Conforming Voronoi Mesh Generation Without Clipping
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Solution Overview
Problem
Conventional Voronoi domain decomposition methods rely on clipping, leading to undesirable properties such as large aspect ratios and non-convex cells, lacking a robust approach that does not require clipping.
Innovation Solution
A computing system performs Voronoi domain decomposition without clipping by identifying seeds both inside and outside an enclosed domain, ensuring facets are coincident with the domain's edges, and populating the interior with seeds to create a conforming Voronoi mesh with bounded aspect ratios.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional Voronoi domain decomposition relies on clipping, then domain decomposition can be performed, but the resulting Voronoi cells have large aspect ratios and may be non-convex or non-star-shaped
Solution Approach 1:
The patent applies preliminary action by pre-positioning seeds at locations that guarantee desirable Voronoi cell properties before the decomposition process begins. Specifically, seeds are strategically placed such that their Voronoi facets will be coincident with domain edges, preventing the need for clipping and ensuring cells maintain convexity and star-shaped properties from the outset.
Solution Approach 2:
The patent changes the parameter of seed positioning from conventional approaches to specific locations that ensure facets are coincident with domain boundaries. By carefully selecting seed positions and adjusting the decomposition parameters, the method achieves both ease of decomposition and high-quality cell shapes without requiring post-processing clipping operations.
2Productivity
If clipping is used in Voronoi domain decomposition, then decomposition can be completed, but the process becomes less robust and may create cells with undesirable properties
Solution Approach 1:
The patent extracts the clipping operation from the Voronoi domain decomposition process entirely. By taking out this problematic step and replacing it with careful seed positioning, the method achieves both productivity (decomposition completion) and reliability (robustness), as the decomposition proceeds without needing to clip cells that would otherwise have undesirable properties.
3Device complexity
If seeds are placed only inside the domain, then decomposition is simple, but facets cannot be made coincident with domain edges without clipping
Solution Approach 1:
The patent applies another dimension by extending seed placement from the interior 2D domain to include positions on the domain boundary itself. This dimensional extension allows seeds to be placed precisely where needed to create facets coincident with edges, achieving manufacturing precision without significantly increasing overall complexity, as the boundary placement follows systematic rules.
Data Source
AI summary
A computing system is described herein, where the computing system includes a processor and memory storing instructions that, when executed by the processor, cause the processor to perform the following acts: 1) receiving a computer-implemented definition of an enclosed geometric domain, wherein the geometric domain is two-dimensional; 2) determining locations of seeds for the enclosed geometric domain; 3) decomposing the enclosed geometric domain into a conforming Voronoi mesh based on the locations of the seeds, wherein the conforming Voronoi mesh comprises Voronoi cells, and further wherein the conforming Voronoi mesh is bounded by the enclosed domain; and 4) performing a numerical simulation to generate simulation results, wherein the numerical simulation is based on at least one Voronoi cell in the Voronoi cells of the conforming Voronoi mesh.