Triangulation-Agnostic 3D Mesh Mapping With Neural Gradient Fields
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Solution Overview
Problem
Conventional three-dimensional modeling systems face challenges in generating accurate and flexible mappings of three-dimensional meshes due to significant geometric and topological variation, and the need to preserve detail while being agnostic to differing triangulations.
Innovation Solution
The use of neural networks to generate mappings of three-dimensional meshes by producing sets of matrices over an ambient space for polygons, combining extracted features and a global code, and determining a gradient field by restricting these matrices to tangent spaces, allowing for detail-preserving mappings that are independent of triangulation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional systems use fixed triangulation methods to generate mappings, then the process is computationally simpler, but the accuracy and detail preservation deteriorate due to geometric and topological variation
Solution Approach 1:
The patent replaces conventional mechanical/mathematical triangulation systems with a neural network-based system. The neural network learns to generate mappings by training on example mappings between source and target meshes, substituting traditional geometric algorithms with a data-driven approach that handles geometric and topological variation more effectively
Solution Approach 2:
The patent changes the parameter representation by using a global code (latent vector) to represent the target mesh geometry rather than fixed triangulation parameters. This allows the system to adapt to different geometries and topologies by varying the global code while maintaining a consistent mapping framework
2Manufacturing precision
If conventional systems use detailed mesh representations to preserve detail, then mapping accuracy improves, but computational resources and processing time increase significantly
Solution Approach 1:
The patent performs preliminary action by pre-training the neural network on large datasets of mesh mappings before deployment. This pre-training phase captures complex geometric relationships and detail preservation strategies, allowing the system to generate accurate mappings efficiently during runtime without processing excessive detail information
3Measurement precision
If conventional systems are designed for specific triangulations to achieve accuracy, then mapping precision improves for those cases, but adaptability to different triangulations deteriorates
Solution Approach 1:
The patent implements universality by designing a neural network framework that works across different triangulations and mesh representations. The network takes as input features from any triangulation and produces mappings that preserve detail regardless of the source or target mesh structure, making the system applicable to a wide variety of 3D modeling tasks
Data Source
AI summary
Methods, systems, and non-transitory computer readable storage media are disclosed for generating digital chain pull paintings in digital images. The disclosed system generate, utilizing a neural network, a plurality of matrices over an ambient space for a plurality of polygons of a three-dimensional mesh based on a plurality of features of the plurality of polygons associated with the three-dimensional mesh. The disclosed system determines a gradient field based on the plurality of matrices of the plurality of polygons. The disclosed system generates a mapping for the three-dimensional mesh based on the gradient field and a differential operator corresponding to the three-dimensional mesh.