MARKLOGIC SERVER

value but a latitude and longitude pair. Picture a long array of structures holding lat/
long values and associated document IDs, sorted by latitude major and longitude minor,
held in a memory-mapped file. (Latitude major and longitude minor means they're
sorted first by latitude, then by longitude for points with the same latitude.)
Point queries can be easily resolved by finding the matching points within the pre-sorted
index and extracting the corresponding document ID or IDs. Box queries (looking for
matches between two latitude values and two longitude values) can be resolved by first
finding the subsection of the geospatial index within the latitude bounds, then finding
the sections within that range that also reside within the longitude bounds. 11
For circle and polygon constraints, MarkLogic employs a high-speed comparator to
determine if a given point in the range index resides inside or outside the circle or
polygon constraint. The geospatial indexes use this comparator where a string-based
range index would use a string collation comparator. The comparator can compare 1
million to 10 million points per second per core, allowing for a fast scan through the
range index. The trick is to look northward or southward from any particular point,
counting arc intersections with the bounding shape: an even number of intersections
means the point is outside, odd means it's inside.
As an accelerator for circles and polygons, MarkLogic uses a set of first-pass bounding
boxes (a box or series of boxes that fully contain the circle or polygon) to limit the
number of points that have to be run through the detailed comparator. A circle
constraint thus doesn't require comparing every point, only those within the bounding
box around the circle.
Searches on certain parts of the globe complicate matters. The poles represent
singularities where all longitude lines converge, so MarkLogic uses special trigonometry
to help resolve searches there. For geospatial shapes that cross the anti-meridian (where
longitude values switch from negative to positive), the server generates multiple smaller
regions that don't cross this special boundary and unions the results.
This subject is described more in Geospatial Search Applications.
11 The worst-case performance on bounding boxes? A thin vertical slice.
81