polygon operators

Area - calculates the surface area of each polygon
Centroid - center of mass of each polygon
mid - a point in the polygon, cheaper than Centroid
outer_single_polygon - outer ring of a single polygon (drops holes)
outer_multi_polygon - outer ring(s) of each multi_polygon (drops the holes)
geos_buffer - buffer of a (multi)polygon, geos implementation
canyon - street-canyon heights for road points from surrounding heights
Centroid_or_mid - the centroid if located within the polygon, otherwise a mid-point
Poly2grid - a grid representation of polygons
poly2grid_untiled - a grid representation of polygons (untiled variant)
poly2allgrids - a cross-table representation of polygons and raster cells
poly2allgrids_uint64 - a uint64 cross-table representation of polygons and raster cells
Lower_bound - the lowest X and Y values of the points in each polygon
Upper_bound - the highest X and Y values of the points in each polygon
Center_bound - the center X and Y values of the points in each polygon
points2polygon - create polygons from sequences of points
Sub (difference) - element-wise cutout of one polygon from another, where both domains match or one is void
Mul (polygon intersection) - element-wise overlap of two polygon arrays, where both domains match or one is void
Add (union) - element-wise union of two polygon arrays, where both domains match or one is void
box_connectivity - find connected polygons based on bounding box overlap (faster, but less precise than Polygon_connectivity)
Polygon_connectivity - find all pairs of polygons in one set that overlap or touch, as relations F1 and F2 (integer coordinates)

Finding pairs of polygons:

Two families of operators find the pairs of polygons that meet, one pair per row of a new Domain unit with a relation towards each polygon of the pair. The xxx_overlay_polygon operators compute the intersection geometry of every pair as well; the xxx_polygon_connectivity operators return the relations only. Both take one polygon set, for the pairs within it (each pair once, first_rel < second_rel), or two sets, for the pairs between them. The libraries differ in which pairs they find: the bp_, bg_ and cgal_ variants pair polygons with a common interior point, the geos_ variants also pair polygons that only touch, along an edge or at a point, with an empty geometry for such a pair. The unprefixed Polygon_connectivity pairs touching polygons too and names its relations F1 and F2, as does box_connectivity, which only compares bounding boxes. For the intersection of two polygons that are already paired element by element, use mul (polygon intersection) or one of the xxx_intersect operators below.

operator	pairs	a pair when	result items
bp_overlay_polygon, bg_overlay_polygon, cgal_overlay_polygon	within one set, or between two sets	the polygons have a common interior point	geometry, first_rel, second_rel
geos_overlay_polygon	within one set, or between two sets	the polygons overlap or touch; a touching pair has an empty geometry	geometry, first_rel, second_rel
bp_polygon_connectivity, bg_polygon_connectivity, cgal_polygon_connectivity	within one set, or between two sets	the polygons have a common interior point	first_rel, second_rel
geos_polygon_connectivity	within one set, or between two sets	the polygons overlap or touch	first_rel, second_rel
dms_overlay_polygon	within one set, or between two sets	the polygons have a common interior point; the operands need not be valid	geometry, first_rel, second_rel
dms_polygon_connectivity	within one set, or between two sets	the polygons have a common interior point; the operands need not be valid	first_rel, second_rel
Polygon_connectivity	within one set, integer coordinates	the polygons overlap or touch	F1, F2
box_connectivity	within one set	the bounding boxes overlap or touch	F1, F2

Ring order (winding) operators:

reverse_polygon - reverse the winding order of every ring, without changing the sequence layout
fix_winding_order - give every ring the clockwise-outer / counter-clockwise-hole order, deriving the ring roles from their nesting; repairs half-flipped multi-polygons that a reversal cannot
has_correct_winding - True for each element whose ring order is certifiably correct; the replacement for the area(g) < 0 test, which misses a half-flipped feature
fix_polygon - fix_winding_order plus repair of self-intersections and other invalidity (GEOS MakeValid)

Operators based on the geos library (recommended: faster, reliable, supports float64/dpoint coordinates):

geos_buffer_multi_polygon - creates a buffer polygon for each multi polygon
geos_difference - element-wise difference of two polygon arrays (A minus B); also invoked by the - operator for fpoint/dpoint coordinates
geos_intersect - element-wise intersection of two polygon arrays; also invoked by the * and & operators for fpoint/dpoint coordinates
geos_minkowski_sum - grow each geometry by a kernel: the kernel as a polygon argument, or one of six named shapes at a given size
geos_minkowski_difference - shrink each geometry by a kernel; the eroding counterpart
geos_overlay_polygon - spatial overlay between two polygon datasets, producing all intersecting pairs with their intersection geometry
geos_polygon - clean and validate polygon geometry using GEOS
geos_polygon_connectivity - find all pairs of adjacent or overlapping polygons
geos_simplify_multi_polygon - simplify the geometry of a multi polygon
geos_split_polygon - split multi-polygons into individual single-polygon parts, each as a separate domain entry
geos_split_union_polygon - dissolve polygons (optionally grouped by attribute), then split into individual parts
geos_union - element-wise union of two polygon arrays; also invoked by the + and | operators for fpoint/dpoint coordinates
geos_union_polygon - dissolve all polygons into one, optionally grouped by a partition attribute
geos_xor - element-wise symmetric difference of two polygon arrays; also invoked by the ^ operator for fpoint/dpoint coordinates

To be potentially developed operators:

geos_simplify_single_polygon - simplify the geometry of a single polygon; see geos_simplify_multi_polygon
geos_buffer_single_polygon - creates a buffer polygon for each single polygon; see geos_buffer_multi_polygon
geos_outer_single_polygon - selects only the outer ring of a single polygon; see bg_outer_multi_polygon
geos_outer_multi_polygon - selects only the outer ring of a multi polygon; see bg_outer_multi_polygon

Operators based on the boost polygon library (usually slower than the _bg__-variants, and can only process integer coordinates):

~~bp_buffer_multi_polygon~~ - removed in 20.13.0: never implemented; use bg_buffer_multi_polygon or geos_buffer_multi_polygon
bp_difference - element-wise difference of two polygon arrays (integer coordinates)
bp_intersect - element-wise intersection of two polygon arrays (integer coordinates)
bp_overlay_polygon (the former Overlay_polygon, a name that was removed in 18.0.0) - spatial overlay between two polygon datasets, or within one, producing all intersecting pairs with their intersection geometry (integer coordinates)
bp_polygon - clean and validate polygon geometry using Boost Polygon (integer coordinates)
bp_polygon_connectivity - find all pairs of overlapping polygons, between two datasets or within one, as relations only (integer coordinates); not a renaming of Polygon_connectivity, which pairs touching polygons too and names its relations F1 and F2
bp_split_polygon (or old syntax Split_polygon) - split multi-polygons into individual single-polygon parts (integer coordinates)
bp_split_union_polygon (or old syntax split_partitioned_union_polygon) - dissolve polygons (optionally grouped by attribute), then split into individual parts (integer coordinates). Combination of Split_polygon and partitioned_union_polygon
bp_union - element-wise union of two polygon arrays (integer coordinates)
bp_union_polygon (or old syntax Union_polygon (dissolve) or Partitioned_union_polygon (dissolve by attribute)) - dissolve all polygons into one, optionally grouped by a partition attribute (integer coordinates)
bp_polygon_filtered, bp_union_polygon_filtered, bp_split_polygon_filtered, bp_split_union_polygon_filtered - bp-set operations that drop rings smaller than the given area
bp_polygon_inflated, bp_union_polygon_inflated, bp_split_polygon_inflated, bp_split_union_polygon_inflated - bp-set operations after growing the polygons with the given distance
bp_polygon_deflated, bp_union_polygon_deflated, bp_split_polygon_deflated, bp_split_union_polygon_deflated - bp-set operations after shrinking the polygons with the given distance
bp_minkowski_sum - grow each geometry by a kernel: the kernel as a polygon argument, or one of six named shapes at a given size
bp_minkowski_difference - shrink each geometry by a kernel; the eroding counterpart
~~bp kernel-suffix variants~~ - DEPRECATED since 20.18.0: the 48 names bp_polygon_i4HV … bp_split_union_polygon_dXD (12 kernels x {plain, union, split, split_union}) that carried the kernel shape in the operator name. They still work but warn, naming the replacement. The kernel is an argument now: use bp_minkowski_sum / bp_minkowski_difference on the result of the same operator without the suffix. See the migration table on Boost polygon functions.
bp_xor - element-wise symmetric difference of two polygon arrays (integer coordinates)
Polygon inflated - increases each polygon by expanding its boundary outward
Polygon deflated - decreases each polygon by contracting its boundary inward

Several boost polygon functions can be combined in a single operator; for the full list of those combinations, see here.

Operators based on the boost geometry library (float64/dpoint coordinates; largely superseded by their geos equivalents):

Bg_buffer_multi_polygon - creates a buffer polygon for each multi polygon
bg_buffer_single_polygon - creates a buffer polygon for each single polygon; see Bg_buffer_multi_polygon
bg_difference - element-wise difference of two polygon arrays
bg_intersect - element-wise intersection of two polygon arrays
bg_minkowski_sum - grow each geometry by a kernel: the kernel as a polygon argument, or one of six named shapes at a given size
bg_minkowski_difference - shrink each geometry by a kernel; the eroding counterpart
bg_outer_multi_polygon - selects only the outer ring of each multi polygon (removes holes)
bg_outer_single_polygon - selects only the outer ring of each single polygon; see for documentation: bg_outer_multi_polygon
bg_overlay_polygon - spatial overlay between two polygon datasets, producing all intersecting pairs
bg_polygon - clean and validate polygon geometry using Boost Geometry
bg_polygon_connectivity - find all pairs of adjacent or overlapping polygons
bg_simplify_multi_polygon - simplify the geometry of a multi polygon
bg_simplify_polygon - DEPRECATED: simplify the geometry of a single polygon; see for documentation: bg_simplify_multi_polygon
bg_split_polygon - split multi-polygons into individual single-polygon parts
bg_split_union_polygon - dissolve polygons (optionally grouped by attribute), then split into individual parts
bg_union - element-wise union of two polygon arrays
bg_union_polygon - DO NOT USE: current implementation does not produce reliable results
bg_xor - element-wise symmetric difference of two polygon arrays

For examples, see here.

Operators based on the cgal library:

cgal_difference - element-wise difference of two polygon arrays (CGAL)
cgal_intersect - element-wise intersection of two polygon arrays (CGAL)
cgal_minkowski_sum - grow each geometry by a kernel, through CGAL::minkowski_sum_2: the exact one of the four backends
cgal_minkowski_difference - shrink each geometry by a kernel; the eroding counterpart
cgal_overlay_polygon - spatial overlay between two polygon datasets, producing all intersecting pairs (CGAL)
cgal_polygon - clean and validate polygon geometry using CGAL
cgal_polygon_connectivity - find all pairs of adjacent or overlapping polygons (CGAL)
cgal_split_polygon - split multi-polygons into individual single-polygon parts (CGAL)
cgal_split_union_polygon - dissolve polygons (optionally grouped by attribute), then split into individual parts (CGAL)
cgal_union - element-wise union of two polygon arrays (CGAL)
cgal_union_polygon - dissolve all polygons into one, optionally grouped by a partition attribute (CGAL)
cgal_xor - element-wise symmetric difference of two polygon arrays (CGAL)

Operators implemented by GeoDMS itself (prefix `dms_`), since 20.20.0:

A snap-rounding sweep of GeoDMS’s own, the fifth family next to the four libraries. Its distinction is fault tolerance: the operands need not be valid polygons. Rings may self-intersect, self-touch, overlap, touch or fail to close, and are read under the even-odd rule, and an optional third argument gives the grid size that near-coincident vertices and slivers snap to. All six point types; the result has clockwise shells, counter-clockwise holes and no collinear vertices. The infix operators *, +, - and ^ keep their bp_ (integer) and geos_ (float) bindings. The family page is dms polygon operators; the worked example is Cleaning invalid polygons.

dms_intersect - element-wise intersection of two polygon arrays, with an optional grid size as tolerance
dms_union - element-wise union of two polygon arrays, with an optional grid size as tolerance
dms_difference - element-wise difference of two polygon arrays (A minus B), with an optional grid size as tolerance
dms_xor - element-wise symmetric difference of two polygon arrays, with an optional grid size as tolerance
dms_polygon - read each element under the even-odd rule and write it back as a valid polygon: the clean-up
dms_union_polygon - dissolve all polygons into one, optionally grouped by a partition attribute
dms_split_polygon - split multi-polygons into their single polygons
dms_split_union_polygon - dissolve, then split into single polygons
dms_overlay_polygon - all intersecting pairs of two polygon sets, or within one, with their intersection geometry
dms_polygon_connectivity - the same pairs, as relations only
dms_minkowski_sum - grow each geometry by a kernel
dms_minkowski_difference - shrink each geometry by a kernel