Voronoi Mesh Generation Without Clipping for Arbitrary Domains
Find Innovative SolutionsGenerate Solutions
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 involve clipping.
Innovation Solution
A computing system performs Voronoi domain decomposition without clipping by identifying seeds outside and inside the domain, ensuring facets are coincident with the domain boundaries, and populating the interior with seeds to maintain bounded aspect ratios, resulting in a conforming Voronoi mesh.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional Voronoi domain decomposition relies on clipping to handle arbitrary-shaped domains, then the domain can be decomposed into Voronoi cells, but the clipped cells exhibit undesirable properties such as large aspect ratios and non-convex shapes
Solution Approach 1:
The patent applies preliminary action by pre-positioning seeds outside the domain boundaries before performing Voronoi tessellation. This anticipatory placement ensures that the resulting Voronoi cells naturally conform to the domain geometry without requiring subsequent clipping operations, thereby maintaining cell quality properties such as bounded aspect ratios and convexity while handling arbitrary-shaped domains
Solution Approach 2:
The patent inverts the conventional approach by placing seeds outside the domain rather than inside. This inversion causes the Voronoi cell boundaries to naturally align with the domain boundary, eliminating the need for clipping and preserving desirable cell geometric properties throughout the decomposition process
2Manufacturing precision
If clipping is used to constrain Voronoi cells within domain boundaries, then cells conform to the boundary, but clipping creates non-convex and star-shaped cells that are undesirable for numerical simulations
Solution Approach 1:
The patent pre-positions seeds outside the domain boundaries before tessellation, which anticipatorily ensures that Voronoi cell facets will naturally align with the domain boundary. This eliminates the need for clipping operations that would otherwise compromise cell convexity and create undesirable non-convex or star-shaped cells
Solution Approach 2:
The patent converts the potential harm of having seeds outside the domain into a benefit. By intentionally placing seeds outside, the method causes Voronoi cell boundaries to naturally conform to the domain geometry, achieving both boundary conformity and cell convexity without the harmful effects of clipping
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 three-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.