3D Mesh Hole Filling with Recursive Boundary Splitting
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Solution Overview
Problem
Existing methods for filling mesh holes in 3D digital models often produce suboptimal geometries or require complex postprocessing, especially for mesh holes with complex or degenerated boundaries, and may not terminate reliably.
Innovation Solution
A method that uses a divide-and-conquer approach to split the boundary curve of a mesh hole at suitable locations, recursively dividing it into smaller curves using a maximized triple of boundary vertices connected by a tangential connecting curve, ensuring the new curves are smaller than the original, and adding Steiner vertices as needed to ensure termination.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If the advancing front approach is used to fill mesh holes, then the hole filling can be achieved, but the method may produce suboptimal geometries and require postprocessing steps
Solution Approach 1:
The boundary curve is divided into multiple segments by identifying split points where the curve intersects with the mesh surface. Each segment is then processed independently to create triangular patches, allowing for more precise control over the geometry of each portion of the filled hole while maintaining overall coherence
Solution Approach 2:
The boundary curve is preprocessed by finding intersection points with the mesh surface and dividing it into segments before the actual hole filling process. This preliminary segmentation ensures that subsequent triangulation operations work with manageable, well-defined portions of the boundary, eliminating the need for postprocessing corrections
2Manufacturing precision
If Laplace equation is used for surface interpolation, then the mathematically correct surface is obtained, but the filled mesh hole tends to be not very natural when the natural surface has mean curvature different from zero
Solution Approach 1:
Instead of applying a global Laplace interpolation that enforces zero mean curvature everywhere, the method creates local triangular patches that follow the boundary curve segments. Each patch is constructed to match the local geometry and curvature characteristics of the surrounding mesh, preserving natural surface variations while maintaining mathematical correctness
3Manufacturing precision
If the advancing front approach is used for mesh hole filling, then hole filling can be performed, but it may be difficult to ensure termination for mesh holes with complex or degenerated boundaries
Solution Approach 1:
The boundary curve is segmented at intersection points with the mesh surface, creating a finite number of well-defined segments. This segmentation transforms the continuous boundary problem into a discrete set of manageable segments, ensuring that the algorithm progresses through a finite sequence of operations and must terminate
Solution Approach 2:
The boundary curve is preprocessed to identify all intersection points and establish a segmentation before the filling process begins. This preliminary analysis ensures that even complex or degenerated boundaries are properly divided into valid segments, guaranteeing that the algorithm can handle any boundary configuration and will terminate
4Device complexity
If 3D hole filling problems are turned into 2D problems, then the complexity is reduced, but insufficient results are obtained for mesh holes with complex boundaries
Solution Approach 1:
The method works directly in 3D space by finding where the boundary curve intersects with the mesh surface and creating 3D triangular patches. This maintains the full spatial information and geometric relationships without reducing to 2D, ensuring accurate results for complex boundaries while managing complexity through systematic 3D triangulation
Data Source
AI summary
The invention relates to a method for filling a mesh hole in a mesh of a 3D digital model. A boundary of the mesh hole is provided by a first closed boundary curve comprising boundary edges connecting boundary vertices of a first plurality of boundary vertices. The method comprises selecting a maximized triple of boundary vertices comprising a first, a second and a third boundary vertex. The selected maximized triple is maximized by selecting a boundary vertex of the first plurality of boundary vertices as the third boundary vertex of the selected maximized triple. The selected maximized triple satisfies a first criterion. The first and the second vertex of the selected maximized triple are connected using a connecting curve from the first to the second boundary vertex.