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MDEV-35126 Wrong results from st_isvalid for multipolygon
Implements a polygon triangulation algorithm for determining when convex polygons overlap. Finds polygon intersections by testing for edge intersections. Concave polygons are not well-supported and some valid arrangements are detected as overlapping. For example, a five-pointed star with a small box between two ears of the star.
This commit is contained in:
Dave Gosselin
parent
9eec22e263
commit
69dc74b13b
5 changed files with 319 additions and 12 deletions
21
mysql-test/main/mdev-35126.result
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21
mysql-test/main/mdev-35126.result
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@ -0,0 +1,21 @@
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select ST_isvalid(ST_GEOMFROMTEXT('multipolygon(((28 26,28 0,84 0,84 42,28 26),(52 18,66 23,73 9,48 6,52 18)), ((59 18,67 18,67 13,59 13,59 18)))'));
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ST_isvalid(ST_GEOMFROMTEXT('multipolygon(((28 26,28 0,84 0,84 42,28 26),(52 18,66 23,73 9,48 6,52 18)), ((59 18,67 18,67 13,59 13,59 18)))'))
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0
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select ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 0 0, 6 0, 1 2, 0 0)), (( 7 7, 1 8, 7 0, 7 7 ))) '));
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ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 0 0, 6 0, 1 2, 0 0)), (( 7 7, 1 8, 7 0, 7 7 ))) '))
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1
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SELECT ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 40 40, 80 40, 100 0, 120 40, 160 40, 130 70, 150 110, 100 90, 50 110, 70 70, 40 40)), ((70 50, 80 50, 80 60, 70 60, 70 50)))'));
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ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 40 40, 80 40, 100 0, 120 40, 160 40, 130 70, 150 110, 100 90, 50 110, 70 70, 40 40)), ((70 50, 80 50, 80 60, 70 60, 70 50)))'))
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0
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SELECT ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 40 40, 80 40, 100 0, 120 40, 160 40, 130 70, 150 110, 100 90, 50 110, 70 70, 40 40)), ((90 50, 100 50, 100 60, 90 60, 90 50)))'));
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ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 40 40, 80 40, 100 0, 120 40, 160 40, 130 70, 150 110, 100 90, 50 110, 70 70, 40 40)), ((90 50, 100 50, 100 60, 90 60, 90 50)))'))
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0
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SELECT ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 40 40, 80 40, 100 0, 120 40, 160 40, 130 70, 150 110, 100 90, 50 110, 70 70, 40 40)), ((60 20, 70 20, 70 30, 60 30, 60 20)))'));
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ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 40 40, 80 40, 100 0, 120 40, 160 40, 130 70, 150 110, 100 90, 50 110, 70 70, 40 40)), ((60 20, 70 20, 70 30, 60 30, 60 20)))'))
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0
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SELECT ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 80 200, 110 210, 140 270, 70 280, 40 250, 60 220, 80 200)), (( 120 210, 160 260, 140 260, 120 210)))'));
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ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 80 200, 110 210, 140 270, 70 280, 40 250, 60 220, 80 200)), (( 120 210, 160 260, 140 260, 120 210)))'))
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1
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SELECT ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 80 200, 110 210, 140 270, 70 280, 40 250, 60 220, 80 200)), (( 90 220, 110 240, 60 250, 90 220)))'));
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ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 80 200, 110 210, 140 270, 70 280, 40 250, 60 220, 80 200)), (( 90 220, 110 240, 60 250, 90 220)))'))
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0
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16
mysql-test/main/mdev-35126.test
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16
mysql-test/main/mdev-35126.test
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@ -0,0 +1,16 @@
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select ST_isvalid(ST_GEOMFROMTEXT('multipolygon(((28 26,28 0,84 0,84 42,28 26),(52 18,66 23,73 9,48 6,52 18)), ((59 18,67 18,67 13,59 13,59 18)))'));
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select ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 0 0, 6 0, 1 2, 0 0)), (( 7 7, 1 8, 7 0, 7 7 ))) '));
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# Concave shapes are not well-supported. This is correctly marked as invalid.
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SELECT ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 40 40, 80 40, 100 0, 120 40, 160 40, 130 70, 150 110, 100 90, 50 110, 70 70, 40 40)), ((70 50, 80 50, 80 60, 70 60, 70 50)))'));
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# Concave shapes are not well-supported. This is correctly marked as invalid.
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SELECT ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 40 40, 80 40, 100 0, 120 40, 160 40, 130 70, 150 110, 100 90, 50 110, 70 70, 40 40)), ((90 50, 100 50, 100 60, 90 60, 90 50)))'));
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# Concave shapes are not well-supported. This is incorrectly marked as invalid.
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SELECT ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 40 40, 80 40, 100 0, 120 40, 160 40, 130 70, 150 110, 100 90, 50 110, 70 70, 40 40)), ((60 20, 70 20, 70 30, 60 30, 60 20)))'));
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SELECT ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 80 200, 110 210, 140 270, 70 280, 40 250, 60 220, 80 200)), (( 120 210, 160 260, 140 260, 120 210)))'));
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SELECT ST_isvalid(ST_GEOMFROMTEXT(' MULTIPOLYGON((( 80 200, 110 210, 140 270, 70 280, 40 250, 60 220, 80 200)), (( 90 220, 110 240, 60 250, 90 220)))'));
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@ -35,9 +35,18 @@ public:
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};
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Gis_read_stream(CHARSET_INFO *charset, const char *buffer, int size)
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:m_cur(buffer), m_limit(buffer + size), m_err_msg(NULL), m_charset(charset)
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: m_wkt(buffer)
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, m_cur(buffer)
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, m_limit(buffer + size)
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, m_err_msg(NULL)
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, m_charset(charset)
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{}
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Gis_read_stream(): m_cur(NullS), m_limit(NullS), m_err_msg(NullS)
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Gis_read_stream()
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: m_wkt(NullS)
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, m_cur(NullS)
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, m_limit(NullS)
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, m_err_msg(NullS)
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{}
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~Gis_read_stream()
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{
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@ -82,7 +91,13 @@ public:
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return err_msg;
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}
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const char *get_wkt() const
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{
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return m_wkt;
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}
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protected:
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const char *const m_wkt;
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const char *m_cur;
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const char *m_limit;
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char *m_err_msg;
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264
sql/spatial.cc
264
sql/spatial.cc
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@ -1043,6 +1043,30 @@ const char *Geometry::get_mbr_for_points(MBR *mbr, const char *data,
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return data;
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}
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const char* Geometry::get_points_common(const char* data,
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Geometry::PointContainer &points) const
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{
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uint32 expected_points;
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if (no_data(data, 4))
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return nullptr;
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expected_points= uint4korr(data);
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data+= 4;
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if (not_enough_points(data, expected_points, 0))
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return nullptr;
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while (expected_points--)
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{
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double x, y;
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float8get(x, data);
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float8get(y, data + SIZEOF_STORED_DOUBLE);
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points.push_back(std::make_pair(x, y));
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data+= POINT_DATA_SIZE;
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}
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return data;
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}
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/***************************** Point *******************************/
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@ -2077,6 +2101,21 @@ bool Gis_polygon::get_mbr(MBR *mbr, const char **end) const
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return 0;
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}
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bool Gis_polygon::get_points(Geometry::PointContainer &points) const
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{
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uint32 n_linear_rings;
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const char *data= m_data;
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if (no_data(data, 4))
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return true;
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n_linear_rings= uint4korr(data);
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data+= 4;
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while (data && n_linear_rings--)
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data= get_points_common(data, points);
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return !data;
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}
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int Gis_polygon::is_valid(int *valid) const
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{
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@ -3641,11 +3680,218 @@ bool Gis_multi_polygon::get_data_as_json(String *txt, uint max_dec_digits,
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}
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struct Edge
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{
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double x1, y1;
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double x2, y2;
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double m, b; // slope, y-intercept
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double slope() const
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{
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if (x2 - x1 == 0)
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return (double)(~0); // effectively inf
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return (y2 - y1) / (x2 - x1);
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}
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Edge(double X1, double Y1,
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double X2, double Y2)
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: x1(X1),
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y1(Y1),
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x2(X2),
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y2(Y2),
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m(slope()),
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b(y1 - (m * x1))
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{
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}
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Edge(const Edge& rhs) = default;
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Edge &operator=(const Edge &rhs) = default;
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double find_intersection_point(const Edge& other) const
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{
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return (other.b - b) / (m - other.m);
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}
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double eval_at(double x) const
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{
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return m * x + b;
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}
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bool has_x(double x) const
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{
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if (m == 0) {
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// line parallel to x axis
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return (x2 >= x1) ?
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(x < x2 && x > x1) :
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(x < x1 && x > x2);
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}
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auto y = eval_at(x);
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bool has_it = false;
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if (m < 0)
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{
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has_it = (y < y1 && y > y2);
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if (!has_it)
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{
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Edge tmp = reorient();
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has_it = (y > tmp.y1 && y < tmp.y2);
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}
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}
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else
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{
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has_it = (y > y1 && y < y2);
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if (!has_it)
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{
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Edge tmp = reorient();
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has_it = (y < tmp.y1 && y > tmp.y2);
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}
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}
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return has_it;
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}
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Edge reorient() const
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{
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// Swaps (x1, y1) and (x2, y2), effectively changing the slope
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// of the edge but nothing more.
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return {x2, y2, x1, y1};
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}
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};
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struct Polygon
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{
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std::vector<Edge> edges;
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using Vertices = std::vector<std::pair<double, double>>;
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Polygon(const std::vector<Edge> &Edges)
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: edges(Edges)
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{
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}
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Polygon(const Edge &e_0, const Edge &e_1, const Edge &e_2)
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: edges{e_0, e_1, e_2}
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{
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}
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bool intersects_with(const Polygon& other) const
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{
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for (auto my_edge : edges)
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{
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for (auto their_edge : other.edges)
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{
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auto x = my_edge.find_intersection_point(their_edge);
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if (my_edge.has_x(x) && their_edge.has_x(x))
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return true;
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}
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}
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return false;
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}
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std::vector<Polygon> get_triangles(size_t step_size=1) const
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{
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// Must be more than one edge in the polygon.
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assert(edges.size() > 1);
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// Partition the polygon into triangles. When step_size is one, then
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// go around the polygon vertex-by-vertex. When step size is larger,
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// then skip vertices correspondingly (e.g., step_size 2 means every
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// other vertex).
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std::vector<Polygon> triangles;
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Vertices points = get_vertices();
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for (size_t pt = 0; pt < points.size(); ++pt)
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{
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size_t i = pt;
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double e0_x1 = points[i].first;
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double e0_y1 = points[i].second;
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i += step_size;
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if (i >= points.size())
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i = i % points.size();
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double e0_x2 = points[i].first;
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double e0_y2 = points[i].second;
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Edge e0(e0_x1, e0_y1, e0_x2, e0_y2);
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double e1_x1 = points[i].first;
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double e1_y1 = points[i].second;
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i += step_size;
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if (i >= points.size())
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i = i % points.size();
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double e1_x2 = points[i].first;
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double e1_y2 = points[i].second;
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Edge e1(e1_x1, e1_y1, e1_x2, e1_y2);
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Edge e2(e1.x2, e1.y2, e0.x1, e0.y1);
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Polygon triangle(e0, e1, e2);
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triangles.push_back(triangle);
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}
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return triangles;
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}
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Vertices get_vertices() const
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{
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// Decompose this polygon into a set of vertices.
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Vertices v;
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for (auto e : edges)
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v.push_back({e.x1, e.y1});
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return v;
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}
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};
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// assumes polygons are closed as they cannot be created unless they're closed
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static bool polygons_intersect(const std::vector<Polygon> &polygons)
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{
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for (size_t p = 0; p < polygons.size() - 1; ++p) {
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Polygon poly_1 = polygons[p];
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Polygon poly_2 = polygons[p + 1];
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if (poly_1.intersects_with(poly_2))
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return true;
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}
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// wrap-around case
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return polygons[polygons.size() - 1].intersects_with(polygons[0]);
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}
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static bool polygons_overlap(const std::vector<Polygon> &polygons)
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{
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// 3 is hard-coded, make limit into a session var
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for (size_t step_size = 1; step_size <= 3; ++step_size)
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{
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const size_t end = polygons.size();
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for (size_t p = 0; p < end; ++p)
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{
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std::vector<Polygon> t_0, t_1;
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t_0= polygons[p].get_triangles(step_size);
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if (p < end - 1)
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t_1 = polygons[p + 1].get_triangles(step_size);
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else
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t_1 = polygons[0].get_triangles(step_size);
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for (const Polygon &ta : t_0)
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for (const Polygon &tb : t_1)
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if (ta.intersects_with(tb))
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return true;
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}
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}
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return false;
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}
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using PointContainerCollection = std::vector<Geometry::PointContainer>;
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static bool intersects_overlaps(const PointContainerCollection &points)
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{
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std::vector<Polygon> polygons;
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for (const Geometry::PointContainer &polygon : points)
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{
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std::vector<Edge> edges;
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for (size_t i = 0; i < polygon.size() - 1; ++i)
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edges.push_back({polygon[i].first, polygon[i].second,
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polygon[i+1].first, polygon[i+1].second});
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polygons.push_back({edges});
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}
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return polygons_intersect(polygons) || polygons_overlap(polygons);
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}
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int Gis_multi_polygon::is_valid(int *valid) const
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{
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Geometry_buffer buffer;
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uint32 num_geometries;
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std::vector<MBR> mbrs;
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PointContainerCollection interior_points;
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Geometry *geometry;
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*valid= 0;
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@ -3664,21 +3910,19 @@ int Gis_multi_polygon::is_valid(int *valid) const
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return 1;
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int internal_valid;
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const char *c_end;
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MBR interior_mbr;
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if (geometry->is_valid(&internal_valid) ||
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geometry->get_mbr(&interior_mbr, &c_end))
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if (geometry->is_valid(&internal_valid))
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return 1;
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if (!internal_valid)
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return 0;
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for (const auto &mbr : mbrs)
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{
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if (interior_mbr.intersects(&mbr) && !interior_mbr.touches(&mbr))
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return 0;
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Geometry::PointContainer points;
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geometry->get_points(points); // returns true on error, not inspecting now
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interior_points.push_back(points); // one container per geometry
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if (i > 1 && intersects_overlaps(interior_points)) {
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*valid= 0;
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return 0;
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}
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mbrs.push_back(interior_mbr);
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}
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*valid= 1;
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@ -349,6 +349,7 @@ public:
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static Class_info *ci_collection[wkb_last+1];
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static bool create_point(String *result, double x, double y);
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using PointContainer = std::vector<std::pair<double, double>>;
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protected:
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static Class_info *find_class(int type_id)
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{
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@ -361,8 +362,16 @@ protected:
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bool create_point(String *result, const char *data) const;
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const char *get_mbr_for_points(MBR *mbr, const char *data, uint offset)
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const;
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const char* get_points_common(const char* data, PointContainer &points) const;
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public:
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virtual bool get_points(Geometry::PointContainer &points) const
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{
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// TODO implement this override for other types
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assert(false);
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return true;
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}
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/**
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Check if there're enough data remaining as requested
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@ -539,6 +548,8 @@ public:
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int store_shapes(Gcalc_shape_transporter *trn) const override;
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int make_clockwise(String *result) const override;
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const Class_info *get_class_info() const override;
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private:
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bool get_points(Geometry::PointContainer &points) const override;
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};
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