3D Model UV Expansion Preventing Triangular Patch Flipping
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Solution Overview
Problem
Existing UV expansion methods for three-dimensional models often result in flipping, leading to local overlaps and information loss due to the lack of prevention mechanisms during two-dimensional expansion, causing poor UV expansion quality.
Innovation Solution
An expansion method that determines a rigid transformation matrix and a deformation matrix for each triangular patch, using energy functions to prevent flipping, ensuring that the expansion result does not include flipped patches, thereby maintaining the integrity of the three-dimensional model's information.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional UV expansion methods are used on three-dimensional models, then the expansion process is simple and fast, but flipping occurs causing local overlaps and information loss
Solution Approach 1:
The patent applies preliminary anti-action by introducing an obstacle function component before the flipping problem occurs. This component proactively prevents flipping by adding a penalty term to the energy function that becomes active when triangular patches approach a flipped state, thereby stopping the harmful effect before it can cause information loss
Solution Approach 2:
The patent changes the parameter of the energy function by adding an obstacle function component that dynamically adjusts based on the orientation of triangular patches. This parameter change allows the system to transition from a simple expansion energy minimization to a constrained optimization that prevents flipping while maintaining expansion quality
2Loss of information
If flipping prevention mechanisms are added to UV expansion, then information loss is prevented, but the complexity of the expansion method increases
Solution Approach 1:
The patent implements feedback by continuously monitoring the orientation of triangular patches during the expansion process through the obstacle function component. This component provides real-time feedback to the energy minimization process, automatically adjusting the expansion to prevent flipping without requiring external intervention or complex control mechanisms
Solution Approach 2:
The expansion method performs self-service by incorporating the flipping prevention mechanism directly into the energy function itself. The obstacle function component automatically identifies and corrects potential flipping issues during the optimization process, eliminating the need for separate post-processing or complex external control systems
3Use of energy by moving object
If conventional expansion methods are used, then the process is computationally efficient, but flipping causes local overlaps in the expansion result
Solution Approach 1:
The obstacle function component applies preliminary anti-action by preventing the triangular patches from entering a flipped state that would cause local overlaps. This proactive approach maintains the computational efficiency of the energy minimization process while ensuring the geometric integrity of the expansion result
Data Source
AI summary
This application provides an expansion method and an expansion apparatus for a three-dimensional model, a device, a computer-readable storage medium and a computer program product. The method includes: obtaining an initial expansion result of a to-be-expanded three-dimensional model, where none of a plurality of triangular patches included in the initial expansion result is flipped; determining a rigid transformation matrix of each triangular patch based on coordinate information of each triangular patch in the expansion result; determining first corrected coordinate information of each triangular patch based on the rigid transformation matrix of each triangular patch and a first energy function; when it is determined, based on the first corrected coordinate information of each triangular patch, that there is a flipped triangular patch, second corrected coordinate information of each triangular patch is determined based on the rigid transformation matrix of each triangular patch and a second energy function; and determining a target expansion result based on the second corrected coordinate information of each triangular patch when it is determined that a preset convergence condition is met.