Spatial Index for Point in Polygon Operations
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Solution Overview
Problem
Conventional point in poly operations are processor-intensive due to the need for full geometric analysis of irregular geographic boundaries, which can be time-consuming and inefficient when dealing with large numbers of points in location-based services.
Innovation Solution
A pre-generated geographic index is created by subdividing the geographic area into regular geometric shapes and indexing them, allowing for a simplified comparison of sample points, which can be combined with existing quad-tree or r-tree indexes to reduce processing time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If full geometric analysis is performed on irregular geographic boundaries, then measurement precision is improved, but processing time increases
Solution Approach 1:
The geographic area is segmented into multiple hierarchical levels of rectangular boxes. The boundary box is divided into first level boxes, which are further divided into second level boxes, and so on. This segmentation allows the system to check points against progressively finer divisions, achieving accurate results while reducing the need for full geometric analysis in all cases.
Solution Approach 2:
The rectangular boxes at various hierarchical levels are pre-generated and stored as an index structure before actual point queries. This preliminary action creates a ready-to-use spatial index that enables fast lookup during point in polygon operations, avoiding the need to perform complex geometric analysis from scratch for each query.
2Productivity
If hierarchical rectangular box indexing is implemented, then processing speed is improved, but device complexity increases
Solution Approach 1:
The complex geographic boundary problem is segmented into manageable hierarchical levels of rectangular boxes. Each level divides the space into uniform grids, transforming an irregular geometric problem into a structured hierarchical search problem that is easier to process efficiently.
Solution Approach 2:
The problem is transformed from checking points against irregular 2D polygon boundaries to checking points against a hierarchical structure of rectangular boxes. This dimensional transformation to a regular grid-based hierarchy simplifies the computational geometry while maintaining spatial accuracy.
Data Source
AI summary
An improved method is provided for determining whether a sample point is within a defined geographic area. Indexes for the geographic area of interest are generated in advance. Such indexes complement the traditional spatial indexing techniques such as quad tree and r-tree. The geographic area, as defined by an outer boundary, is subdivided into some regular geometric shape, preferably a rectangle, encoded into a suitable form, and indexed. Then, a simplified comparison of the sample point to the indexed regular shapes is made.