3D Mesh Compression via 2D Grid Parameterization
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Solution Overview
Problem
Current compression methods for 3D CAD models are either lossy, irreversible, or require significant increases in data size to maintain detail, especially for non-watertight models with high topology genus, leading to inefficiencies in storage and processing.
Innovation Solution
A method that parameterizes a 3D mesh in a 2D plane, assigns vertices to grid intersections using a repulsion technique, and applies compression schemes like discrete cosine transform or wavelet transformations, ensuring the process is lossless and reversible, allowing exact recovery of the original mesh.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If straightforward storage without compression is used, then data losslessness and stability are maintained, but storage size is not optimized
Solution Approach 1:
The patent segments the mesh data into two distinct parts: connectivity data (topology) and geometry data (vertex positions). This segmentation allows different compression strategies to be applied to each part, enabling lossless compression of connectivity data while using lossy compression for geometry data, thus reducing overall storage size while maintaining data integrity where needed
Solution Approach 2:
The patent changes the parameter representation by transforming vertex coordinates into a compressed format using discrete cosine transform (DCT) or wavelet transformations. By changing from direct coordinate storage to transform-domain representation, the patent achieves significant compression ratios while allowing reconstruction of the original geometry data
2Quantity of substance
If remeshing is used to reduce storage space, then storage efficiency is improved, but the original mesh details are lost and the process is irreversible
Solution Approach 1:
The patent performs preliminary action by separating connectivity data from geometry data before compression. The connectivity data is processed and compressed in advance using lossless methods, preserving the topological structure. This preliminary separation ensures that when geometry data is later reconstructed from compressed form, the original mesh connectivity and details can be fully recovered
Solution Approach 2:
The patent creates a compressed copy of the geometry data using transform methods (DCT or wavelets) rather than physically remeshing the original data. This copying approach allows the original mesh to be preserved in compressed form without altering its topological structure, enabling exact reconstruction of the original mesh details when needed
3Quantity of substance
If geometry image representation is used, then compression efficiency is improved, but connectivity data is lost and small details may disappear
Solution Approach 1:
The patent merges the advantages of geometry image representation with traditional mesh storage by combining lossless compression of connectivity data with compressed representation of geometry data. Unlike pure geometry image approaches that discard connectivity information, this patent preserves and compresses connectivity data separately, then merges it with the compressed geometry data during reconstruction, achieving both compression efficiency and preservation of mesh structure
Solution Approach 2:
The patent introduces an intermediary step of transforming geometry data into frequency domain representation (using DCT or wavelets) before compression. This intermediary transformation allows efficient compression while preserving all geometric information, and serves as a bridge between the compressed representation and the original mesh structure, enabling exact reconstruction without losing connectivity data
Data Source
AI summary
It is proposed a computer-implemented method for compressing a three-dimensional modeled object. The method comprises: providing a mesh of the three-dimensional modeled object; parameterizing (u,v) the mesh in a two-dimensional plane, the parameterization of the mesh resulting in a set of vertices having two-dimensional coordinates; providing a grid on the two-dimensional plane; and modifying the two-dimensional coordinates of each vertex by assigning one vertex to one intersection of the grid. Such compression method is lossless, completely reversible, suitable to efficiently reduce the storage size of a CAD file.