Triangular Mesh Field Representation via Adaptive Recursion
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Solution Overview
Problem
Existing methods for mapping arbitrary fields onto 3D triangular meshes face challenges with uneven field resolution and storage efficiency, particularly for meshes with significant intrinsic curvature, leading to lower sampling accuracy and increased computing resources.
Innovation Solution
The technique involves creating separate 2D triangular maps for each triangle in a 3D triangular mesh using adaptive recursion, subdividing triangles into sub-triangles, sampling field values at leaf nodes, calculating average values for non-leaf nodes, and pruning nodes with low variance to store only necessary data, allowing for hierarchical and multi-resolution representation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If texture mapping is used to map arbitrary fields onto 3D triangular meshes, then the field can be represented over the entire surface of the model, but the data fields require considerable time and computing resources to create and result in very large and complex datasets
Solution Approach 1:
The patent segments the 3D mesh surface into multiple 2D triangular maps, one for each triangle. Each 2D map is further subdivided into sub-triangles through adaptive recursion. This segmentation allows the large complex dataset to be broken into smaller manageable pieces that can be processed and stored more efficiently, directly addressing the issue of very large and complex datasets while maintaining sampling accuracy through localized high-resolution mapping.
Solution Approach 2:
The patent applies local quality by using adaptive recursion to subdivide triangles into sub-triangles based on local field variance. Regions with high field variation receive finer subdivision (higher local resolution), while regions with low variation use coarser subdivision. This ensures sampling accuracy is maintained where needed without unnecessarily increasing data field size in all regions, thus resolving the contradiction between precision and data quantity.
2Ease of operation
If simple texture mapping approaches are used for irregular topologies and curvatures, then the mapping process is simpler, but the mappings become uneven with equally-sized surface regions assigned to very differently sized data field regions
Solution Approach 1:
The patent employs dynamic adaptive recursion that automatically adjusts the level of subdivision based on local field characteristics. The recursion depth and subdivision density are dynamically determined by calculating field variance in each triangular region. This dynamic approach maintains mapping simplicity (ease of operation) while ensuring uniform field resolution, as the system automatically adapts to irregular topologies and curvatures without manual intervention, resolving the contradiction between simplicity and resolution uniformity.
3Reliability
If all sampled leaf nodes are stored to specify the field over a domain of general topology, then complete field information is available, but storage efficiency is reduced and computational resources are increased
Solution Approach 1:
The patent extracts and stores only the essential field information by calculating average field values for non-leaf nodes and using variance-based pruning. Instead of storing all sampled leaf node values, the system extracts representative average values for parent nodes and selectively prunes branches where the field variation falls below a threshold. This extraction approach maintains field information completeness (reliability) for regions that need it while significantly reducing storage requirements by eliminating redundant data from low-variation regions.
4Measurement precision
If high-resolution field data is stored for the entire mesh surface, then sampling accuracy is improved, but storage efficiency decreases and dynamic loading becomes less effective
Solution Approach 1:
The patent segments the mesh into multiple 2D triangular maps with hierarchical multi-resolution structures. Each map is divided into triangles and sub-triangles that can be independently loaded. This segmentation enables dynamic loading by allowing the system to load only the specific triangular maps and sub-triangles needed for the current view or region of interest, rather than loading the entire high-resolution mesh. This maintains sampling accuracy for visible regions while improving storage efficiency through selective loading of only necessary data portions.
Data Source
AI summary
Methods and apparatus for representing a field over a triangular mesh are disclosed. A two-dimensional (2D) triangular map may be created for each triangle of a three-dimensional (3D) triangular mesh. The triangular map may be recursively subdivided to create a plurality of sub-triangles. The sub-triangles may be sampled, and an field may be measured or calculated at each level of the recursion. The map of field values may use various compression techniques and may also employ a delayed reading technique. The map may be multi-resolution, hierarchical, and partitioned.