Recursive Triangle Classification for Mated Surface Area Calculation
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Solution Overview
Problem
Existing computer-aided design (CAD) methods fail to accurately determine the surface area of the outer layer of multi-member objects, as they do not account for mated portions which are not on the outer layer, leading to inaccurate paint or coating estimates.
Innovation Solution
A recursive process is employed to analyze each triangle of a three-dimensional object represented by multiple members, classifying triangles as part of the outer layer or mated surface, and subdividing unclassified triangles to accurately determine the mated surface and surface area, ensuring accurate estimation of the outer layer surface area.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If the surface area is determined by summing the area of triangles of all members, then the calculation is simple, but the result is inaccurate for multi-member objects
Solution Approach 1:
The patent segments the surface area calculation into two distinct components: outer layer surface area and mated surface area. By dividing the total surface area into these segments and calculating them separately using different methods (outer layer through triangle area summation, mated surface through projection), the patent achieves both computational simplicity and measurement precision for multi-member objects.
2Measurement precision
If mated portions are excluded from the outer layer, then the outer layer surface area is accurately determined, but the calculation complexity increases
Solution Approach 1:
The patent extracts and removes mated portions from the outer layer surface area calculation. By identifying and excluding these portions through projection-based methods, the patent accurately determines only the outer layer surface area while managing calculation complexity through systematic exclusion rather than inclusive calculation.
Solution Approach 2:
The patent introduces projection as an intermediary mechanism to determine mated surfaces. By projecting member surfaces onto a reference plane and analyzing the projected areas, the patent creates an intermediate representation that simplifies the identification and exclusion of mated portions from the outer layer calculation.
Data Source
AI summary
A method for determining a mated portion of an object can include receiving design data defining a three-dimensional object having a first member mated with a second member. Each member can be represented by a plurality of triangles. The method can include determining an outer layer of the three-dimensional object and a mated surface of the three-dimensional object. The mated surface may be determined by utilizing a recursive process to analyze each specific triangle of the plurality of triangles. The recursive process can classify a triangle as: (i) on the outer layer when all of its vertices are on the outer layer, and (ii) in the mated surface when none of its vertices are on the outer layer. When a triangle has at least one but not all of its vertices on the outer layer, the triangle can be subdivided into sub-triangles, which are then analyzed individually.