2D Artwork Animation Using Complex Number Deformation
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Solution Overview
Problem
Existing methods for animating electronic characters and artwork are often too slow for smooth real-time deformations, particularly on mobile devices, due to inefficient computation of handle affine transformations.
Innovation Solution
The method represents vertex coordinates as real and complex portions of complex numbers to minimize a closed-form expression for handle affine transformations, combining local and global steps into a single formula, allowing for faster computation with minimal stretching and skewing, and uses convex-concave procedures to solve for these transformations efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If the alternating local/global deformation algorithm using singular value decomposition is used, then the mesh deformation maintains rigidity and minimizes stretching, but the computation becomes too slow for real-time animations on mobile devices
Solution Approach 1:
The patent extracts and removes the computationally expensive singular value decomposition step from the deformation algorithm, replacing it with a simpler closed-form solution that achieves comparable deformation quality without the iterative computational overhead
Solution Approach 2:
The patent substitutes the mechanical iterative optimization process (alternating local/global steps with SVD) with a direct closed-form mathematical solution, eliminating the need for iterative computation while maintaining deformation accuracy
2Manufacturing precision
If the alternating local/global iterative process is implemented, then optimal rigid transformations are achieved for each rotation cluster, but the multiple iterations required make it inefficient for real-time processing
Solution Approach 1:
The patent performs preliminary computation by pre-calculating the closed-form expression components and deformation parameters before real-time animation is needed, so that during actual animation only simple parameter interpolation is required rather than full iterative optimization
Solution Approach 2:
The patent uses a simplified closed-form solution that provides sufficient deformation accuracy for visual purposes without completing the full iterative optimization process, accepting a partial solution that is computationally efficient enough for real-time applications
Data Source
AI summary
Systems and methods disclosed improve the speed of animating artwork by determining the handle affine transformations used to animate 2 Dimensional (2D) artwork in a computationally simpler manner than prior techniques. The improved technique represents vertex coordinates (e.g., x1, y1) in 2D artwork as the real and complex portions of complex numbers. Doing so allows minimizing a closed form expression to find handle affine transformations that provide a deformation of the object with minimal stretching and squashing in local areas. Determining handle affine transformation parameters in this way is more efficient computationally than prior techniques because it combines the local and global steps into a single formula. Moreover, the formulation can be quickly evaluated with only additions, multiplications, and square roots without any need for conditional branches. Furthermore, the form of the function allows it to be solved with a simple optimization method.