3D Model Re-meshing Using Implicit Surface Modeling
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Solution Overview
Problem
Existing methods for re-meshing three-dimensional models into quadrilateral meshes struggle to preserve global properties like symmetry and often result in meshes with too many elements, as they are surface-based and dependent on original connectivity, failing to capture important geometric features effectively.
Innovation Solution
The approach involves building a volumetric representation using implicit surface modeling techniques like Moving Least Squares (MLS), which creates a sequence of implicit approximating surfaces starting from a coarse approximation and converging to the input shape, allowing for the incremental construction of a quadrilateral mesh that captures global symmetry and reduces surface details progressively.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If surface-based re-meshing methods are used, then the mesh can be generated from the input model, but the global properties such as symmetry are not preserved and the number of elements becomes large
Solution Approach 1:
The patent transitions from surface-based 2D re-meshing to volume-based 3D implicit surface modeling. By representing the object as an implicit distance field in 3D space and extracting iso-contours, the method captures global geometric properties including symmetry while generating quadrilateral meshes with fewer elements. This dimensional shift from surface to volume enables better preservation of global properties.
2Measurement precision
If the mesh captures all surface details, then the input features are preserved, but the base mesh becomes too complex with millions of triangles
Solution Approach 1:
The patent segments the mesh generation process into multiple resolution levels. A coarse base mesh is generated first with fewer elements, then detail information is added through offset vectors and detail levels. This hierarchical segmentation allows the base mesh to remain simple while still capturing all surface details through progressive refinement across multiple levels.
Solution Approach 2:
The patent uses progressive implicit approximating levels that can be adjusted dynamically. The implicit distance field allows for multi-resolution representation where the level of detail can be controlled by selecting different approximating levels, enabling the mesh complexity to be adapted based on the required precision without capturing unnecessary details at the base level.
3Ease of manufacture
If local re-meshing operations are applied, then the quad mesh can be generated, but the original connectivity dependency causes failure to preserve global properties
Solution Approach 1:
The patent introduces an implicit distance field as an intermediary between the input mesh and the output quad mesh. Instead of directly manipulating mesh connectivity through local operations, the method uses the implicit field to guide the generation of quadrilateral meshes. This intermediary enables the generation of structured quad meshes that preserve global symmetry without being constrained by the original mesh connectivity.
Data Source
AI summary
A method, system and program product for re-meshing of a three-dimensional (3D)input model using progressive implicit approximating levels are provided. Specifically, an initial quadrilateral mesh for a 3D input model is provided. Then, an implicit approximating field is built for a first approximating level (L) of the 3D input model using an implicit surface modeling technique. An iso-contour of the implicit approximating field is then extracted, and the quadrilateral mesh is fit to the first approximating level (L). The fit between the quadrilateral mesh and the first approximating level (L) is then estimated, and it is determined whether the fit meets a predetermined quality criterion. If not, the quadrilateral mesh is refined using one or more of a sequence of topological operations are performed to improve the fit. The process is then iteratively repeated for subsequent approximation levels until one of the subsequent approximation levels is fit to the 3D input model.