628818 -1.451715} [250] p:{-9.893959 -2.152269} [252] p:{-0.080468 0.026109} [252] p:{-2.194826 -0.221739} [252] p:{-4.728305 -2.359363} [252] p:{-5.109735 -0.646837} [255] p:{-16.738022 -1.685705} [255] p:{-18.102158 -1.849558} [255] p:{-18.325047 -2.112545} [255] p:{-20.006651 -2.309665} [257] p:{-10.490153 -2.302852} [257] p:{-10.738206 -1.467668} [257] p:{-10.760550 -1.470926} [259] p:{-10.087907 -1.372831} [259] p:{-9.746279 -2.094493} [259] p:{-9.893959 -2.152269} [259] p:{-9.957594 -1.353827} [261] p:{-13.336119 -1.277086} [261] p:{-14.743880 -1.692756} [261] p:{-16.738022 -1.685705} [261] p:{-18.325047 -2.112545} [263] p:{-9.405672 -1.961240} [263] p:{-9.568854 -1.297135} [263] p:{-9.746279 -2.094493} [263] p:{-9.957594 -1.353827} [266] p:{-6.602332 -0.864510} [266] p:{-9.405672 -1.961240} [266] p:{-9.568854 -1.297135} [268] p:{-13.347639 -1.529087} [268] p:{-14.743880 -1.692756} [268] p:{-15.334239 -1.867071} [26] p:{-3.916646 -22.527483} [26] p:{-4.425184 -20.745045} [26] p:{-5.611146 -17.215162} [26] p:{-5.638680 -17.229322} [278] p:{1.533043 0.094574} [278] p:{1.623343 -1.551223} [278] p:{4.469060 -0.771186} [280] p:{-10.974771 -1.250936} [280] p:{-11.014673 -1.132173} [280] p:{-13.347639 -1.529087} [282] p:{-10.869467 -1.486810} [282] p:{-10.894306 -1.490433} [282] p:{-10.945479 -1.247502} [282] p:{-10.974771 -1.250936} [284] p:{-10.760550 -1.470926} [284] p:{-10.837291 -1.234820} [284] p:{-10.869467 -1.486810} [284] p:{-10.945479 -1.247502} [286] p:{-10.738206 -1.467668} [286] p:{-10.760550 -1.470926} 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