[postgis-tickets] [SCM] PostGIS branch master updated. 3.3.0rc2-1172-g37b3c90b5
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- Log -----------------------------------------------------------------
commit 37b3c90b52ae06ca94204ed1cb0e75f675eaa830
Author: Martin Davis <mtnclimb at gmail.com>
Date: Thu Jul 6 14:52:33 2023 -0700
Add doc math definitions for relations
diff --git a/doc/reference_relationship.xml b/doc/reference_relationship.xml
index b496161da..d26c9ad3d 100644
--- a/doc/reference_relationship.xml
+++ b/doc/reference_relationship.xml
@@ -431,6 +431,9 @@ ST_Point | t | t | f | f
Equivalently, tests that no point of A lies outside (in the exterior of) B.
</para>
+ <para>In mathematical terms:
+ <emphasis>ST_CoveredBy(A, B) ⇔ A ⋂ B = A </emphasis></para>
+
<para>ST_CoveredBy is the converse of <xref linkend="ST_Covers"/>.
So, <code>ST_CoveredBy(A,B) = ST_Covers(B,A)</code>.</para>
@@ -519,6 +522,9 @@ FROM (SELECT ST_Buffer(ST_GeomFromText('POINT(1 2)'), 10) As smallc,
Equivalently, tests that no point of B lies outside (in the exterior of) A.
</para>
+ <para>In mathematical terms:
+ <emphasis>ST_Covers(A, B) ⇔ A ⋂ B = B </emphasis></para>
+
<para>ST_Covers is the converse of <xref linkend="ST_CoveredBy"/>.
So, <code>ST_Covers(A,B) = ST_CoveredBy(B,A)</code>.</para>
@@ -615,10 +621,11 @@ SELECT ST_Covers(geog_poly, geog_pt) As poly_covers_pt,
and must have dimension less than the maximum dimension
of the two input geometries, and the intersection of the two
geometries must not equal either geometry. Otherwise, it
- returns <varname>false</varname>.</para>
+ returns <varname>false</varname>.
+ The crosses relation is symmetric and irreflexive.</para>
<para>In mathematical terms:
- <emphasis>ST_Crosses(A, B) ⇔ (dim( Int(A) ⋂ Int(B) ) < max( dim( Int(A) ), dim( Int(B) ) )) ∧ (a ⋂ b ≠ a) ∧ (a ⋂ b ≠ b) </emphasis></para>
+ <emphasis>ST_Crosses(A, B) ⇔ (dim( Int(A) ⋂ Int(B) ) < max( dim( Int(A) ), dim( Int(B) ) )) ∧ (A ⋂ B ≠ A) ∧ (A ⋂ B ≠ B) </emphasis></para>
<para>Geometries cross if their DE-9IM Intersection Matrix matches:</para>
@@ -776,9 +783,17 @@ WHERE ST_Crosses(roads.geom, highways.geom);</programlisting>
</refsynopsisdiv>
<refsection>
<title>Description</title>
- <para>Overlaps, Touches, Within all imply geometries are not spatially disjoint. If any of the aforementioned
- returns true, then the geometries are not spatially disjoint.
- Disjoint implies false for spatial intersection.</para>
+
+ <para>Returns <varname>true</varname> if two geometries are disjoint.
+ Geometries are disjoint if they have no point in common.
+ </para>
+
+ <para>If any other spatial relationship is true for a pair of geometries, they are not disjoint.
+ Disjoint implies that <xref linkend="ST_Intersects"/> is false.
+ </para>
+
+ <para>In mathematical terms:
+ <emphasis>ST_Disjoint(A, B) ⇔ A ⋂ B = ∅ </emphasis></para>
<important>
<para role="enhanced" conformance="3.0.0">Enhanced: 3.0.0 enabled support for <varname>GEOMETRYCOLLECTION</varname></para>
@@ -841,14 +856,21 @@ SELECT ST_Disjoint('POINT(0 0)'::geometry, 'LINESTRING ( 0 0, 0 2 )'::geometry);
<refsection>
<title>Description</title>
- <para>Returns <varname>true</varname> if the given geometries are "spatially
- equal". Use this for a 'better' answer than '='.
- Note by spatially equal we mean ST_Within(A,B) = true and ST_Within(B,A) = true and
- also mean ordering of points can be different but
- represent the same geometry structure. To verify the order of points is consistent, use
- ST_OrderingEquals (it must be noted ST_OrderingEquals is a little more stringent than simply verifying order of
+ <para>Returns <varname>true</varname> if the given geometries are "topologically equal".
+ Use this for a 'better' answer than '='.
+ Topological equality means that the geometries have the same dimension,
+ and their point-sets occupy the same space.
+ This means that the order of vertices may be different in topologically equal geometries.
+ To verify the order of points is consistent use
+ <xref linkend="ST_OrderingEquals"/> (it must be noted ST_OrderingEquals is a little more stringent than simply verifying order of
points are the same).</para>
+ <para>In mathematical terms:
+ <emphasis>ST_Equals(A, B) ⇔ A = B </emphasis></para>
+
+ <para>The following relation holds:
+ <emphasis>ST_Equals(A, B) ⇔ ST_Within(A,B) ∧ ST_Within(B,A) </emphasis></para>
+
<important>
<para role="enhanced" conformance="3.0.0">Enhanced: 3.0.0 enabled support for <varname>GEOMETRYCOLLECTION</varname></para>
</important>
@@ -920,7 +942,7 @@ SELECT ST_Equals(ST_Reverse(ST_GeomFromText('LINESTRING(0 0, 10 10)')),
</refsynopsisdiv>
<refsection>
<title>Description</title>
- <para>Compares two geometries and returns <varname>true</varname> if they intersect.
+ <para>Returns <varname>true</varname> if two geometries intersect.
Geometries intersect if they have any point in common.
</para>
@@ -928,6 +950,9 @@ SELECT ST_Equals(ST_Reverse(ST_GeomFromText('LINESTRING(0 0, 10 10)')),
For geography, a distance tolerance of 0.00001 meters is used
(so points that are very close are considered to intersect).</para>
+ <para>In mathematical terms:
+ <emphasis>ST_Intersects(A, B) ⇔ A ⋂ B ≠ ∅ </emphasis></para>
+
<para>Geometries intersect if their DE-9IM Intersection Matrix matches one of:
</para>
@@ -1236,9 +1261,12 @@ SELECT ST_OrderingEquals(ST_Reverse(ST_GeomFromText('LINESTRING(0 0, 10 10)')),
their interiors intersect in that dimension.
and each has at least one point inside the other
(or equivalently, neither one covers the other).
- The overlaps relationship is symmetric and irreflexive.
+ The overlaps relation is symmetric and irreflexive.
</para>
+ <para>In mathematical terms:
+ <emphasis>ST_Overlaps(A, B) ⇔ ( dim(A) = dim(B) = dim( Int(A) ⋂ Int(B) )) ∧ (A ⋂ B ≠ A) ∧ (A ⋂ B ≠ B) </emphasis></para>
+
<note><para>&index_aware;
To avoid index use, use the function <function>_ST_Overlaps</function>.</para></note>
@@ -1686,7 +1714,7 @@ SELECT pat.name AS relationship, pat.val AS pattern,
since points do not have a boundary.</para>
<para>In mathematical terms:
- <emphasis>ST_Touches(A, B) ⇔ (Int(A) ⋂ Int(B) ≠ ∅) ∧ (a ⋂ b ≠ ∅) </emphasis></para>
+ <emphasis>ST_Touches(A, B) ⇔ (Int(A) ⋂ Int(B) ≠ ∅) ∧ (A ⋂ B ≠ ∅) </emphasis></para>
<para>This relationship holds if the DE-9IM Intersection Matrix for the two geometries matches one of:</para>
@@ -1836,8 +1864,12 @@ SELECT ST_Touches('LINESTRING(0 0, 1 1, 0 2)'::geometry, 'POINT(0 2)'::geometry)
sense, the source geometries must both be of the same coordinate projection,
having the same SRID.
</para>
- <para>The within relationship is reflexive: every geometry is within itself.
- The relationship is antisymmetric: if <code>ST_Within(A,B) = true</code> and <code>ST_Within(B,A) = true</code>, then
+
+ <para>In mathematical terms:
+ <emphasis>ST_Within(A, B) ⇔ (A ⋂ B = A) ∧ (Int(A) ⋂ Int(B) ≠ ∅) </emphasis></para>
+
+ <para>The within relation is reflexive: every geometry is within itself.
+ The relation is antisymmetric: if <code>ST_Within(A,B) = true</code> and <code>ST_Within(B,A) = true</code>, then
the two geometries must be topologically equal (<code>ST_Equals(A,B) = true</code>).</para>
<para>ST_Within is the converse of <xref linkend="ST_Contains"/>.
-----------------------------------------------------------------------
Summary of changes:
doc/reference_relationship.xml | 64 +++++++++++++++++++++++++++++++-----------
1 file changed, 48 insertions(+), 16 deletions(-)
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