4D Concave Polygon Routing for Moving Avoidance Zones
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Solution Overview
Problem
Existing navigation systems face challenges in accurately and efficiently routing around concave polygon avoidances, particularly when these avoidances are moving, as they often require computationally intensive conversions to convex polygons, which can reduce accuracy and increase computational demands.
Innovation Solution
A navigation system that maintains four-dimensional data in a database, generates and shifts concave polygons based on displacement vectors, identifies and removes internal edges, and compares the polygons to cells to output navigation alerts, thereby directly handling moving concave polygons without the need for conversion to convex forms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If concave polygon avoidances are converted to convex polygons for routing calculations, then the routing can be performed using existing algorithms, but the computational complexity increases and accuracy decreases
Solution Approach 1:
Instead of converting concave polygons to convex polygons to use existing routing algorithms, the patent inverts the approach by directly processing concave polygons using a specialized algorithm that handles their unique geometric properties, including identifying and managing internal edges and vertices
Solution Approach 2:
The patent changes the parameter representation by introducing a data structure that explicitly tracks internal edges and vertices of concave polygons, allowing the routing algorithm to work directly with the concave geometry without conversion, thereby maintaining both accuracy and computational efficiency
2Ease of manufacture
If concave polygon avoidances are converted to convex polygons, then routing algorithms can be applied, but the processing time increases
Solution Approach 1:
The patent performs preliminary actions by pre-identifying and marking internal edges and vertices of concave polygons before the routing calculation begins. This preprocessing step allows the main routing algorithm to proceed efficiently without needing to perform geometric conversions during execution
Solution Approach 2:
The patent segments the concave polygon into manageable components by identifying internal edges and vertices, allowing the routing algorithm to process each segment independently or in a structured manner, reducing overall computational time compared to converting the entire polygon
3Ease of manufacture
If concave polygon avoidances are converted to convex polygons, then existing routing algorithms can be used, but the accuracy of the navigation solution decreases
Solution Approach 1:
Instead of approximating concave polygons as convex polygons which loses geometric accuracy, the patent inverts the conventional approach by directly processing the true concave geometry, preserving all original vertices, edges, and internal structures for accurate routing calculations
Data Source
AI summary
A navigation system includes a navigation database and a route generator. The route generator receives an avoidance, generates a concave polygon representing the avoidance with respect to four-dimensional data of the navigation database, identifies a displacement vector of the avoidance, shifts the concave polygon using the displacement vector, identifies each gap between vertices of the shifted concave polygon, adds an added edge to the to connect vertices across each identified gap, determines, for each edge of the concave polygon, if the edge includes an internal edge, removes each internal edge from the concave polygon, compares the concave polygon to the plurality of cells, identifies one or more cells in which the concave polygon is located, and outputs a navigation alert based on the identified one or more cells.