Polygon Simplification Using Vertex Reduction Thresholds
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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 polygon expanding and reducing logic in computing devices to generate a simplified polygon by creating new vertices outside or inside the original polygon, and removing intermediate vertices within a threshold distance of proposed segments, thereby reducing the number of vertices and simplifying the polygon while ensuring it encompasses or is encompassed by the original polygon.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If specialized operations are performed on complex polygons with hundreds or thousands of vertices, then operational completeness may be achieved, but computational resources are exhausted and processing time increases significantly
Solution Approach 1:
The patent segments the complex polygon into multiple simplified polygon representations at different levels of detail. Each segmented representation contains fewer vertices and can be used for different operational contexts, allowing the system to balance operational completeness with computational resource consumption by selecting appropriate segmentation levels.
Solution Approach 2:
The patent applies partial action by performing operations on a simplified version of the polygon that contains only the necessary vertices for the specific task, rather than processing all vertices. This partial processing approach reduces computational resources while maintaining sufficient operational completeness for the given context.
2Measurement precision
If specialized operations are performed on polygons with many vertices, then accurate results may be obtained, but processing time becomes excessive
Solution Approach 1:
The patent implements dynamic polygon simplification where the level of detail is adjusted based on the specific operational requirements and context. The system can dynamically switch between different polygon representations with varying vertex counts, optimizing the balance between result accuracy and processing time for different operations.
Solution Approach 2:
The patent changes the parameter of vertex count to create multiple polygon representations. By varying this parameter, the system can select appropriate levels of geometric detail that provide sufficient accuracy for specific operations while minimizing processing time through reduced vertex counts.
3Reliability
If hardware or software resources are increased to handle complex polygons, then operational success rate improves, but system complexity and cost increase
Solution Approach 1:
The patent performs preliminary action by pre-processing complex polygons into multiple simplified representations before operations are executed. This pre-segmentation and simplification reduces the computational burden during actual operations, improving operational success rate without requiring proportionally increased hardware or software resources.
Solution Approach 2:
The patent creates multiple simplified copies of the original polygon, each with different levels of detail. These copied representations can be used instead of the full-complexity original polygon for various operations, reducing system complexity and resource requirements while maintaining operational success through appropriate copy selection.
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.