3D Mesh Decimation via Successive Self-Parameterization
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Solution Overview
Problem
Conventional mesh decimation techniques are inflexible, lack support for edge collapsing, and fail to maintain correspondence between coarse and high-resolution three-dimensional models, leading to poor quality simplifications and difficulties in transferring textures and edits.
Innovation Solution
The system employs successive self-parameterization of three-dimensional meshes with edge collapsing, utilizing surface mappings to create bijective maps between coarse and high-resolution models, allowing for flexible edge collapses and accurate parameterization preservation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If conventional mesh decimation techniques are used, then the mesh complexity is reduced, but the quality of the coarser version deteriorates due to lack of edge collapse support
Solution Approach 1:
The system dynamically adapts the decimation process by supporting edge collapse operations that adjust the mesh structure flexibly. The parameterization is updated dynamically during the decimation process to maintain correspondence, allowing the system to adapt to different mesh configurations and preserve quality while reducing complexity.
Solution Approach 2:
The system changes the parameterization parameters during the decimation process. By updating the parameterization to reflect the collapsed edges and maintain bijective correspondence, the system preserves mesh quality while reducing complexity. The parameter changes ensure that the coarser mesh maintains the necessary geometric properties.
2Device complexity
If conventional mesh decimation techniques without conformal mapping are used, then the decimation process is simpler, but the correspondence between coarse and high-resolution models is lost
Solution Approach 1:
The system performs preliminary conformal mapping before the decimation process to establish a correspondence framework. This preliminary action ensures that the parameterization is set up to maintain bijective correspondence throughout the decimation process, preventing loss of correspondence information while managing complexity.
Solution Approach 2:
The conformal mapping serves as an intermediary that connects the coarse and high-resolution models. By using conformal mapping as a mediator, the system maintains correspondence information throughout the decimation process, allowing accurate texture and edit transfer between resolution levels.
3Measurement precision
If high-resolution meshes with many vertices are used, then the model detail increases, but the processing power and time required increases
Solution Approach 1:
The system segments the mesh processing into different resolution levels. By creating a multi-resolution representation with coarse and fine meshes, the system allows processing at different detail levels. Users can work with coarse meshes for overall operations and only process high-resolution meshes when detailed work is needed, reducing overall processing time.
Solution Approach 2:
The system dynamically adjusts the resolution level based on processing needs. The bijective correspondence enabled by conformal mapping allows seamless switching between resolution levels, enabling the system to use lower resolution for time-critical operations and higher resolution only when detail is required, optimizing processing time while preserving model detail capability.
4Quantity of substance
If conventional mesh decimation techniques are used, then the computing resource usage is reduced, but the ability to transfer textures and edits between resolutions is prevented
Solution Approach 1:
The conformal mapping acts as an intermediary that enables texture and edit transfer between resolution levels. By maintaining bijective correspondence through conformal mapping, the system allows textures and edits to be transferred accurately from high-resolution to coarse meshes and vice versa, preserving adaptability while reducing computing resource usage through efficient multi-resolution processing.
Data Source
AI summary
Methods, systems, and non-transitory computer readable storage media are disclosed for iteratively decimating a three-dimensional mesh utilizing successive self-parameterization. For example, the disclosed system can self-parameterize local geometries of a three-dimensional mesh using surface mappings within a two-dimensional surface mapping space. The disclosed system can collapse edges in the three-dimensional mesh to create new vertices from the collapsed edges. The disclosed system can parameterize the collapsed edges based on the surface mappings to collapse corresponding edges within the surface mapping space. The disclosed system can thus generate a decimated three-dimensional mesh by collapsing edges in the three-dimensional mesh while providing a bijective map between points in the decimated three-dimensional mesh and corresponding points in the three-dimensional mesh.