de9im is a Javascript library that provides spatial predicate
functions defined by the Dimensionally Extended Nine-Intersection Model
(DE-9IM) and works with GeoJSON objects. It can
test if two geometries have one of the following relationships: contains,
coveredby, covers, crosses, disjoint, equals, intersects,
overlaps, touches, within. It can be used client-side in a browser or
server-side with Node.js.
See de9im examples for examples of geometries that satisfy
the various predicates using de9im.
See pouchdb-geospatial for an example application that
uses de9im to perform spatial querying of GeoJSON objects in a database.
de9im depends on the Turf.js library for performing spatial
operations which must be also included for client-side processing since Turf.js
is not bundled with de9im.
<script src="https://unpkg.com/@turf/turf" charset="utf-8"></script>
<script src="https://unpkg.com/de9im" charset="utf-8"></script>npm install de9im
const de9im = require('de9im');Then call a predicate function on two geometries
const line = {'type': 'LineString', 'coordinates': [[0, 0], [1, 1], [2, 2]]};
const point = {'type': 'Point', 'coordinates': [1, 1]};
de9im.contains(line, point);
// = true
de9im.disjoint(line, point);
// = falseThe de9im object has the following spatial predicate functions available:
contains
coveredby
covers
crosses
disjoint
equals
intersects
overlaps
touches
withinEach predicate takes two GeoJSON arguments and an optional boolean argument:
de9im.predicate(geojson1, geojson2, [error=true])It returns true, false, or throws an exception if the geometry types provided
are not supported. If the optional argument error is false then unsupported
geometries return false instead of throwing an exception. Each predicate should
be interpreted as the first argument operating on the second. For example,
de9im.contains(line, point)should be read as
line contains point?The arguments for every predicate can be any GeoJSON type: Geometry,
Feature, GeometryCollection, FeatureCollection. All geometry types are
supported: Point, LineString, Polygon, MultiPoint, MultiLineString,
MultiPolygon. However, only homogenous geometries are supported in
collections. For example, a FeatureCollection can have points but can not mix
points and lines.
Each predicate has a unique combination of first and second argument geometries that it supports.
-
contains,covers1st / 2nd Point Line Polygon Point ✔️ ❌ ❌ Line ✔️ ✔️ ❌ Polygon ✔️ ✔️ ✔️ -
coveredby,within1st / 2nd Point Line Polygon Point ✔️ ✔️ ✔️ Line ❌ ✔️ ✔️ Polygon ❌ ❌ ✔️ -
crosses1st / 2nd Point Line Polygon Point ❌ ✔️ ✔️ Line ✔️ ✔️ ✔️ Polygon ✔️ ✔️ ❌ -
disjoint,intersects1st / 2nd Point Line Polygon Point ✔️ ✔️ ✔️ Line ✔️ ✔️ ✔️ Polygon ✔️ ✔️ ✔️ -
equals,overlaps1st / 2nd Point Line Polygon Point ✔️ ❌ ❌ Line ❌ ✔️ ❌ Polygon ❌ ❌ ✔️ -
touches1st / 2nd Point Line Polygon Point ❌ ✔️ ✔️ Line ✔️ ✔️ ✔️ Polygon ✔️ ✔️ ✔️
The following are some best practices on using de9im:
-
Data is expected to be in WGS 84 coordinates as per the GeoJSON standard.
-
Data with the GeoJSON
bboxattribute already defined will process faster. -
Data with complex geometries (e.g., self-intersections, repeated coordinates) may produce invalid results.
-
Data coordinates should be truncated to avoid unrealistically high precision (more than 6 decimal places).
The de9im library uses a partition approach to determine if two geometries
satisfy a given relation. This approach is different from the standard node/edge
labeling used by most DE-9IM implementations. Labeling approaches are only
defined for single geometries and not multi-geometries or collections and it is
not clear how to extend them to cover those cases.
Instead, de9im partitions each input geometry into elementary facets, where
each facet is either inside or outside the other geometry. For example, to test
two (multi-) polygons, the first (multi-) polygon is triangulated. This
triangulation gets intersected with the other (multi-) polygon's triangulation.
This intersection gets re-triangulated to create a decomposition of the first
(multi-) polygon such that each partition triangle (facet) is entirely inside or
outside the second (multi-) polygon. Finally, the decision of whether the
geometries satisfy the given predicate can be reduced to determining if the
individual facets satisfy the relation. The same goes for lines using segments
as the facets instead of triangles. This allows any geometry or collection type
to be processed.
Finally, while de9im has turf as a dependency, it does not use its DE-9IM
functions since it has only limited functionality and only covers a small subset
of all possible geometry and predicate combinations. The goal of de9im is to
cover all possible combinations. The turf library is only used for basic
spatial processing and geometry utility functions.
To build and test the library locally:
npm install
npm testBenchmark timing results can be found at bench.md.
Copyright (c) 2019 Daniel Pulido mailto:[email protected]
Source code is released under the MIT License.
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