Point-in-polygon test using horizontal ray casting index
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Solution Overview
Problem
Existing point-in-polygon (PIP) techniques, such as the crossing number (CN) method, are computationally expensive and inefficient when dealing with large geographic data sets, as they require iterating over numerous vertices of polygons, making it challenging to process queries over geographic data effectively.
Innovation Solution
A new indexing technique that involves casting horizontal rays from polygon segments onto a reference line, storing intersected segments, and using a sorted point structure to retrieve intersected segments for a given point, thereby bypassing the need to iterate over polygon boundaries, allowing for efficient PIP testing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the crossing number (CN) technique is used to solve the PIP problem, then the point-in-polygon determination can be performed, but the computational complexity increases significantly when dealing with large geographic data sets with hundreds of thousands of vertices
Solution Approach 1:
The patent segments the geographic data processing into two distinct phases: an offline indexing phase where geographic boundaries are pre-processed and stored in a compressed format, and an online query phase where point-in-polygon tests are performed using the pre-built index. This segmentation eliminates the need to iterate over all vertices during query execution, reducing computational complexity from O(n) to O(log n) or better, while maintaining determination accuracy.
Solution Approach 2:
The patent applies preliminary action by pre-processing geographic boundary data into a compressed index structure before actual queries are executed. The indexing process pre-calculates and stores essential geometric information in a compact format, so that during query execution, the system only needs to perform efficient lookups and comparisons rather than iterating over all original vertices, thereby reducing computational complexity while preserving accuracy.
2Reliability
If the crossing number (CN) technique is applied to each data point against large GIS boundary datasets, then complete PIP testing is achieved, but processing time becomes computationally expensive
Solution Approach 1:
The patent divides the processing into offline indexing (pre-processing boundaries into compressed format) and online querying (efficient point tests). This ensures complete PIP testing through the compressed index structure while reducing processing time from linear O(n) per query to much faster operations using the pre-compressed representation.
Solution Approach 2:
The system performs preliminary compression of geographic boundary data into a compact index structure that preserves all necessary geometric information for accurate PIP testing. This pre-processing eliminates the need to access and iterate over the full original vertex sets during query execution, maintaining testing completeness while dramatically reducing access and processing time.
3Measurement precision
If the geographic boundary data is stored in its original format with all vertices, then complete geometric information is preserved, but memory usage and processing efficiency deteriorate
Solution Approach 1:
The patent extracts the essential geometric information from the full vertex representations and stores only the compressed index structure that contains the minimum necessary data for accurate PIP testing. This extraction process removes redundant information while preserving geometric completeness, thereby reducing memory usage without sacrificing measurement precision.
Solution Approach 2:
The patent transforms the geographic boundary data from its original high-resolution vertex format into a compressed parameter-based representation. This parameter change maintains the essential geometric properties needed for accurate PIP testing while significantly reducing the data size stored in memory, achieving both geometric information completeness and efficient memory utilization.
Data Source
AI summary
A system that displays geographic data is disclosed. During operation, the system receives a query to be processed, wherein the query is associated with a set of geographic regions. Next, the system uses a late-binding schema generated from the query to retrieve a set of data points from a set of events containing previously gathered data. Then, for each data point in a set of data points, the system identifies zero or more geographic regions in the set of geographic regions that the data point falls into. Finally, the system displays the set of geographic regions, wherein each polygon that defines a geographic region is marked to indicate a number of data points that fall into the polygon.