Triangular Grid Subdivision for 3D Object Representation
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Solution Overview
Problem
Converting 3D object representations between formats introduces differences that affect the accuracy of curved surface representation and slicing for 3D printing, particularly when transitioning from NURBS to mesh formats, as existing methods struggle to ensure sufficient precision and efficiency in capturing surface details.
Innovation Solution
A method involving subdividing parametric space into triangular grids, calculating differences between corresponding sections, and iteratively refining the grid based on error thresholds to create curved triangles that accurately represent the 3D object, allowing for more precise conversion and slicing, using techniques such as Steiner Patches and barycenter calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a uniform triangular grid is used for initial subdivision, then the processing is simple and fast, but the accuracy of curved surface representation is insufficient
Solution Approach 1:
The patent applies segmentation by dividing the parametric space into multiple triangular grids with varying levels of subdivision. Areas with high curvature or large conversion errors are subdivided into smaller triangles, while flat areas use larger triangles. This adaptive segmentation allows the system to achieve high accuracy where needed while maintaining processing efficiency in less critical areas.
Solution Approach 2:
The patent implements local quality by applying different subdivision densities to different regions of the parametric space based on local curvature characteristics and error metrics. Regions with high curvature or large conversion errors receive finer subdivision, while regions with low curvature use coarser subdivision. This local adaptation optimizes the balance between accuracy and processing efficiency.
2Manufacturing precision
If the triangular grid is refined to improve accuracy, then the surface representation precision improves, but the computational complexity and processing time increase
Solution Approach 1:
The patent applies dynamics by implementing an iterative refinement process where the triangular grid is dynamically adjusted based on calculated error metrics. The system starts with a coarse grid, calculates conversion errors, and selectively refines only those regions where errors exceed a threshold. This dynamic adaptation continues until convergence, optimizing the balance between accuracy and computational complexity.
Solution Approach 2:
The patent uses partial action by applying refinement only to specific regions where it is most needed, rather than uniformly refining the entire parametric space. By identifying and targeting only the regions with high conversion errors or high curvature, the system achieves high overall accuracy with significantly reduced computational complexity compared to uniform refinement.
3Measurement precision
If iterative refinement is performed to meet accuracy standards, then the conversion accuracy improves, but the processing time increases
Solution Approach 1:
The patent implements feedback by calculating conversion errors between NURBS and mesh representations at each iteration and using this error information to guide subsequent refinement steps. The error metrics feed back into the subdivision process, directing refinement to regions where conversion accuracy is insufficient. This feedback-driven approach ensures that processing time is invested efficiently in achieving the required accuracy level.
Solution Approach 2:
The patent applies preliminary action by performing error calculations and curvature analysis before committing to full refinement. The system evaluates which regions require refinement and prepares a targeted subdivision plan, avoiding unnecessary processing in regions that already meet accuracy requirements. This preliminary assessment optimizes the subsequent refinement process.
Data Source
AI summary
An example of a non-transitory computer-readable medium storing machine-readable instructions. The instructions may cause the processor to receive a three-dimensional (3D) object representation and subdivide it into a triangular grid. Curved triangles may be calculated for triangles in the triangular grid. The triangles may be subdivided and differences calculated between corresponding sections of the curved triangles and the received 3D object representation.