Texture Mapping on Deformable Surfaces Using Rigidity Maps
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Computer animation techniques face challenges in minimizing distortions introduced by surface deformation, particularly in polygonal meshes, where optimal parameterizations for original surfaces often become suboptimal for deformed surfaces, leading to inefficient reparameterization and impractical vertex placement in sensitive regions.
Innovation Solution
A method that uses a user-supplied rigidity map to guide non-linear optimization for axis-aligned deformation of a non-uniform grid in texture space, minimizing distortions in specified rigid features by warping the parameter-space mesh, allowing for precalculation and real-time remapping with minimal storage and computational cost.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If an optimal parameterization is used for the original surface, then mapping quality is improved, but the parameterization becomes suboptimal for the deformed surface
Solution Approach 1:
The patent applies dynamics by making the parameterization adaptive to deformation. Instead of using a static optimal parameterization for the original surface, the system dynamically adjusts the parameterization based on the deformation state. The rigidity map and non-linear optimization process enable the parameterization to adapt automatically as the surface deforms, transforming a static mapping solution into a dynamic one that maintains quality across different deformation states.
Solution Approach 2:
The patent changes parameters by introducing a rigidity map that assigns different rigidity values to different regions of the surface. This allows the system to differentiate between rigid features that should maintain their parameterization and flexible regions that can adapt to deformation. The non-linear optimization process then adjusts the parameterization based on these rigidity parameters, enabling selective adaptation across the surface.
2Manufacturing precision
If reparameterization is performed to maintain quality after deformation, then distortion is reduced, but computational complexity and vertex placement become impractical
Solution Approach 1:
The patent applies local quality by using a rigidity map that assigns different properties to different regions of the surface. Rigid features are identified and given high rigidity values, while flexible regions have lower rigidity values. This allows the optimization process to focus computational effort locally on regions that require distortion reduction, rather than uniformly processing the entire surface, thereby reducing overall computational complexity.
Solution Approach 2:
The patent segments the surface into regions based on rigidity characteristics. By dividing the surface into rigid and flexible regions through the rigidity map, the system can apply different processing strategies to different segments. This segmentation simplifies the reparameterization problem by allowing independent optimization of rigid features while letting flexible regions adapt naturally to deformation.
3Measurement precision
If dense discretization is used to improve piecewise-linear approximation, then approximation quality is improved, but storage and computational cost increase
Solution Approach 1:
The patent applies local quality by concentrating discretization effort in regions that require higher precision. The rigidity map identifies rigid features that benefit from denser sampling, while flexible regions can use coarser discretization. This non-uniform discretization strategy maintains high approximation quality where needed while reducing storage and computational costs in regions where lower precision is acceptable.
Data Source
AI summary
A method is disclosed for reducing distortions introduced by deformation of a surface with an existing parameterization. In one embodiment, the distortions are reduced over a user-specified convex region in texture space ensuring optimization is locally contained in areas of interest. A distortion minimization algorithm is presented that is guided by a user-supplied rigidity map of the specified region. In one embodiment, non-linear optimization is used to calculate the axis-aligned deformation of a non-uniform grid specified over the region's parameter space, so that when the space is remapped from the original to the deformed grid, the distortion of the rigid features is minimized. Since grids require minimal storage and the remapping from one grid to another entails minimal cost, grids can be precalculated for animation sequences and used for real-time texture space remapping that minimizes distortions on specified rigid features.