Consensus Mesh Generation via Triangle Frequency Sorting
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Solution Overview
Problem
Existing mesh generation techniques often produce meshes with unwanted flaws or holes due to parameter tuning and initial conditions, which can lead to inconsistent and low-quality results when covering sets of points with triangle meshes.
Innovation Solution
A method is developed to generate a consensus mesh by varying parameter values of an interpolating meshing technique, sorting triangles by frequency, and iteratively adding compatible triangles to create a stable and robust mesh that maximizes triangle frequency, ensuring manifold and orientable triangulation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If parameter values of an interpolating meshing technique are varied to generate different meshes, then mesh quality and robustness can be improved, but the complexity of the meshing process increases
Solution Approach 1:
The patent segments the meshing process into multiple independent stages: generating multiple candidate meshes with different parameters, extracting triangles from each mesh, counting triangle frequencies, and iteratively constructing the consensus mesh. This segmentation allows complex parameter variation to be managed through systematic, modular steps rather than a single complex operation.
Solution Approach 2:
The patent performs preliminary actions by generating multiple candidate meshes with different parameter values before final mesh construction. Triangles are pre-extracted and frequency-counted from all candidate meshes, allowing the consensus mesh to be built from pre-validated triangular elements rather than attempting to construct it directly from scratch.
2Manufacturing precision
If multiple meshes are generated by varying parameters, then holes and flaws in the mesh can be reduced, but the computational time increases
Solution Approach 1:
The patent creates multiple copies of the mesh structure by generating candidate meshes with varied parameters. Instead of repeatedly refining a single mesh, the system generates multiple triangular representations of the same surface, counts their frequencies, and uses the most consistent triangles to build the final mesh. This copying approach efficiently identifies reliable triangular elements without requiring extensive iterative refinement of each individual mesh.
3Stability of the object's composition
If triangles are sorted by frequency and iteratively added to ensure manifold and orientable triangulation, then mesh consistency is improved, but the processing complexity increases
Solution Approach 1:
The patent implements feedback through triangle frequency counting, where triangles from candidate meshes are evaluated based on how frequently they appear across different parameter variations. This frequency information feeds back into the mesh construction process, guiding the iterative addition of triangles that maintain manifold and orientable properties. The feedback mechanism systematically identifies and prioritizes the most reliable triangular elements.
Solution Approach 2:
The patent changes parameters (such as search radius, number of triangles, or other meshing parameters) to generate multiple candidate meshes with different characteristics. By varying these parameters systematically, the method explores different mesh configurations and identifies triangular elements that consistently appear across parameter variations, ensuring robustness without requiring complex manual intervention.
Data Source
AI summary
Techniques are disclosed for generating a consensus mesh to cover a received set of points. In one embodiment, a meshing application generates multiple meshes that cover the received point set by varying parameters of an interpolating meshing technique, such as the ball-pivoting technique, tangent-space Delaunay triangulation, and the like. Different values for the one or more parameters are used to generate each of the meshes. After generating the multiple meshes, the meshing application may sort triangles in the meshes based on the frequency in which the triangles appear in the meshes. The meshing application may then iteratively add next-best triangles which are also compatible with the current consensus mesh to the consensus mesh, with the next-best triangle being a most frequently occurring triangle which has not yet been added to the consensus mesh. Compatibility may be defined using various criteria, such as producing a manifold and orientable triangulation.