Comparing RTree and Geopoly for Point Searches in SQLite

Issue Overview: RTree Works, Geopoly Fails for Point Searches

The core issue revolves around the comparison of two SQLite extensions, RTree and Geopoly, for spatial indexing and querying of geographical points. The user has set up two virtual tables, mRtree and mGeopoly, to store and query geographical coordinates (latitude and longitude). While the RTree implementation successfully retrieves points within specified bounding boxes, the Geopoly implementation fails to return any results for the same queries. This discrepancy suggests a fundamental difference in how these two extensions handle spatial data, particularly when dealing with zero-area shapes (points).

The user’s setup involves creating a base table m with latitude (lat) and longitude (lng) columns, followed by the creation of two virtual tables: mRtree using the RTree extension and mGeopoly using the Geopoly extension. Data is inserted into both tables using a JavaScript script that generates zero-area shapes (points) for each latitude and longitude pair. The query logic involves selecting points within randomly generated bounding boxes, where RTree consistently returns results, but Geopoly does not.

The discussion highlights that RTree and Geopoly handle zero-area shapes differently. RTree, which is designed to store bounding boxes, can handle points (zero-area shapes) without issue. In contrast, Geopoly, which is designed to handle polygonal shapes, struggles with zero-area shapes due to ambiguities in the ordering of polygon vertices. This difference in handling zero-area shapes is the root cause of the observed behavior.

Possible Causes: Ambiguities in Geopoly’s Handling of Zero-Area Shapes

The primary cause of the issue lies in how the Geopoly extension processes zero-area shapes. When inserting data into the mGeopoly table, the user generates a polygon with all four vertices at the same coordinates (since minX = maxX and minY = maxY for points). This results in a polygon with zero area, which introduces ambiguity in the vertex ordering. Geopoly relies on the order of vertices to determine the orientation of the polygon (clockwise or counter-clockwise), and this ambiguity can lead to incorrect or missing results when querying the data.

In contrast, the RTree extension does not suffer from this issue because it stores only the bounding box coordinates (minX, maxX, minY, maxY). Since RTree is designed to handle bounding boxes, it can effectively store and query points without any ambiguity. This fundamental difference in how the two extensions handle spatial data explains why RTree works as expected while Geopoly fails.

Another potential cause is the way the geopoly_within function is used in the query. The function is designed to check if one polygon is entirely within another polygon. However, when dealing with zero-area shapes, the function may not behave as expected due to the aforementioned vertex ordering ambiguity. This could result in the function returning false negatives, i.e., failing to identify points that should be within the specified bounding box.

Additionally, the user’s implementation of the _shape column in the mGeopoly table may contribute to the issue. The _shape column is populated with a polygon representation of the point, but this representation may not be compatible with Geopoly’s internal logic for handling zero-area shapes. This incompatibility could further exacerbate the problem, leading to the observed failure in querying points.

Troubleshooting Steps, Solutions & Fixes: Addressing Geopoly’s Limitations with Zero-Area Shapes

To resolve the issue, several steps can be taken to ensure that Geopoly handles zero-area shapes correctly. The first step is to modify the data insertion process to avoid creating zero-area shapes. Instead of generating a polygon with all vertices at the same coordinates, a small offset can be introduced to create a polygon with a non-zero area. This approach eliminates the ambiguity in vertex ordering and allows Geopoly to process the data correctly.

For example, the JavaScript code for inserting data into the mGeopoly table can be modified as follows:

const offset = 0.000001; // Small offset to create a non-zero area
for (row of rows) {
  id++;
  minX = row.lng;
  maxX = row.lng + offset;
  minY = row.lat;
  maxY = row.lat + offset;
  ll = `[${minX},${minY}]`;
  lr = `[${maxX},${minY}]`;
  ur = `[${maxX},${maxY}]`;
  ul = `[${minX},${maxY}]`;
  _shape = `[${ll},${lr},${ur},${ul},${ll}]`;
  
  insGeopoly.run({_shape, lat: row.lat, lng: row.lng});
}

By introducing a small offset, the polygon will have a non-zero area, and Geopoly will be able to process it correctly. This modification ensures that the geopoly_within function behaves as expected when querying the data.

Another solution is to use a different approach for querying points in the mGeopoly table. Instead of using the geopoly_within function, the geopoly_contains_point function can be used to check if a point is within a polygon. This function is specifically designed for point-in-polygon queries and does not suffer from the same limitations as geopoly_within when dealing with zero-area shapes.

The query logic can be modified as follows:

selGeopoly = `SELECT * 
        FROM mGeopoly g JOIN m ON g.lng = m.lng AND g.lat = m.lat 
        WHERE geopoly_contains_point(_shape, @x, @y)`;
for (let i = 0, j = 50; i < j; i++) {
  minX = randomLng();
  maxX = minX + 5;
  minY = randomLat();
  maxY = minY + 5;
  x = (minX + maxX) / 2; // Center of the bounding box
  y = (minY + maxY) / 2; // Center of the bounding box
  selGeopoly.all({x, y});
}

By using the geopoly_contains_point function, the query logic becomes more robust and can handle points correctly. This approach avoids the issues associated with zero-area shapes and ensures that the query returns the expected results.

In addition to these solutions, it is important to validate the latitude and longitude values before inserting them into the database. As suggested in the discussion, the latitude should be within the range of -87 to 87 degrees to avoid significant distortion in calculations. The following SQL code can be used to enforce this constraint:

CREATE TABLE IF NOT EXISTS m (
    id INTEGER PRIMARY KEY,
    longitude REAL CHECK (abs(longitude) <= 180),
    latitude REAL CHECK (abs(latitude) < 87),
    desc TEXT
);

This constraint ensures that the latitude values are within a safe range, reducing the risk of distortion and improving the accuracy of spatial calculations.

Finally, it is important to document the limitations and best practices for using the Geopoly extension. Users should be aware that Geopoly is designed for polygonal shapes and may not handle zero-area shapes correctly. By following the recommended practices, such as avoiding zero-area shapes and using the appropriate query functions, users can achieve reliable results with Geopoly.

In conclusion, the issue of Geopoly failing to return results for point searches can be resolved by modifying the data insertion process to avoid zero-area shapes, using the appropriate query functions, and validating the input data. By addressing these issues, users can leverage the full potential of the Geopoly extension for spatial indexing and querying in SQLite.