Invalid turns generation (detected as inconsistency in set and relational operations).

[awulkiew]

@barendgehrels I've noticed that some operations became inconsistent after recent changes in set operations (with VS2015, msvc-14.0, x86). Consider:

red = POLYGON((5 0,7 10,0 15,10 15,15 25,20 15,30 15,22 10,25 0,15 5,5 0))
green = POLYGON((15 0,17 10,10 15,20 15,25 25,30 15,40 15,32 10,35 0,25 5,15 0))
blue = MULTIPOLYGON(((10 15,15 25,20 15,10 15)),((10 15,17 10,15.90909090909091 4.545454545454546,15 5,5 0,7 10,0 15,10 15)),((23.69565217391304 4.347826086956522,25 0,20 2.5,23.69565217391304 4.347826086956522)))

where:

bg::difference(red, green, blue)

blue should therefore be within red:

assert(bg::within(blue, red) == true)

but it is not. Here it is how it looks like with turns calculated internally in within or relation:

The lower right blue triangle has the following points:

{23.695652173913043, 4.3478260869565215}
{25.000000000000000, 0.00000000000000000}
{20.000000000000000, 2.5000000000000000}
{23.695652173913043, 4.3478260869565215}

the lower right arm of the red star is formed from the points:

{22.000000000000000, 10.000000000000000}
{25.000000000000000, 0.00000000000000000}
{15.000000000000000, 5.0000000000000000}

and the corresponding turns are:

0: touch u/i at {25.000000000000000, 0.00000000000000000}
1: crosses i/u at {20.000001500000678, 2.5000007500003396}
2: crosses u/i at {23.695651652173520, 4.3478258260867602}

(note: turns indexes are different than in within)

So it looks like at {25, 0} (turn 0) the blue triangle goes outside the red and then crosses it from the outside at {20.000001500000678, 2.5000007500003396} (turn 1), goes inside and then at {23.695651652173520, 4.3478258260867602} (turn 2) outside again. Also the coordinates looks consistent with topology since {20.000001500000678, 2.5000007500003396} is above and on the right of {20.000000000000000, 2.5000000000000000} and {23.695651652173520, 4.3478258260867602} is below and on the left of {23.695652173913043, 4.3478260869565215}.

However this should not be the case. All turns for this triangle should be detected as lying on the edges. And this is not some numerical floating point error. Consider the POINT(20.0 2.5). It's exactly in the half of the SEGMENT(25 0, 15 5) but the turn point calculated for this point is {20.000001500000678, 2.5000007500003396}. The error is huge.

Btw, turns in relate are calculated like this: https://github.com/boostorg/geometry/blob/develop/include/boost/geometry/algorithms/detail/relate/areal_areal.hpp#L225

Or am I missing something?

EDIT:
Is this a bug?
Should turns be generated in a different way now?
Is this low accuracy expected?

Note that if such low accuracy was expected (e.g. was a side effect of your changes) we would have to for instance compare all of the points (for equality) in the library WRT to this accuracy.

[barendgehrels]

Thanks for the report. As far as I know, for within calculations rescaling is not used? Then it might be influenced by my recent changes indeed.
It might be that there is a start turn added?
Do you happen to have a test project and can we bisect it?

[barendgehrels]

It looks indeed like the start turn can cause this, and also some false positives about validity.
Looking at it right now, hope to send a PR soon.

[barendgehrels]

I can exclude the start-turns for non-overlay operations, and I will.
However, I added also your testcase to the within unit test but it still fails. Are you sure it should return really "within" (so: true)?

About the calculated turn, that (resulting coordinates) is all not affected (as far as I'm aware) by my changes. I only changed things in turns, not in the calculations themselves.

[awulkiew]

I can exclude the start-turns for non-overlay operations, and I will.

Ok but will then set operations and relational operations be consistent with each other?

Are you sure it should return really "within" (so: true)?

Yes. C = A \ B <=> C in A

that (resulting coordinates) is all not affected (as far as I'm aware) by my changes

I only checked that the result is different in 1.69 and 1.70. It may be something different. I'll try to find the specific commit when the behavior changes.

I only changed things in turns, not in the calculations themselves.

Turns generated now are different than the ones before. It's not only the coordinates.

[awulkiew]

Btw, my test program is more or less:

#include <boost/geometry.hpp>
#include <boost/geometry/geometries/geometries.hpp>
#include <iostream>

template <typename Geometry>
inline void read_wkt(std::string const& wkt, Geometry & geometry)
{
    namespace bg = boost::geometry;
    bg::read_wkt(wkt, geometry);
    bg::correct(geometry);
}

int main()
{
    namespace bg = boost::geometry;
    typedef bg::model::point<double, 2, bg::cs::cartesian> point;
    typedef bg::model::polygon<point> polygon;
    typedef bg::model::multi_polygon<polygon> mpolygon;

    polygon red, green;

    read_wkt("POLYGON((5 0,7 10,0 15,10 15,15 25,20 15,30 15,22 10,25 0,15 5,5 0))", red);
    read_wkt("POLYGON((15 0,17 10,10 15,20 15,25 25,30 15,40 15,32 10,35 0,25 5,15 0))", green);

    mpolygon blue;
    bg::difference(red, green, blue);

    bool w1 = bg::within(blue, red);
    std::string s1 = bg::relation(blue, red).str();

    std:: cout << (w1 == true ? "OK" : "WRONG") << std::endl;
    std:: cout << s1 << std::endl;

    std::cout << std::setprecision(16);
    std::cout << bg::wkt(red) << std::endl;
    std::cout << bg::wkt(green) << std::endl;
    std::cout << bg::wkt(blue) << std::endl;
}

[barendgehrels]

Thanks for your testprogram!

Ok but will then set operations and relational operations be consistent with each other?

Good point - I have to check that indeed. Will come back to this, but cannot do that right now.

[barendgehrels]

I checked the cases failing with starting points and I'm able to solve them differently now.
Created PR #589 (it disables two cases failing, but locally I've changes still to be committed which will fix them).
Closing this for now.

[awulkiew]

I've checked the case reported in this issue with your branch (barendgehrels:bugfix/disable_start_turns) but the result didn't change, still the same turns are generated. I'm going to find the exact commit which introduced the regression to be sure what is the cause. Blind fixing is probably not a good strategy. ;)

[awulkiew]

@barendgehrels I found the cause. It seems my commit introduced this regression and your initial thought about rescaling was correct. Here is the commit: 5ea1abc

Reverting it fixes the problem however this was a change made in this PR: #550 so it needs re-testing in case it was important and not only made for consistency. I don't remember exactly.

The issue is caused by rescaling. It also affects set operations. I checked the result of the difference of red - blue and it contains these invalid turns like POINT(20.000001500000678 2.5000007500003396):

MULTIPOLYGON(((10 15,20 15,30 15,22 10,23.69565165217352 4.34782582608676,20.00000150000068 2.50000075000034,15.90909090909091 4.545454545454546,17 10,10 15)))

[awulkiew]

Reverting 5ea1abc causes the following difference cases to fail as it was before #550 was merged:

algorithms_difference
difference: mysql_23023665_6_b not valid Multi-polygon has intersecting interiors type: d
difference: mysql_23023665_6_s not valid Multi-polygon has intersecting interiors type: d

algorithms_difference_multi
difference: mysql_21965285_b_s not valid Multi-polygon has intersecting interiors type: d

So I'm not sure what is the correct course of action here.

[awulkiew]

The above means this issue is still on the table.