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libgeos / geos

Geometry Engine, Open Source
https://libgeos.org
GNU Lesser General Public License v2.1
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Inconsistent intersection between (Multi)Polygons #454

Closed BuonOmo closed 3 years ago

BuonOmo commented 3 years ago

Hi,

Thanks for the great lib, since I'm now a maintainer of https://github.com/rgeo/rgeo, hence I use it a lot 🙂

Context

We recently encountered a weird intersection issue. I'll try to give you some context here, you can skip to reproduction if you want. We have a geometry subtraction tool in my company, so when we sub a geometry a from a geometry b, we get c (= b - a). The issue is that due to border simplification we sometimes have tiny polygons left here and there. So we added a tool to remove those if area is small enough. So now we get d (= filter(c, area > 1e-4). The issue is that it changes the intersection between the result (d or c) and a. Meaning inter(c, a) is a MultiLineString, which is expected. However inter(d, a) is a GeometryCollection containing a small polygon. And this really is not expected.

Reproduction

WKT files The result of `b - a` (save it under c.wkt): ```wkt MULTIPOLYGON (((-2.621863 47.411589, -2.621022 47.4132, -2.617341 47.411687, -2.622267 47.409085, -2.626996 47.411454, -2.621863 47.411589)), ((-2.396067 46.725287, -2.394785 46.726343, -2.386636 46.727524, -2.386744 46.729856, -2.383932 46.730746, -2.381656 46.733492, -2.376994 46.732368, -2.374453 46.733779, -2.370908 46.731882, -2.362734 46.730762, -2.360788 46.72923, -2.358503 46.729831, -2.354402 46.727892, -2.347617 46.72901, -2.344215 46.727768, -2.342028 46.725752, -2.343392 46.723519, -2.340689 46.72024, -2.338244 46.719071, -2.333706 46.718947, -2.328172 46.720731, -2.31797 46.719928, -2.318151 46.718269, -2.311047 46.712271, -2.306086 46.711201, -2.30527 46.709631, -2.297268 46.705275, -2.292895 46.700497, -2.285616 46.695338, -2.282817 46.691852, -2.286244 46.691103, -2.28997 46.692848, -2.295227 46.693234, -2.300247 46.692511, -2.311692 46.696084, -2.31451 46.695542, -2.315733 46.693043, -2.318217 46.691689, 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47.083041, -0.478752 47.081727, -0.484783 47.081687, -0.487739 47.080881, -0.490791 47.082896, -0.493101 47.083353, -0.504174 47.079332, -0.507317 47.079241, -0.511785 47.077466, -0.51525 47.078035, -0.525741 47.073919, -0.535313 47.0722, -0.544635 47.068135, -0.546309 47.066274, -0.557553 47.06409, -0.559461 47.061813, -0.5567 47.060691, -0.554371 47.05726, -0.558239 47.056069, -0.558275 47.053228, -0.556006 47.044378, -0.556265 47.042695, -0.548737 47.04057, -0.542042 47.034972, -0.542997 47.033622, -0.542336 47.032532, -0.54533 47.030668, -0.54581 47.029103, -0.547006 47.028835, -0.547965 47.029652, -0.551732 47.029048, -0.555679 47.030902, -0.562342 47.030496, -0.564087 47.026005, -0.563775 47.02414, -0.564869 47.020141, -0.569053 47.018291, -0.574987 47.017828, -0.580904 47.014612, -0.587014 47.009192, -0.586932 47.006709, -0.58775 47.005337, -0.594749 47.002794, -0.597171 47.000769, -0.593961 46.998759, -0.595493 46.99791, -0.601611 46.997764, -0.618781 46.992342, -0.621938 46.993911, -0.62494 46.992792, -0.624561 46.994115, -0.627917 46.995691, -0.626743 46.996879, -0.63266 46.997508, -0.635438 46.995724, -0.640352 46.996116, -0.641046 46.994672, -0.642167 46.994818, -0.645504 46.99212, -0.646962 46.992308, -0.646391 46.99368, -0.649992 46.994917, -0.648025 46.996594, -0.650398 46.997689, -0.653462 46.997772, -0.657311 46.999199, -0.657708 46.9986, -0.660979 46.998839, -0.661627 46.997686, -0.669937 47.000802, -0.670368 47.002636, -0.671843 47.003185, -0.674719 47.001621, -0.676179 47.001885, -0.676831 47.000296, -0.674732 46.999172, -0.676007 46.997074, -0.675567 46.996648, -0.68038 46.993238, -0.678529 46.992114, -0.677686 46.989976, -0.680188 46.987659, -0.682981 46.98842, -0.686887 46.988065, -0.689599 46.990414, -0.689629 46.993058, -0.693412 46.992411, -0.696663 46.994873, -0.698748 46.99461, -0.700809 46.992531, -0.70435 46.992196, -0.703637 46.991424, -0.704682 46.990212, -0.712202 46.986674, -0.715947 46.98402, -0.718107 46.987193, -0.72926 46.995934, -0.732543 46.997508, -0.739475 46.998787, -0.743405 47.000992, -0.743626 46.994335, -0.74298 46.992012, -0.747754 46.991537, -0.753551 46.992972, -0.756819 46.991958, -0.761515 46.992264, -0.76411 46.992997, -0.765475 46.994016, -0.76528 46.994815, -0.767098 46.995785, -0.768885 46.995031, -0.768693 46.998337, -0.767998 46.99898, -0.768472 47.001449, -0.769335 47.002974, -0.771352 47.003471, -0.772268 47.004577, -0.773718 47.004606, -0.776458 47.003002, -0.778001 47.00428, -0.779699 47.004275, -0.781774 47.002141, -0.783438 47.001813, -0.784541 47.002807, -0.784486 47.004214, -0.786724 47.005452, -0.78967 47.003752, -0.789635 47.002406, -0.791189 47.0001, -0.796264 46.996051, -0.800662 46.994378, -0.804104 46.99387, -0.807032 46.994405, -0.810871 46.991732, -0.809145 46.99059, -0.808373 46.991571, -0.805102 46.989541, -0.807346 46.988608, -0.808466 46.986718, -0.809551 46.988562, -0.812299 46.989251, -0.812597 46.990568, -0.815701 46.989765, -0.811339 46.991774, -0.811747 46.994549, -0.815426 46.993264, -0.817527 46.993124, -0.81869 46.994079, -0.826568 46.992643, -0.836343 46.985762, -0.839504 46.985428, -0.842993 46.990173, -0.846592 46.986729, -0.847436 46.986872, -0.847915 46.982014, -0.849641 46.981979, -0.857129 46.978461, -0.85654 46.977397, -0.849242 46.97382, -0.8526 46.971008, -0.854617 46.971188, -0.860658 46.968886, -0.861437 46.969427, -0.861169 46.970234, -0.862803 46.970306, -0.862043 46.971125, -0.863063 46.971487, -0.863054 46.972617, -0.866704 46.973134, -0.867239 46.972541, -0.868179 46.973273, -0.869896 46.972059, -0.872356 46.973921, -0.87925 46.974666, -0.880167 46.975259, -0.879569 46.976065, -0.882064 46.977455, -0.882176 46.976556, -0.884937 46.977334, -0.885156 46.976298, -0.886918 46.976492, -0.888462 46.975566, -0.892187 46.976082, -0.892484 46.978577, -0.895071 46.979177, -0.894874 46.980231, -0.896843 46.980815, -0.893065 46.984496, -0.895727 46.985249, -0.89623 46.985842, -0.895404 46.986335, -0.898968 46.988701, -0.897484 46.989799, -0.90103 46.991734, -0.902515 46.993922, -0.904396 46.994915, -0.907873 46.994955, -0.908708 46.99287, -0.9117 46.995997, -0.912372 46.995659, -0.910853 46.994271, -0.912311 46.992815, -0.915289 46.992611, -0.915649 46.993302, -0.914227 46.994688, -0.916525 46.996111, -0.918747 46.995522, -0.918685 46.996536, -0.921435 46.998028, -0.917958 46.998454, -0.916957 46.999858, -0.914871 47.000633, -0.915853 47.001637, -0.919365 47.002324, -0.919706 47.003377, -0.925021 47.002535, -0.925042 46.999834, -0.928445 47.000682, -0.928661 47.002451, -0.935226 47.002345, -0.93278 47.00456, -0.931063 47.003357, -0.931039 47.004519, -0.928248 47.00382, -0.927473 47.006346, -0.929194 47.008111, -0.932389 47.006069, -0.932015 47.007985, -0.93295 47.007838, -0.933399 47.009041, -0.935539 47.007348, -0.934844 47.005633, -0.936462 47.005257, -0.937296 47.003048, -0.938529 47.0034, -0.938673 47.002401, -0.939634 47.002783, -0.939812 47.002193, -0.940278 47.003189, -0.941698 47.00358, -0.944993 46.998988, -0.947166 46.999717, -0.948313 47.001307, -0.947959 47.003694, -0.951958 47.002736, -0.953334 47.000764, -0.95504 46.999919, -0.955661 46.99757, -0.954756 46.995966, -0.956737 46.996404, -0.958285 46.99543, -0.957388 46.994887, -0.960803 46.994723, -0.959851 46.995287, -0.962158 46.995809, -0.961741 46.997277, -0.963159 46.996458, -0.964354 46.997292, -0.963447 46.998099, -0.964984 46.999584, -0.963101 47.00063, -0.963229 47.001985, -0.964014 47.003068, -0.966535 47.002838, -0.968005 47.004208, -0.967052 47.005199, -0.965982 47.004729, -0.968678 47.006687, -0.967816 47.007355, -0.970504 47.007588, -0.972909 47.009056, -0.973483 47.008101, -0.975229 47.008652, -0.974932 47.010525, -0.973166 47.012531, -0.975314 47.013218, -0.973361 47.016124, -0.975663 47.01687, -0.976156 47.018317, -0.978354 47.018918, -0.981873 47.018124, -0.981502 47.017046, -0.982976 47.016083, -0.980279 47.014309, -0.982174 47.010593, -0.995514 47.017676, -0.999529 47.020687, -1.002179 47.02152, -1.000567 47.022544, -1.002044 47.024403, -1.000672 47.02556, -0.999402 47.025138, -1.000446 47.022611, -0.997423 47.022981, -0.995461 47.024415, -1.000034 47.027594, -1.001848 47.027837, -1.003761 47.02556, -1.005871 47.027086, -1.008565 47.027608, -1.00369 47.029205, -1.003499 47.034155)) ```

Having the data saved in correct file, you can compile (I did it on a macos with clang and GEOS 3.9.1) and run the next source file:

#include <stdio.h>
#include <stdlib.h>
#include <geos_c.h>

static char* read_file(const char * filename);
static void print_inter_type(const GEOSContextHandle_t handle, const GEOSGeom a, const GEOSGeom b);
static GEOSGeom geom_from_file(const GEOSContextHandle_t handle, const char * filename);
static GEOSGeom remove_little_polygons(const GEOSContextHandle_t handle, const GEOSGeom geom);

int main(int argc, char const *argv[]) {
    GEOSContextHandle_t handle;
    GEOSGeom a, c, d;

    handle = GEOS_init_r();

    c = geom_from_file(handle, "c.wkt");
    a = geom_from_file(handle, "a.wkt");

    d = remove_little_polygons(handle, c);

    print_inter_type(handle, c, a);
    print_inter_type(handle, d, a);

    GEOSGeom_destroy_r(handle, a);
    GEOSGeom_destroy_r(handle, c);
    GEOSGeom_destroy_r(handle, d);
    GEOS_finish_r(handle);
    return 0;
}

static char* read_file(const char * filename) {
    char * buffer;
    long length;
    FILE * f = fopen (filename, "rb");

    if (f)
    {
        fseek (f, 0, SEEK_END);
        length = ftell (f);
        fseek (f, 0, SEEK_SET);
        buffer = malloc (length);
        if (buffer)
        {
            fread (buffer, 1, length, f);
        }
        fclose (f);
    }

    return buffer;
}

static void print_inter_type(const GEOSContextHandle_t handle, const GEOSGeom a, const GEOSGeom b) {
    GEOSGeom inter;
    char *buffer;
    inter = GEOSIntersection_r(handle, a, b);
    buffer = GEOSGeomType_r(handle, inter);
    printf("intersection type: %s\n", buffer);
    GEOSGeom_destroy_r(handle, inter);
    GEOSFree_r(handle, buffer);
}

static GEOSGeom geom_from_file(const GEOSContextHandle_t handle, const char * filename) {
    GEOSGeom result;
    GEOSWKTReader *reader;
    char *buffer;
    reader = GEOSWKTReader_create_r(handle);
    buffer = read_file(filename);
    result = GEOSWKTReader_read_r(handle, reader, buffer);
    free(buffer);
    GEOSWKTReader_destroy_r(handle, reader);
    return result;
}

static GEOSGeom remove_little_polygons(const GEOSContextHandle_t handle, const GEOSGeom geom) {
    size_t size, ngeoms = 0;
    GEOSGeom *geoms;
    GEOSGeom result;
    double area;
    size = GEOSGetNumGeometries_r(handle, geom);
    geoms = malloc(size * sizeof(GEOSGeom));
    for (size_t i = 0; i < size; i++)
    {
        const GEOSGeometry *temp = GEOSGetGeometryN_r(handle, geom, i);
        GEOSArea_r(handle, temp, &area);
        if (area > 1e-4) {
            geoms[ngeoms++] = GEOSGeom_clone_r(handle, temp);
        }
    }

    result = GEOSGeom_createCollection_r(handle, GEOS_MULTIPOLYGON, geoms, ngeoms);
    free(geoms);
    return result;
}

expected:

intersection type: MultiLineString
intersection type: MultiLineString

actual:

intersection type: MultiLineString
intersection type: GeometryCollection

I can also give you the ruby reproduction, however I did the C version to make sure the issue was not rgeo related.

Thank you for reading, please let me know if you need more information, or more data.

Cheers, Ulysse

pramsey commented 3 years ago

How would you expect a heterogeneous intersection result to be returned, if not in a geometrycollection? It's not hard to draw examples that return such results. Why not iterate on the collection and throw away the bits you don't want?

@dr-jts has argued that the "sensible" result of an intersection of a polygon/polygon is only and ever a polygon, and that overlay should do that. There's flags at the C++ level to allow that kind of "intuitive" behaviour, at the cost of losing the fully expressive behaviour.

BuonOmo commented 3 years ago

@pramsey I'm not expecting a GeometryCollection because I should not get a polygon at all.

Simplified, my example could be, for two polygons a and b:

a - b # Gives a MultiPolygon
(a - b).inter(b) # Gives only LineStrings
(a - b).remove_cruft.inter(b) # Gives a Polygon and LineStrings

Where remove_cruft would be the process of only keeping the main polygon.

This means that when I remove polygons, I end up with a larger intersection than originally. I really do not see how that can be a normal behaviour. I may have overlooked some part of the process, but I really don't know which..

pramsey commented 3 years ago

You are quite certain your approach is filtering out all the little polygons? Because I looked at your polygons and there's some quite large ones there. Have you visually inspected the contents of the final GeometryCollection?

pramsey commented 3 years ago

screenshot_681

Also worth noting that it's possible for a pair of polygons you think are perfectly border aligned to pop out a polygon sliver from an intersection, due to coordinate precision issues. You can force things into more strict alignment by pushing a tolerance into the intersection with GEOSIntersectionPrec

BuonOmo commented 3 years ago

@pramsey

You are quite certain your approach is filtering out all the little polygons? Because I looked at your polygons and there's some quite large ones there. Have you visually inspected the contents of the final GeometryCollection?

My approach did not filter real islands, however those a far away from the intersection zone and should not have anything to do with it.

Also worth noting that it's possible for a pair of polygons you think are perfectly border aligned to pop out a polygon sliver from an intersection, due to coordinate precision issues. You can force things into more strict alignment by pushing a tolerance into the intersection with GEOSIntersectionPrec

I'll have to dig into that then, thanks for pointing it out.

By the way, the issue I have is that intersection should give me a consistant result in Postgis. However I'm not sure this is ported is postgis isn't it ? (https://postgis.net/docs/RT_ST_Intersection.html)

BuonOmo commented 3 years ago

Ok, GEOSIntersectionPrec fixes the issue, this may be due to a floating point issue then. Even though I still don't understand why removing polygons make the issue appear (shouldn't computation be consistent?)

Anyway, this may mean that we'll have to port this precision notion to https://github.com/rgeo/rgeo (FYI @keithdoggett).

And for usage Within postgis, I guess we could use ST_SnapToGrid anytime we interact with a geometry to prevent floating point issues. Do you agree on that or maybe shall I look for a Postgis Q&A?

dr-jts commented 3 years ago

You are correct that this result is inconsistent- in a theoretically perfect world, removing polygon elements should not cause the intersection result to increase in dimension. However, GEOS necessarily operates in the imperfect world of finite precision arithmetic. This sometimes results in inconsistencies of various kinds.

In this case, the two polygonal inputs contain many line segments which are nearly coincident. This situation often results in robustness errors occurring during overlay processing. GEOS overlay contains heuristic snapping code to resolve these situations and allow overlay to complete. But in this case the result happens to produce an apparent inconsistency.

But here's the surprising thing: the second result is more correct than the first one! In fact the intersection of the two original polygons should contain many sliver polygons, since the linework along their shared border contains numerous overlapping vertices. The following image uses the JTS TestBuilder Reveal Topology view to show some of this situations (note that these discrepancies are very, very small):

image

Because the nearly-coincident linework induces robustness problems, the overlay snapping code kicks in and results in the linework being snapped together, which produces the MultiLineString intersection result. The second (apparently inconsistent) result must occur because the removal of some polygonal element changes the snapping enough to actually produce a polygonal element in the result (which is actually more reflective of the theoretically correct result).

As Paul points out, one way to produce more consistent results is to provide a precision grid for the overlay operation. This forces overlay to use a snap-rounding approach, which will produce more consistent results. The snap-rounding forces the input to be snapped to a precision grid, which compensates for the fact that the inputs do not align perfectly. (Note that the snap-rounded results still do not reflect the theoretically-perfect result from the original linework).

dr-jts commented 3 years ago

@dr-jts has argued that the "sensible" result of an intersection of a polygon/polygon is only and ever a polygon, and that overlay should do that. There's flags at the C++ level to allow that kind of "intuitive" behaviour, at the cost of losing the fully expressive behaviour.

To clarify this, I advocated that the results of overlay operations should be homogeneous. So the result of polygon/polygon intersection could be a (Multi)Poygon, (Multi)LIneString, or (Multi)Point, but not a mixed geometry collection.

This is mostly to allow overlay operations to be chained, and to avoid the buildup of complexity. However, in this case this strategy would have resulted in a possibly even more non-intuitive result, in that the second result would have consisted of a single small polygon!

dr-jts commented 3 years ago

And for usage Within postgis, I guess we could use ST_SnapToGrid anytime we interact with a geometry to prevent floating point issues. Do you agree on that or maybe shall I look for a Postgis Q&A?

PostGIS allows specifying a grid size on overlay operations (e.g. see ST_Intersection). This is passed to the GEOS overlay code as the operating precision, which invokes the snap-rounding strategy.

Using ST_SnapToGrid is dangerous, since it doesn't necessarily produce topologically valid output. PostGIS now provides ST_ReducePrecision, which is topologically safe. However, for an overlay operation it's more efficient just to use the gridSize parameter.

BuonOmo commented 3 years ago

Thank you very much @dr-jts!

Unfortunately, the gridSize parameter is not yet available on heroku's PostGIS version... I think we'll just use a 0.1 meter buffer to avoid any conflict (ST_Buffer(geom, 1e-6)).

And about RGeo, I guess we'll have to take into account a precision grid. I'll open a related issue at some point.

I guess we could close the issue.

EDIT: For the question below, please look at the Q&A here.

One last question if I may @dr-jts, however it is only postgis related, I'd understand if you'd rather not answer, I'll look for a more appropriate place to ask!

ST_Dimension still gives me a wrong result for a GEOMETRY_COLLECTION only containing LineStrings..

select a.g a, b.g b,
    st_intersection(st_difference(a.g, b.g), b.g), st_dimension(st_intersection(st_difference(a.g, b.g), b.g))
from zz a, zz b
where a.name ilike 'name a' and b.name ilike 'name b';
Result a ``` MULTIPOLYGON(((-2.223153 46.965271,-2.242445 46.965359,-2.254398 46.958123,-2.264375 46.960877,-2.286789 46.983497,-2.301095 46.989048,-2.302032 46.997617,-2.292519 47.012555,-2.304205 47.025061,-2.287233 47.024618,-2.277069 47.029038,-2.252069 47.027966,-2.240136 47.017854,-2.225623 47.016855,-2.218334 47.007817,-2.218812 46.991713,-2.231746 46.989711,-2.237473 46.981958,-2.230739 46.973216,-2.220245 46.973677,-2.157181 46.950033,-2.147438 46.934194,-2.148214 46.913529,-2.153252 46.906933,-2.153899 46.895779,-2.167939 46.911178,-2.173528 46.925286,-2.181421 46.93705,-2.198072 46.951171,-2.223153 46.965271)),((-2.28612 46.695672,-2.301825 46.692466,-2.314184 46.695298,-2.32201 46.689371,-2.333909 46.686336,-2.34084 46.692271,-2.362824 46.694297,-2.383825 46.706769,-2.398721 46.717509,-2.398761 46.723952,-2.382963 46.732132,-2.371518 46.732424,-2.344996 46.726619,-2.340309 46.720187,-2.319808 46.719333,-2.304788 46.709424,-2.28612 46.695672)),((-0.88901 46.970996,-0.877125 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47.149197),LINESTRING(-0.788176 47.149197,-0.789696 47.147616),LINESTRING(-0.789696 47.147616,-0.790662 47.148312),LINESTRING(-0.790662 47.148312,-0.792366 47.147384),LINESTRING(-0.792366 47.147384,-0.796446 47.14782),LINESTRING(-0.796446 47.14782,-0.79675 47.150273),LINESTRING(-0.79675 47.150273,-0.798743 47.152046),LINESTRING(-0.798743 47.152046,-0.7999000000000001 47.151605),LINESTRING(-0.7999000000000001 47.151605,-0.8017 47.153203),LINESTRING(-0.8017 47.153203,-0.802353 47.157038),LINESTRING(-0.802353 47.157038,-0.805691 47.156591)) ``` st_dimension ``` 2 ```

The result is a geometry collection even though it contains only LineStrings, and its dimension is 2. Shouldn't it be 1?

dr-jts commented 3 years ago

One last question if I may @dr-jts, however it is only postgis related, I'd understand if you'd rather not answer, I'll look for a more appropriate place to ask!

ST_Dimension still gives me a wrong result for a GEOMETRY_COLLECTION only containing LineStrings.. The result is a geometry collection even though it contains only LineStrings, and its dimension is 2. Shouldn't it be 1?

That is very bizarre. You should ask this on the PostGIS list, or GIS StackExchange, or create a PostGIS issue.

BuonOmo commented 3 years ago

@dr-jts @pramsey thank you both for your time!

@dr-jts and later readers, for the last question I asked, you can see (and maybe answer) it on GIS StackExchange.