Triangulation of Planar Figures with Holes via Grid Segmentation
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Solution Overview
Problem
Existing methods for dividing a two-dimensional planar figure into triangle elements are computationally intensive and lack robustness, especially when dealing with figures containing holes, limiting their applicability and efficiency.
Innovation Solution
A method that segments a virtual plane into quadrangular cells, adds points at edge-cell intersections, generates triangle elements within each cell to fill the region without overlap, and removes elements outside the figure, reducing computational burden and enabling handling of figures with internal holes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If all points are connected by line segments and overlapping segments are removed (related art method), then triangle elements can be generated, but computation time increases and robustness decreases especially for figures with holes
Solution Approach 1:
The virtual plane is segmented into multiple quadrangular cells arranged in a grid pattern. Each cell is independently processed to generate triangle elements, which reduces the overall computational complexity and improves robustness by localizing the processing to manageable sections rather than treating the entire figure as one complex problem.
2Adaptability or versatility
If the method handles two-dimensional planar figures with holes, then applicability improves, but existing methods lack robustness and become computationally intensive
Solution Approach 1:
By dividing the virtual plane into quadrangular cells, the method can independently handle different regions including those with holes. Each cell is processed separately, allowing the method to adapt to complex geometries with holes while maintaining computational efficiency and simplicity in the overall approach.
Solution Approach 2:
Additional points are introduced at intersections of cell borders and at vertices to serve as intermediary elements. These additional points facilitate the generation of triangle elements in complex regions with holes by providing stable reference points for triangulation, thereby improving robustness without significantly increasing method complexity.
3Ease of operation
If traditional triangulation methods are used, then triangle elements can be generated, but the methods are computationally intensive and lack ease of troubleshooting
Solution Approach 1:
The computation is divided into independent cell-level operations, making it easier to identify and troubleshoot specific problems in particular regions without having to analyze the entire figure. This segmentation also reduces computation time by allowing parallel processing of multiple cells and avoiding the need to process the entire figure as one complex operation.
Data Source
AI summary
A triangle element division method includes acquiring position information of a plurality of feature points positioned on a border of a two-dimensional planar figure, segmenting a virtual plane including the two-dimensional planar figure into a plurality of quadrangular cells, disposing additional points at positions where edges as line segments connecting two adjacent feature points on the border of the two-dimensional planar figure and borders of the plurality of cells cross, and vertices of the plurality of cells, for each of the plurality of cells, generating a plurality of triangle elements with the feature points and the additional points in the cell as vertices such that conditions that a region in the cell is filled with a plurality of the triangle elements and the triangle elements do not overlap each other are satisfied, and removing the triangle elements positioned outside the two-dimensional planar figure.