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About this paper
Dong Xiao, Renjie Chen, Bailin Deng
This work introduces Domain-Varying Green Coordinates (DVGC) to unify Harmonic Coordinates (HC) and Green Coordinates (GC) within 2D cage-based deformation, utilizing a generalized Green's third identity. The framework establishes the Green's function domain as a novel control parameter, allowing a continuous transition of deformation effects from cage-consistent to shape-preserving, with closed-form solutions derived for disk-shaped domains.
Key insights
- HC and GC can be unified under a generalized Green's third identity, providing a deeper understanding of their mathematical relationship and establishing a continuous spectrum of deformation properties.
- The Green's function domain (Θ) serves as a new, continuous control space, allowing users to precisely tune deformation effects between cage-consistent and shape-preserving outcomes.
- Deriving closed-form solutions for DVGC in specific domains (e.g., disks) significantly improves computational efficiency and accuracy for 2D applications.
Summary by alphaXiv.
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