2D Shape Pair Nesting for Minimum Waste Sheet Layouts
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Solution Overview
Problem
Conventional methods fail to optimally fit non-rectangular 2D shapes on a rectangular 2D sheet, leading to inefficiencies in material usage and resource wastage in manufacturing industries.
Innovation Solution
A method and system that generate pairs of 2D shapes at various orientations, determine optimal arrangements, and calculate the maximum number of repetitions based on sheet dimensions and parameters to minimize part-to-part distance, thereby identifying the optimal pair combination for efficient packing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of substance
If conventional nesting techniques are used to place multiple copies of geometric shapes on 2D sheets, then the manufacturing process can be completed, but material efficiency is poor and resource wastage occurs
Solution Approach 1:
The system dynamically adjusts orientation angles and positioning coordinates of part copies based on real-time calculations. Instead of using fixed standard orientations, the algorithm iteratively optimizes the orientation of each part copy to maximize space utilization and minimize material waste on the 2D sheet.
Solution Approach 2:
The invention changes the parameters of part placement by considering continuous orientation angles rather than discrete standard orientations. The system calculates optimal orientation parameters and positioning coordinates for each part copy, transforming the nesting problem from a discrete standard-based approach to a continuous parameter optimization approach.
2Ease of manufacture
If standard pairing techniques are used for given combinations of orientations, then the nesting process is simplified, but optimal fitting of non-rectangular 2D shapes cannot be achieved
Solution Approach 1:
The system segments the nesting problem into multiple evaluation stages. First, standard pairing techniques are used to generate initial candidate arrangements. Then, a fitness evaluation function segments the assessment into multiple criteria including area utilization, orientation compatibility, and geometric constraints. This multi-stage segmentation allows both computational efficiency and optimization precision.
Solution Approach 2:
The invention implements a feedback mechanism where the fitness evaluation function assesses each candidate arrangement and provides feedback for iterative improvement. The system uses the evaluation results to adjust orientation parameters and positioning coordinates in subsequent iterations, continuously improving the nesting arrangement until optimality is achieved.
Data Source
AI summary
This disclosure relates to method and system for optimally fitting shapes in a 2-Dimensional (2D) sheet. The method includes receiving discretized geometric data corresponding to a 2D shape; generating a pair of copies of the 2D shape including a first copy and a second copy using the discretized geometric data; determining an optimal arrangement of the first copy and the second copy on the 2D sheet to obtain an optimally arranged pair; generating first copy of the optimally arranged pair and second copy of the optimally arranged pair; determining a pair combination with a minimum distance between the first copy and the second copy; calculating a maximum number of repetitions possible for the pair combination on the 2D sheet based on sheet dimensions and a set of pair combination parameters; and identifying an optimal pair combination from a plurality of pair combinations based on the maximum number of repetitions.