Aircraft-in-Airspace Containment Checking with Angular Boundary Indexing
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Solution Overview
Problem
Current systems are inefficient in accurately and timely determining whether an aircraft is within an airspace area of interest, particularly when there are a large number of aircraft or the airspace area has an irregular shape, leading to prolonged processing times.
Innovation Solution
Convert vertex points defining the airspace area of interest to vertex angles in a polar coordinate system and store them in a binary search tree, then convert object locations to object angles for rapid identification of line segment crossings using these angles to determine if the object is inside the area.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If current systems are used to determine whether an aircraft is within an airspace area of interest, then the determination can be made, but the processing time is prolonged when there are a large number of aircraft or the airspace area has an irregular shape
Solution Approach 1:
The patent transforms the traditional Cartesian coordinate system into a polar coordinate system, representing vertices by (r, θ) pairs instead of (x, y) coordinates. This dimensional transformation enables the use of angular sorting and binary search algorithms, reducing the time complexity from O(N) to O(log N) while maintaining accurate determination of whether objects lie within irregular polygonal boundaries
Solution Approach 2:
The patent changes the parameter representation from linear coordinates to angular parameters. By converting vertex positions into polar coordinates and sorting them by angle, the system enables efficient binary search operations. The key parameter change is representing spatial relationships through angular measurements from a reference point, which allows for logarithmic-time querying of object locations within irregular airspace boundaries
2Quantity of substance
If a large number of aircraft are monitored, then comprehensive coverage is achieved, but the processing time increases significantly
Solution Approach 1:
The patent performs preliminary sorting of vertex angles and pre-computes the polar coordinate representations of all boundary vertices before actual object detection. This preprocessing step organizes the spatial data in advance, allowing subsequent object location queries to be resolved efficiently through binary search without requiring complex real-time calculations, thereby maintaining high processing efficiency even when monitoring large numbers of aircraft
Solution Approach 2:
The patent replaces traditional geometric computation methods with a data structure-based approach using polar coordinates and binary search trees. Instead of performing iterative geometric tests for each object, the system uses angular indexing and logarithmic-time search algorithms, substituting mechanical geometric processing with efficient computational data structure operations that scale better with the number of objects monitored
3Shape
If traditional coordinate systems are used to define airspace boundaries, then the boundaries can be represented, but the determination of object location within irregular shapes is computationally intensive
Solution Approach 1:
The patent transforms the representation of irregular polygonal boundaries from Cartesian coordinates to polar coordinates, where each vertex is represented as (r, θ). By introducing angular dimension θ and using a reference point inside the polygon, the system converts complex 2D spatial containment tests into simpler angular interval queries, reducing computational complexity while accurately representing arbitrary irregular shapes
Solution Approach 2:
The patent pre-sorts the vertex angles θ in ascending order and stores them in an indexed data structure before performing object location determination. This preliminary organization of angular data allows subsequent queries to use binary search algorithms, transforming the computational complexity from linear O(N) to logarithmic O(log N), making the system feasible for real-time monitoring applications
Data Source
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AI summary
A computer-implemented method and system for identifying an object in an area of interest. The area of interest is enclosed by a boundary comprising a plurality of line segments extending between vertex points. A reference point relative to the area of interest and a reference direction from the reference point are determined and used to determine a vertex angle of each vertex point. The reference point and reference direction also are used to determine an object angle of the object from location information identifying a location of the object. The object angle and the vertex angles are used to identify a number of line segment crossings in the plurality of line segments. An indicator is generated to indicate whether the object is in the area of interest based on the number of line segment crossings.