Alpha Shape Determination via Percentage-Based Triangulation
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Solution Overview
Problem
Existing methods for determining alpha shapes from sets of points lack predictability and efficiency, particularly in scaling and memory usage, leading to inconsistent results and high processing demands.
Innovation Solution
A system that receives a percentage value from a client device, determines a triangulation, calculates an alpha value based on edge lengths or triangle areas, and generates an alpha shape by identifying edges or triangles that define the shape without enclosing other points, ensuring consistent results across scaled sets of points and reducing memory and processing requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing methods determine alpha shapes from sets of points, then alpha shapes can be generated, but the results lack predictability and consistency across scaled datasets
Solution Approach 1:
The patent changes the parameter used to determine alpha shapes from fixed geometric calculations to a percentage-based selection method. By selecting edges or triangles based on a specified percentage of the total number of edges or triangles in the triangulation, the method achieves predictable and consistent results across scaled datasets. The alpha value is determined by calculating a percentage value based on the total number of edges or triangles, then selecting the corresponding edge or triangle from a sorted list, ensuring scalability and consistency.
2Measurement precision
If existing methods determine alpha shapes with high precision, then accurate region boundaries are obtained, but memory usage and processing demands increase significantly
Solution Approach 1:
The patent extracts only the necessary information needed to determine alpha shapes by working directly with the triangulation structure and selecting specific edges or triangles based on percentage criteria. Instead of computing and storing all possible alpha shapes or maintaining complex data structures, the method extracts the required edges or triangles by sorting and selecting based on the percentage value, significantly reducing memory usage while maintaining boundary accuracy.
Solution Approach 2:
The patent segments the problem into discrete steps: first performing triangulation to divide the point set into triangles, then sorting edges or triangles by length or area, and finally selecting the appropriate number based on the percentage value. This segmentation allows the method to process large datasets efficiently by working with sorted lists and selecting only the necessary components, reducing both memory usage and processing demands.
3Area of stationary object
If existing methods process large sets of points to determine alpha shapes, then complete region coverage is achieved, but processing time and computational efficiency decrease
Solution Approach 1:
The patent performs preliminary triangulation of the point set to establish a structured representation before determining alpha shapes. By pre-computing the triangulation and organizing edges or triangles into sorted lists based on length or area, the method prepares the data in advance for efficient selection. This preliminary organization allows rapid determination of alpha shapes by simply selecting the appropriate number of edges or triangles based on the percentage value, significantly improving processing speed for large datasets.
Data Source
AI summary
Some embodiments provide a non-transitory machine-readable medium that stores a program. The program receives, from a client device, a percentage value for a set of points. The program further determines a triangulation based on the set of points. The program also determines an alpha value based on the triangulation and the percentage value. The program further determines an alpha shape based on the alpha value. The program also provides the client device the alpha shape.