Polygon Simplification Using Buffer-Based Vertex Reduction
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Solution Overview
Problem
Complex polygons with hundreds or millions of vertices require significant computational resources for specialized operations, often leading to resource exhaustion and failure, especially when performing searches or determining item locations within or outside the polygon.
Innovation Solution
Implementing computer-implemented techniques that include polygon expanding and reducing logic to generate a simplified polygon by removing intermediate vertices within a threshold distance of proposed segments, using processes like Minkowski addition and Ramer-Douglas-Peucker vertex reduction, to reduce the number of vertices while ensuring the simplified polygon accurately represents the original polygon.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If specialized operations are performed on complex polygons with many vertices, then operational accuracy is maintained, but computational resources are excessively consumed leading to resource exhaustion
Solution Approach 1:
The patent segments the polygon processing task into two distinct phases: (1) simplification phase where the polygon is reduced to fewer vertices using geometric algorithms, and (2) operation phase where specialized operations are performed on the simplified polygon. This segmentation allows the computationally intensive operations to be performed on a reduced dataset while maintaining result accuracy through buffer zone verification.
Solution Approach 2:
The patent applies preliminary action by performing polygon simplification before executing specialized operations. The buffer simplification process pre-processes the polygon data by removing redundant vertices and creating a simplified representation that preserves essential geometric characteristics. This preliminary simplification reduces the computational burden of subsequent operations while maintaining operational reliability through buffer zone validation.
2Productivity
If polygons are simplified by removing vertices, then computational efficiency is improved, but geometric accuracy may be degraded
Solution Approach 1:
The patent applies local quality by creating buffer zones around the original polygon boundary and using different processing rules for different regions. Vertices within the buffer zone are preserved to maintain geometric accuracy, while vertices outside the buffer zone can be removed to improve computational efficiency. This localized approach ensures that simplification does not compromise the essential geometric characteristics of the polygon.
Solution Approach 2:
The patent uses partial action by selectively removing only those vertices that fall outside the buffer zone rather than uniformly simplifying all vertices. This partial removal strategy maintains geometric accuracy in critical regions while achieving computational efficiency in less critical regions. The buffer zone acts as a threshold that determines which vertices to preserve and which to remove.
3Measurement precision
If data collection becomes more fine-grained, then data definition quality is improved, but polygon complexity increases leading to resource exhaustion
Solution Approach 1:
The patent applies preliminary action by automatically performing buffer simplification on high-definition geospatial data before it is used in specialized operations. This pre-processing step reduces the complexity of fine-grained data while preserving its essential characteristics and measurement precision. The buffer zone methodology ensures that even highly detailed data can be efficiently processed without resource exhaustion.
Solution Approach 2:
The patent changes the parameter of polygon representation by transforming it from a high-vertex-count format to a simplified format with fewer vertices. The buffer zone distance parameter controls the degree of simplification, allowing flexible adjustment between data fidelity and computational efficiency. This parameter change enables the system to handle fine-grained data without being overwhelmed by complexity.
Data Source
AI summary
Processes, machines, and computer-readable media are provided for expanding and simplifying a polygon or reducing and simplifying a polygon. Polygon expanding or reducing logic receives information that represents a polygon having a set of vertices. The polygon expanding or reducing logic determines another polygon having another set of vertices, such that the other polygon encompasses or is encompassed by the polygon, by determining, for each vertex of the set of vertices, a new set of vertices that are derived from the vertex and are at least a particular distance outside or inside the polygon. The vertex reducing logic determines whether an intermediate vertex is within the particular distance of a proposed segment between two other vertices of the other set of vertices, even though the intermediate vertex is not on the proposed segment, and, if so, removing the intermediate vertex from the other set of vertices.