Polygon Mesh Adjustment for Sub-Cell Surface Features
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Solution Overview
Problem
Existing techniques for generating polygon meshes from signed distance fields (SDFs) fail to accurately represent features smaller than one cell, leading to inaccurate or missing representations of small, thin, and sharp object features.
Innovation Solution
Determine a boundary mesh based on cells within a threshold distance of the surface, calculate offset cell positions using corrected corner gradients, and generate an adjusted mesh with displaced vertices to accurately approximate the surface, including small and sharp features.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If linear interpolation between cells with negative and positive values is used to determine surface position, then large objects and features can be rendered, but features smaller than one cell cannot be represented accurately
Solution Approach 1:
The patent segments the surface determination process into two parts: first determining a boundary mesh using traditional linear interpolation, then generating an adjusted mesh by offsetting vertices based on gradient calculations. This segmentation allows the boundary mesh to capture large features while the adjusted mesh recovers sub-cell features that would otherwise be lost.
Solution Approach 2:
The patent performs preliminary action by first creating a boundary mesh that identifies cells within a threshold distance of the surface, then uses this boundary mesh as a foundation for generating the final adjusted mesh. This preliminary boundary determination enables subsequent gradient-based offset calculations to accurately place sub-cell features.
2Productivity
If traditional mesh generation techniques are used, then computational resources are saved, but inaccurate results are produced for objects with sub-cell features
Solution Approach 1:
The patent applies partial action by calculating gradient offsets only for boundary vertices that lie on or near the surface, rather than recalculating all mesh positions. This selective approach maintains computational efficiency while improving accuracy where it matters most - at the surface boundary where sub-cell features exist.
Solution Approach 2:
The patent applies local quality by using gradient-based offset calculations specifically at boundary vertices where sub-cell features are likely to exist, while maintaining the simpler boundary mesh structure elsewhere. This localized refinement improves mesh accuracy at critical locations without unnecessarily increasing overall computational complexity.
Data Source
AI summary
Generating polygon meshes approximating surfaces with sub-cell features. In some implementations, a computer-implemented method includes obtaining a signed distance field (SDF) grid that includes a plurality of cells, the cells including cell values that indicate distances of the cells to a surface that distinguishes an inside and an outside of an object. A boundary mesh is determined having boundary vertices and boundary faces of particular cells in the SDF grid that are based at least on cells within a threshold distance of the surface. Offset cell positions are determined for centers of neighboring cells that neighbor the boundary mesh. The offset cell positions are based on corner gradients of the neighboring cells. An adjusted mesh is generated that approximates the surface, the adjusted mesh defined by mesh vertices that are based on the boundary vertices of the boundary mesh that are displaced based on the offset cell positions.